Nonlinear H-ininity state feedback controllers:

DEFF Research Database (Denmark)

Cromme, Marc; Møller-Pedersen, Jens; Pagh Petersen, Martin

1997-01-01

From a general point of view the state feedback H∞ suboptimal control problem is reasonably well understood. Important problems remain with regard to a priori information of the size of the neighbourhood where the local state feedback H∞ problem is solvable. This problem is solved regionally (sem...... (semiglobally) in this paper, and the obtained control laws are implemented in MAPLE...

Transformation of CLF to ISS-CLF for Nonlinear Systems with Disturbance and Construction of Nonlinear Robust Controller with L2 Gain Performance

Directory of Open Access Journals (Sweden)

Keizo Okano

2014-01-01

Full Text Available A new nonlinear control law for a class of nonlinear systems with disturbance is proposed. A control law is designed by transforming control Lyapunov function (CLF to input-to-state stability control Lyapunov function (ISS-CLF. The transformed CLF satisfies a Hamilton-Jacobi-Isaacs (HJI equation. The feedback system by the proposed control law has characteristics of L2 gain. Finally, it is shown by a numerical example that the proposed control law makes a controller by feedback linearization robust against disturbance.

Cooperative learning neural network output feedback control of uncertain nonlinear multi-agent systems under directed topologies

Science.gov (United States)

Wang, W.; Wang, D.; Peng, Z. H.

2017-09-01

Without assuming that the communication topologies among the neural network (NN) weights are to be undirected and the states of each agent are measurable, the cooperative learning NN output feedback control is addressed for uncertain nonlinear multi-agent systems with identical structures in strict-feedback form. By establishing directed communication topologies among NN weights to share their learned knowledge, NNs with cooperative learning laws are employed to identify the uncertainties. By designing NN-based κ-filter observers to estimate the unmeasurable states, a new cooperative learning output feedback control scheme is proposed to guarantee that the system outputs can track nonidentical reference signals with bounded tracking errors. A simulation example is given to demonstrate the effectiveness of the theoretical results.

Enhancement of entanglement in the nonlinear optical coupler by homodyne-mediated feedback

Energy Technology Data Exchange (ETDEWEB)

Ke Shasha [Department of Physics, Huazhong Normal University, Wuhan 430079 (China); Cheng Guiping [Department of Physics, Huazhong Normal University, Wuhan 430079 (China); Zhang Lihui [Department of Physics, Jianghan University, Wuhan 430056 (China); Li, Gao-xiang [Department of Physics, Huazhong Normal University, Wuhan 430079 (China)

2007-07-28

The enhancement of the intracavity entanglement of a nonlinear coupler via homodyne-mediated quantum feedback is investigated. It is found that the feedback can effectively enhance the squeezing, entanglement and purity of a two-mode field in the nonlinear coupler by appropriately choosing the quadrature angle at which the quantum feedback is introduced.

Nonlinear output feedback control of underwater vehicle propellers using feedback form estimated axial flow velocity

DEFF Research Database (Denmark)

Fossen, T. I.; Blanke, Mogens

2000-01-01

Accurate propeller shaft speed controllers can be designed by using nonlinear control theory and feedback from the axial water velocity in the propeller disc. In this paper, an output feedback controller is derived, reconstructing the axial flow velocity from vehicle speed measurements, using...... a three-state model of propeller shaft speed, forward (surge) speed of the vehicle, and the axial flow velocity. Lyapunov stability theory is used to prove that a nonlinear observer combined with an output feedback integral controller provide exponential stability. The output feedback controller...... compensates for variations in thrust due to time variations in advance speed. This is a major problem when applying conventional vehicle-propeller control systems, The proposed controller is simulated for an underwater vehicle equipped with a single propeller. The simulations demonstrate that the axial water...

Transition from weak to strong measurements by nonlinear quantum feedback control

International Nuclear Information System (INIS)

Zhang Jing; Liu Yuxi; Wu Rebing; Li Chunwen; Tarn, Tzyh-Jong

2010-01-01

We find that feedback control may induce 'pseudo'-nonlinear dynamics in a damped harmonic oscillator, whose centroid trajectory in the phase space behaves like a classical nonlinear system. Thus, similar to nonlinear amplifiers (e.g., rf-driven Josephson junctions), feedback control on the harmonic oscillator can induce nonlinear bifurcation, which can be used to amplify small signals and further to measure quantum states of qubits. Using the cavity QED and the circuit QED systems as examples, we show how to apply our method to measuring the states of two-level atoms and superconducting charge qubits.

Chaotification of vibration isolation floating raft system via nonlinear time-delay feedback control

International Nuclear Information System (INIS)

Zhang Jing; Xu Daolin; Zhou Jiaxi; Li Yingli

2012-01-01

Highlights: ► A chaotification method based on nonlinear time-delay feedback control is present. ► An analytical function of nonlinear time-delay feedback control is derived. ► A large range of parametric domain for chaotification is obtained. ► The approach allows using small control gain. ► Design of chaotification becomes a standard process without uncertainty. - Abstract: This paper presents a chaotification method based on nonlinear time-delay feedback control for a two-dimensional vibration isolation floating raft system (VIFRS). An analytical function of nonlinear time-delay feedback control is derived. This approach can theoretically provide a systematic design of chaotification for nonlinear VIFRS and completely avoid blind and inefficient numerical search on the basis of trials and errors. Numerical simulations show that with a proper setting of control parameters the method holds the favorable aspects including the capability of chaotifying across a large range of parametric domain, the advantage of using small control and the flexibility of designing control feedback forms. The effects on chaotification performance are discussed in association with the configuration of the control parameters.

Effects of error feedback on a nonlinear bistable system with stochastic resonance

International Nuclear Information System (INIS)

Li Jian-Long; Zhou Hui

2012-01-01

In this paper, we discuss the effects of error feedback on the output of a nonlinear bistable system with stochastic resonance. The bit error rate is employed to quantify the performance of the system. The theoretical analysis and the numerical simulation are presented. By investigating the performances of the nonlinear systems with different strengths of error feedback, we argue that the presented system may provide guidance for practical nonlinear signal processing

Law of nonlinear flow in saturated clays and radial consolidation

Institute of Scientific and Technical Information of China (English)

无

2007-01-01

It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and test ones. Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow. Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius. The interaction is an important reason why nonlinear flow in saturated clays occurs. An exact mathematical model was presented for nonlinear flow in micro-scale pore of saturated clays. Dimension and physical meanings of parameters of it are definite. A new law of nonlinear flow in saturated clays was established. It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one. Darcy law is a special case of the new law. A mathematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow. Equations of average mass conservation and moving boundary, and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer, a method of steady state in stead of transient state and a method of integral of an equation. Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained. Results show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay. The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases. Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.

Optimal control of nonlinear continuous-time systems in strict-feedback form.

Science.gov (United States)

Zargarzadeh, Hassan; Dierks, Travis; Jagannathan, Sarangapani

2015-10-01

This paper proposes a novel optimal tracking control scheme for nonlinear continuous-time systems in strict-feedback form with uncertain dynamics. The optimal tracking problem is transformed into an equivalent optimal regulation problem through a feedforward adaptive control input that is generated by modifying the standard backstepping technique. Subsequently, a neural network-based optimal control scheme is introduced to estimate the cost, or value function, over an infinite horizon for the resulting nonlinear continuous-time systems in affine form when the internal dynamics are unknown. The estimated cost function is then used to obtain the optimal feedback control input; therefore, the overall optimal control input for the nonlinear continuous-time system in strict-feedback form includes the feedforward plus the optimal feedback terms. It is shown that the estimated cost function minimizes the Hamilton-Jacobi-Bellman estimation error in a forward-in-time manner without using any value or policy iterations. Finally, optimal output feedback control is introduced through the design of a suitable observer. Lyapunov theory is utilized to show the overall stability of the proposed schemes without requiring an initial admissible controller. Simulation examples are provided to validate the theoretical results.

Controlling chaotic systems via nonlinear feedback control

International Nuclear Information System (INIS)

Park, Ju H.

2005-01-01

In this article, a new method to control chaotic systems is proposed. Using Lyapunov method, we design a nonlinear feedback controller to make the controlled system be stabilized. A numerical example is given to illuminate the design procedure and advantage of the result derived

Feedback linearizing control of a MIMO power system

Science.gov (United States)

Ilyes, Laszlo

Prior research has demonstrated that either the mechanical or electrical subsystem of a synchronous electric generator may be controlled using single-input single-output (SISO) nonlinear feedback linearization. This research suggests a new approach which applies nonlinear feedback linearization to a multi-input multi-output (MIMO) model of the synchronous electric generator connected to an infinite bus load model. In this way, the electrical and mechanical subsystems may be linearized and simultaneously decoupled through the introduction of a pair of auxiliary inputs. This allows well known, linear, SISO control methods to be effectively applied to the resulting systems. The derivation of the feedback linearizing control law is presented in detail, including a discussion on the use of symbolic math processing as a development tool. The linearizing and decoupling properties of the control law are validated through simulation. And finally, the robustness of the control law is demonstrated.

Design Of Combined Stochastic Feedforward/Feedback Control

Science.gov (United States)

Halyo, Nesim

1989-01-01

Methodology accommodates variety of control structures and design techniques. In methodology for combined stochastic feedforward/feedback control, main objectives of feedforward and feedback control laws seen clearly. Inclusion of error-integral feedback, dynamic compensation, rate-command control structure, and like integral element of methodology. Another advantage of methodology flexibility to develop variety of techniques for design of feedback control with arbitrary structures to obtain feedback controller: includes stochastic output feedback, multiconfiguration control, decentralized control, or frequency and classical control methods. Control modes of system include capture and tracking of localizer and glideslope, crab, decrab, and flare. By use of recommended incremental implementation, control laws simulated on digital computer and connected with nonlinear digital simulation of aircraft and its systems.

Nonlinear observer output-feedback MPC treatment scheduling for HIV

Directory of Open Access Journals (Sweden)

Zurakowski Ryan

2011-05-01

Full Text Available Abstract Background Mathematical models of the immune response to the Human Immunodeficiency Virus demonstrate the potential for dynamic schedules of Highly Active Anti-Retroviral Therapy to enhance Cytotoxic Lymphocyte-mediated control of HIV infection. Methods In previous work we have developed a model predictive control (MPC based method for determining optimal treatment interruption schedules for this purpose. In this paper, we introduce a nonlinear observer for the HIV-immune response system and an integrated output-feedback MPC approach for implementing the treatment interruption scheduling algorithm using the easily available viral load measurements. We use Monte-Carlo approaches to test robustness of the algorithm. Results The nonlinear observer shows robust state tracking while preserving state positivity both for continuous and discrete measurements. The integrated output-feedback MPC algorithm stabilizes the desired steady-state. Monte-Carlo testing shows significant robustness to modeling error, with 90% success rates in stabilizing the desired steady-state with 15% variance from nominal on all model parameters. Conclusions The possibility of enhancing immune responsiveness to HIV through dynamic scheduling of treatment is exciting. Output-feedback Model Predictive Control is uniquely well-suited to solutions of these types of problems. The unique constraints of state positivity and very slow sampling are addressable by using a special-purpose nonlinear state estimator, as described in this paper. This shows the possibility of using output-feedback MPC-based algorithms for this purpose.

Kinematic feedback control laws for generating natural arm movements

International Nuclear Information System (INIS)

Kim, Donghyun; Jang, Cheongjae; Park, Frank C

2014-01-01

We propose a stochastic optimal feedback control law for generating natural robot arm motions. Our approach, inspired by the minimum variance principle of Harris and Wolpert (1998 Nature 394 780–4) and the optimal feedback control principles put forth by Todorov and Jordan (2002 Nature Neurosci. 5 1226–35) for explaining human movements, differs in two crucial respects: (i) the endpoint variance is minimized in joint space rather than Cartesian hand space, and (ii) we ignore the dynamics and instead consider only the second-order differential kinematics. The feedback control law generating the motions can be straightforwardly obtained by backward integration of a set of ordinary differential equations; these equations are obtained exactly, without any linear–quadratic approximations. The only parameters to be determined a priori are the variance scale factors, and for both the two-DOF planar arm and the seven-DOF spatial arm, a table of values is constructed based on the given initial and final arm configurations; these values are determined via an optimal fitting procedure, and consistent with existing findings about neuromuscular motor noise levels of human arm muscles. Experiments conducted with a two-link planar arm and a seven-DOF spatial arm verify that the trajectories generated by our feedback control law closely resemble human arm motions, in the sense of producing nearly straight-line hand trajectories, having bell-shaped velocity profiles, and satisfying Fitts Law. (paper)

Nonclassical state generation for linear quantum systems via nonlinear feedback control

International Nuclear Information System (INIS)

Ohki, Kentaro; Tsumura, Koji; Takeuchi, Reiji

2017-01-01

In this paper, we propose a measurement nonlinear feedback control scheme to generate Wigner-function negativity in an optical cavity having dynamics described as a linear quantum system. In general, linear optical quantum systems can be easily constructed with reliable devices; therefore, the idea of constructing the entire system with such an optical system and nonlinear feedback is reasonable for generating Wigner-function negativity. However, existing studies have insufficiently examined the realizability or actual implementation of feedback control, which essentially requires fast responses from the sensors and actuators. In order to solve this problem, we consider the realizable feedback control of the optical phase of a pumping beam supplied to a cavity by using electro-optical modulation, which can be utilized as a fast control actuator. Then, we introduce mathematical models of the feedback-controlled system and evaluate its effect on the generation of the Wigner-function negativity by using numerical simulation. Through various numerical simulations, we show that the proposed feedback control can effectively generate the negativity of the Wigner function. (paper)

Gap-metric-based robustness analysis of nonlinear systems with full and partial feedback linearisation

Science.gov (United States)

Al-Gburi, A.; Freeman, C. T.; French, M. C.

2018-06-01

This paper uses gap metric analysis to derive robustness and performance margins for feedback linearising controllers. Distinct from previous robustness analysis, it incorporates the case of output unstructured uncertainties, and is shown to yield general stability conditions which can be applied to both stable and unstable plants. It then expands on existing feedback linearising control schemes by introducing a more general robust feedback linearising control design which classifies the system nonlinearity into stable and unstable components and cancels only the unstable plant nonlinearities. This is done in order to preserve the stabilising action of the inherently stabilising nonlinearities. Robustness and performance margins are derived for this control scheme, and are expressed in terms of bounds on the plant nonlinearities and the accuracy of the cancellation of the unstable plant nonlinearity by the controller. Case studies then confirm reduced conservatism compared with standard methods.

Power laws and elastic nonlinearity in materials with complex microstructure

Energy Technology Data Exchange (ETDEWEB)

Scalerandi, M., E-mail: marco.scalerandi@infm.polito.it

2016-01-28

Nonlinear ultrasonic methods have been widely used to characterize the microstructure of damaged solids and consolidated granular media. Besides distinguishing between materials exhibiting classical nonlinear behaviors from those exhibiting hysteresis, it could be of importance the discrimination between ultrasonic indications from different physical sources (scatterers). Elastic hysteresis could indeed be due to dislocations, grain boundaries, stick-slip at interfaces, etc. Analyzing data obtained on various concrete samples, we show that the power law behavior of the nonlinear indicator vs. the energy of excitation could be used to classify different microscopic features. In particular, the power law exponent ranges between 1 and 3, depending on the nature of nonlinearity. We also provide a theoretical interpretation of the collected data using models for clapping and hysteretic nonlinearities. - Highlights: • Several materials exhibit a nontrivial nonlinear elastic behavior which can be ascribed to different physical sources. • The quantitative nonlinear response is dependent on the type of microstructure present in the material. • A nonlinear indicator could be defined which depends on the excitation energy of the sample. • Assuming a power law dependence, the exponent depends on the microstructure of the material and could evolve in time. • Experimental results on concrete are discussed and a theoretical description is proposed.

Stability of Nonlinear Systems with Unknown Time-varying Feedback Delay

Science.gov (United States)

Chunodkar, Apurva A.; Akella, Maruthi R.

2013-12-01

This paper considers the problem of stabilizing a class of nonlinear systems with unknown bounded delayed feedback wherein the time-varying delay is 1) piecewise constant 2) continuous with a bounded rate. We also consider application of these results to the stabilization of rigid-body attitude dynamics. In the first case, the time-delay in feedback is modeled specifically as a switch among an arbitrarily large set of unknown constant values with a known strict upper bound. The feedback is a linear function of the delayed states. In the case of linear systems with switched delay feedback, a new sufficiency condition for average dwell time result is presented using a complete type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding switched system with nonlinear perturbations is proven to be exponentially stable inside a well characterized region of attraction for an appropriately chosen average dwell time. In the second case, the concept of the complete type L-K functional is extended to a class of nonlinear time-delay systems with unknown time-varying time-delay. This extension ensures stability robustness to time-delay in the control design for all values of time-delay less than the known upper bound. Model-transformation is used in order to partition the nonlinear system into a nominal linear part that is exponentially stable with a bounded perturbation. We obtain sufficient conditions which ensure exponential stability inside a region of attraction estimate. A constructive method to evaluate the sufficient conditions is presented together with comparison with the corresponding constant and piecewise constant delay. Numerical simulations are performed to illustrate the theoretical results of this paper.

Incremental passivity and output regulation for switched nonlinear systems

Science.gov (United States)

Pang, Hongbo; Zhao, Jun

2017-10-01

This paper studies incremental passivity and global output regulation for switched nonlinear systems, whose subsystems are not required to be incrementally passive. A concept of incremental passivity for switched systems is put forward. First, a switched system is rendered incrementally passive by the design of a state-dependent switching law. Second, the feedback incremental passification is achieved by the design of a state-dependent switching law and a set of state feedback controllers. Finally, we show that once the incremental passivity for switched nonlinear systems is assured, the output regulation problem is solved by the design of global nonlinear regulator controllers comprising two components: the steady-state control and the linear output feedback stabilising controllers, even though the problem for none of subsystems is solvable. Two examples are presented to illustrate the effectiveness of the proposed approach.

Robust fuzzy output feedback controller for affine nonlinear systems via T-S fuzzy bilinear model: CSTR benchmark.

Science.gov (United States)

Hamdy, M; Hamdan, I

2015-07-01

In this paper, a robust H∞ fuzzy output feedback controller is designed for a class of affine nonlinear systems with disturbance via Takagi-Sugeno (T-S) fuzzy bilinear model. The parallel distributed compensation (PDC) technique is utilized to design a fuzzy controller. The stability conditions of the overall closed loop T-S fuzzy bilinear model are formulated in terms of Lyapunov function via linear matrix inequality (LMI). The control law is robustified by H∞ sense to attenuate external disturbance. Moreover, the desired controller gains can be obtained by solving a set of LMI. A continuous stirred tank reactor (CSTR), which is a benchmark problem in nonlinear process control, is discussed in detail to verify the effectiveness of the proposed approach with a comparative study. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Variational approaches to conservation laws for a nonlinear ...

African Journals Online (AJOL)

The conservation laws of a nonlinear evolution equation of time dependent variable coefficients of damping and dispersion is studied. The equation under consideration is not derivable from a variational principle which means that one cannot appeal to the Noether theorem to determine the conservation laws. We utilize the ...

Determination of regression laws: Linear and nonlinear

International Nuclear Information System (INIS)

Onishchenko, A.M.

1994-01-01

A detailed mathematical determination of regression laws is presented in the article. Particular emphasis is place on determining the laws of X j on X l to account for source nuclei decay and detector errors in nuclear physics instrumentation. Both linear and nonlinear relations are presented. Linearization of 19 functions is tabulated, including graph, relation, variable substitution, obtained linear function, and remarks. 6 refs., 1 tab

Nonlinear laser dynamics induced by frequency shifted optical feedback: application to vibration measurements.

Science.gov (United States)

Girardeau, Vadim; Goloni, Carolina; Jacquin, Olivier; Hugon, Olivier; Inglebert, Mehdi; Lacot, Eric

2016-12-01

In this article, we study the nonlinear dynamics of a laser subjected to frequency shifted optical reinjection coming back from a vibrating target. More specifically, we study the nonlinear dynamical coupling between the carrier and the vibration signal. The present work shows how the nonlinear amplification of the vibration spectrum is related to the strength of the carrier and how it must be compensated to obtain accurate (i.e., without bias) vibration measurements. The theoretical predictions, confirmed by numerical simulations, are in good agreement with the experimental data. The main motivation of this study is the understanding of the nonlinear response of a laser optical feedback imaging sensor for quantitative phase measurements of small vibrations in the case of strong optical feedback.

Output Feedback Distributed Containment Control for High-Order Nonlinear Multiagent Systems.

Science.gov (United States)

Li, Yafeng; Hua, Changchun; Wu, Shuangshuang; Guan, Xinping

2017-01-31

In this paper, we study the problem of output feedback distributed containment control for a class of high-order nonlinear multiagent systems under a fixed undirected graph and a fixed directed graph, respectively. Only the output signals of the systems can be measured. The novel reduced order dynamic gain observer is constructed to estimate the unmeasured state variables of the system with the less conservative condition on nonlinear terms than traditional Lipschitz one. Via the backstepping method, output feedback distributed nonlinear controllers for the followers are designed. By means of the novel first virtual controllers, we separate the estimated state variables of different agents from each other. Consequently, the designed controllers show independence on the estimated state variables of neighbors except outputs information, and the dynamics of each agent can be greatly different, which make the design method have a wider class of applications. Finally, a numerical simulation is presented to illustrate the effectiveness of the proposed method.

Jump resonant frequency islands in nonlinear feedback control systems

Science.gov (United States)

Koenigsberg, W. D.; Dunn, J. C.

1975-01-01

A new type of jump resonance is predicted and observed in certain nonlinear feedback control systems. The new jump resonance characteristic is described as a 'frequency island' due to the fact that a portion of the input-output transfer characteristic is disjoint from the main body. The presence of such frequency islands was predicted by using a sinusoidal describing function characterization of the dynamics of an inertial gyro employing nonlinear ternary rebalance logic. While the general conditions under which such islands are possible has not been examined, a numerical approach is presented which can aid in establishing their presence. The existence of the frequency islands predicted for the ternary rebalanced gyro was confirmed by simulating the nonlinear system and measuring the transfer function.

Nonlinear MHD-equations: symmetries, solutions and conservation laws

International Nuclear Information System (INIS)

Samokhin, A.V.

1985-01-01

To investigate stability and nonlinear effects in a high-temperature plasma the system of two scalar nonlinear equations is considered. The algebra of classical symmetries of this system and a certain natural part of its conservation laws are described. It is shown that first, with symmetries one can derive invariant (self-similar) solutions, second, acting with symmetry on the known solution the latter can be included into parametric family

Iterative learning control with sampled-data feedback for robot manipulators

Directory of Open Access Journals (Sweden)

Delchev Kamen

2014-09-01

Full Text Available This paper deals with the improvement of the stability of sampled-data (SD feedback control for nonlinear multiple-input multiple-output time varying systems, such as robotic manipulators, by incorporating an off-line model based nonlinear iterative learning controller. The proposed scheme of nonlinear iterative learning control (NILC with SD feedback is applicable to a large class of robots because the sampled-data feedback is required for model based feedback controllers, especially for robotic manipulators with complicated dynamics (6 or 7 DOF, or more, while the feedforward control from the off-line iterative learning controller should be assumed as a continuous one. The robustness and convergence of the proposed NILC law with SD feedback is proven, and the derived sufficient condition for convergence is the same as the condition for a NILC with a continuous feedback control input. With respect to the presented NILC algorithm applied to a virtual PUMA 560 robot, simulation results are presented in order to verify convergence and applicability of the proposed learning controller with SD feedback controller attached

Prescribed Performance Fuzzy Adaptive Output-Feedback Control for Nonlinear Stochastic Systems

Directory of Open Access Journals (Sweden)

Lili Zhang

2014-01-01

Full Text Available A prescribed performance fuzzy adaptive output-feedback control approach is proposed for a class of single-input and single-output nonlinear stochastic systems with unmeasured states. Fuzzy logic systems are used to identify the unknown nonlinear system, and a fuzzy state observer is designed for estimating the unmeasured states. Based on the backstepping recursive design technique and the predefined performance technique, a new fuzzy adaptive output-feedback control method is developed. It is shown that all the signals of the resulting closed-loop system are bounded in probability and the tracking error remains an adjustable neighborhood of the origin with the prescribed performance bounds. A simulation example is provided to show the effectiveness of the proposed approach.

Convergence of spectral methods for nonlinear conservation laws. Final report

International Nuclear Information System (INIS)

Tadmor, E.

1987-08-01

The convergence of the Fourier method for scalar nonlinear conservation laws which exhibit spontaneous shock discontinuities is discussed. Numerical tests indicate that the convergence may (and in fact in some cases must) fail, with or without post-processing of the numerical solution. Instead, a new kind of spectrally accurate vanishing viscosity is introduced to augment the Fourier approximation of such nonlinear conservation laws. Using compensated compactness arguments, it is shown that this spectral viscosity prevents oscillations, and convergence to the unique entropy solution follows

Nonlinear self-adjointness, conservation laws, and the construction of solutions of partial differential equations using conservation laws

International Nuclear Information System (INIS)

Ibragimov, N Kh; Avdonina, E D

2013-01-01

The method of nonlinear self-adjointness, which was recently developed by the first author, gives a generalization of Noether's theorem. This new method significantly extends approaches to constructing conservation laws associated with symmetries, since it does not require the existence of a Lagrangian. In particular, it can be applied to any linear equations and any nonlinear equations that possess at least one local conservation law. The present paper provides a brief survey of results on conservation laws which have been obtained by this method and published mostly in recent preprints of the authors, along with a method for constructing exact solutions of systems of partial differential equations with the use of conservation laws. In most cases the solutions obtained by the method of conservation laws cannot be found as invariant or partially invariant solutions. Bibliography: 23 titles

Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control

International Nuclear Information System (INIS)

Fu Shi-Hui; Lu Qi-Shao; Du Ying

2012-01-01

Adaptive H ∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated. The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach. Based on Lyapunov's stability theory, linear and nonlinear feedback control of adaptive H ∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an H ∞ -norm constraint. Adaptive H ∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems. Numerical simulations are also given to identify the effectiveness of the theoretical analysis. (general)

Robust stabilization of nonlinear systems: The LMI approach

Directory of Open Access Journals (Sweden)

Šiljak D. D.

2000-01-01

Full Text Available This paper presents a new approach to robust quadratic stabilization of nonlinear systems within the framework of Linear Matrix Inequalities (LMI. The systems are composed of a linear constant part perturbed by an additive nonlinearity which depends discontinuously on both time and state. The only information about the nonlinearity is that it satisfies a quadratic constraint. Our major objective is to show how linear constant feedback laws can be formulated to stabilize this type of systems and, at the same time, maximize the bounds on the nonlinearity which the system can tolerate without going unstable. We shall broaden the new setting to include design of decentralized control laws for robust stabilization of interconnected systems. Again, the LMI methods will be used to maximize the class of uncertain interconnections which leave the overall system connectively stable. It is useful to learn that the proposed LMI formulation “recognizes” the matching conditions by returning a feedback gain matrix for any prescribed bound on the interconnection terms. More importantly, the new formulation provides a suitable setting for robust stabilization of nonlinear systems where the nonlinear perturbations satisfy the generalized matching conditions.

Feedback control for a train-like vehicle

International Nuclear Information System (INIS)

Micaelli, A.

1994-01-01

This paper presents a feedback nonlinear control law for a train-like vehicle (TLV) used in nuclear power-station maintenance. The front cart is either manual or automated guided. The rear carts are feedback controlled. The control objective is to ensure that the rear carts track the path produced (on-line) by the front cart. This controller was experimentally tested on the TLV-prototype. (authors). 4 figs., 4 refs

A switched state feedback law for the stabilization of LTI systems.

Energy Technology Data Exchange (ETDEWEB)

Santarelli, Keith R.

2009-09-01

Inspired by prior work in the design of switched feedback controllers for second order systems, we develop a switched state feedback control law for the stabilization of LTI systems of arbitrary dimension. The control law operates by switching between two static gain vectors in such a way that the state trajectory is driven onto a stable n - 1 dimensional hyperplane (where n represents the system dimension). We begin by briefly examining relevant geometric properties of the phase portraits in the case of two-dimensional systems to develop intuition, and we then show how these geometric properties can be expressed as algebraic constraints on the switched vector fields that are applicable to LTI systems of arbitrary dimension. We then derive necessary and sufficient conditions to ensure stabilizability of the resulting switched system (characterized primarily by simple conditions on eigenvalues), and describe an explicit procedure for designing stabilizing controllers. We then show how the newly developed control law can be applied to the problem of minimizing the maximal Lyapunov exponent of the corresponding closed-loop state trajectories, and we illustrate the closed-loop transient performance of these switched state feedback controllers via multiple examples.

Entropy viscosity method for nonlinear conservation laws

KAUST Repository

Guermond, Jean-Luc

2011-05-01

A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.

Entropy viscosity method for nonlinear conservation laws

KAUST Repository

Guermond, Jean-Luc; Pasquetti, Richard; Popov, Bojan

2011-01-01

A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.

Adaptive Neural Networks Decentralized FTC Design for Nonstrict-Feedback Nonlinear Interconnected Large-Scale Systems Against Actuator Faults.

Science.gov (United States)

Li, Yongming; Tong, Shaocheng

The problem of active fault-tolerant control (FTC) is investigated for the large-scale nonlinear systems in nonstrict-feedback form. The nonstrict-feedback nonlinear systems considered in this paper consist of unstructured uncertainties, unmeasured states, unknown interconnected terms, and actuator faults (e.g., bias fault and gain fault). A state observer is designed to solve the unmeasurable state problem. Neural networks (NNs) are used to identify the unknown lumped nonlinear functions so that the problems of unstructured uncertainties and unknown interconnected terms can be solved. By combining the adaptive backstepping design principle with the combination Nussbaum gain function property, a novel NN adaptive output-feedback FTC approach is developed. The proposed FTC controller can guarantee that all signals in all subsystems are bounded, and the tracking errors for each subsystem converge to a small neighborhood of zero. Finally, numerical results of practical examples are presented to further demonstrate the effectiveness of the proposed control strategy.The problem of active fault-tolerant control (FTC) is investigated for the large-scale nonlinear systems in nonstrict-feedback form. The nonstrict-feedback nonlinear systems considered in this paper consist of unstructured uncertainties, unmeasured states, unknown interconnected terms, and actuator faults (e.g., bias fault and gain fault). A state observer is designed to solve the unmeasurable state problem. Neural networks (NNs) are used to identify the unknown lumped nonlinear functions so that the problems of unstructured uncertainties and unknown interconnected terms can be solved. By combining the adaptive backstepping design principle with the combination Nussbaum gain function property, a novel NN adaptive output-feedback FTC approach is developed. The proposed FTC controller can guarantee that all signals in all subsystems are bounded, and the tracking errors for each subsystem converge to a small

Neural networks for feedback feedforward nonlinear control systems.

Science.gov (United States)

Parisini, T; Zoppoli, R

1994-01-01

This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method.

Nonlinear quenches of power-law confining traps in quantum critical systems

International Nuclear Information System (INIS)

Collura, Mario; Karevski, Dragi

2011-01-01

We describe the coherent quantum evolution of a quantum many-body system with a time-dependent power-law confining potential. The amplitude of the inhomogeneous potential is driven in time along a nonlinear ramp which crosses a critical point. Using Kibble-Zurek-like scaling arguments we derive general scaling laws for the density of excitations and energy excess generated during the nonlinear sweep of the confining potential. It is shown that, with respect to the sweeping rate, the densities follow algebraic laws with exponents that depend on the space-time properties of the potential and on the scaling dimensions of the densities. We support our scaling predictions with both analytical and numerical results on the Ising quantum chain with an inhomogeneous transverse field varying in time.

State-Feedback Control for Fractional-Order Nonlinear Systems Subject to Input Saturation

Directory of Open Access Journals (Sweden)

Junhai Luo

2014-01-01

Full Text Available We give a state-feedback control method for fractional-order nonlinear systems subject to input saturation. First, a sufficient condition is derived for the asymptotical stability of a class of fractional-order nonlinear systems. Then based on Gronwall-Bellman lemma and a sector bounded condition of the saturation function, a linear state-feed back controller is designed. Finally, two simulation examples are presented to show the validity of the proposed method.

Global output feedback stabilisation of stochastic high-order feedforward nonlinear systems with time-delay

Science.gov (United States)

Zhang, Kemei; Zhao, Cong-Ran; Xie, Xue-Jun

2015-12-01

This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability.

Finite-time output feedback stabilization of high-order uncertain nonlinear systems

Science.gov (United States)

Jiang, Meng-Meng; Xie, Xue-Jun; Zhang, Kemei

2018-06-01

This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.

Evidence of fast non-linear feedback in EBR-II rod-drop measurements

International Nuclear Information System (INIS)

Grimm, K.N.; Meneghetti, D.

1987-06-01

Feedback reactivities determine the time dependence of a reactor during and after a transient initiating event. Recent analysis of control-rod drops in the Experimental Breeder Reactor II (EBR-II) Reactor has indicated that some relatively fast feedback may exist which cannot be accounted for by the linear feedback mechanisms. The linear and deduced non-linear feedback reactivities from a control-rod drop in EBR-II run 93A using detailed temperature coefficients of reactivity in the EROS kinetics code have been reported. The transient analyses have now been examined in more detail for times close to the drop to ascertain if additional positive reactivity is being built-in early in the drop which could be gradually released later in the drop

Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

Science.gov (United States)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

Real-time nonlinear feedback control of pattern formation in (bio)chemical reaction-diffusion processes: a model study.

Science.gov (United States)

Brandt-Pollmann, U; Lebiedz, D; Diehl, M; Sager, S; Schlöder, J

2005-09-01

Theoretical and experimental studies related to manipulation of pattern formation in self-organizing reaction-diffusion processes by appropriate control stimuli become increasingly important both in chemical engineering and cellular biochemistry. In a model study, we demonstrate here exemplarily the application of an efficient nonlinear model predictive control (NMPC) algorithm to real-time optimal feedback control of pattern formation in a bacterial chemotaxis system modeled by nonlinear partial differential equations. The corresponding drift-diffusion model type is representative for many (bio)chemical systems involving nonlinear reaction dynamics and nonlinear diffusion. We show how the computed optimal feedback control strategy exploits the system inherent physical property of wave propagation to achieve desired control aims. We discuss various applications of our approach to optimal control of spatiotemporal dynamics.

Dynamic Output Feedback Control for Nonlinear Networked Control Systems with Random Packet Dropout and Random Delay

Directory of Open Access Journals (Sweden)

Shuiqing Yu

2013-01-01

Full Text Available This paper investigates the dynamic output feedback control for nonlinear networked control systems with both random packet dropout and random delay. Random packet dropout and random delay are modeled as two independent random variables. An observer-based dynamic output feedback controller is designed based upon the Lyapunov theory. The quantitative relationship of the dropout rate, transition probability matrix, and nonlinear level is derived by solving a set of linear matrix inequalities. Finally, an example is presented to illustrate the effectiveness of the proposed method.

Further results on global state feedback stabilization of nonlinear high-order feedforward systems.

Science.gov (United States)

Xie, Xue-Jun; Zhang, Xing-Hui

2014-03-01

In this paper, by introducing a combined method of sign function, homogeneous domination and adding a power integrator, and overcoming several troublesome obstacles in the design and analysis, the problem of state feedback control for a class of nonlinear high-order feedforward systems with the nonlinearity's order being relaxed to an interval rather than a fixed point is solved. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Feedbacks between subglacial dynamics and long-term glacial landscape evolution

DEFF Research Database (Denmark)

Brædstrup, Christian; Egholm, D.L.; Ugelvig, Sofie Vej

focus this presentation on feedbacks between the evolving bed topography and the subglacial erosion patterns. We have performed our experiments with different sliding and erosion laws, including highly non-linear rules representing coulomb-type slip at the bed (Schoof, 2010) and a quarrying model...

The effect of continuous, nonlinearly transformed visual feedback on rapid aiming movements.

NARCIS (Netherlands)

Rieger, Martina; Verwey, Willem B.; Massen, Cristina

2008-01-01

We investigated the ability to adjust to nonlinear transformations that allow people to control external systems like machines and tools. Earlier research (Verwey and Heuer 2007) showed that in the presence of just terminal feedback participants develop an internal model of such transformations that

A combined stochastic feedforward and feedback control design methodology with application to autoland design

Science.gov (United States)

Halyo, Nesim

1987-01-01

A combined stochastic feedforward and feedback control design methodology was developed. The objective of the feedforward control law is to track the commanded trajectory, whereas the feedback control law tries to maintain the plant state near the desired trajectory in the presence of disturbances and uncertainties about the plant. The feedforward control law design is formulated as a stochastic optimization problem and is embedded into the stochastic output feedback problem where the plant contains unstable and uncontrollable modes. An algorithm to compute the optimal feedforward is developed. In this approach, the use of error integral feedback, dynamic compensation, control rate command structures are an integral part of the methodology. An incremental implementation is recommended. Results on the eigenvalues of the implemented versus designed control laws are presented. The stochastic feedforward/feedback control methodology is used to design a digital automatic landing system for the ATOPS Research Vehicle, a Boeing 737-100 aircraft. The system control modes include localizer and glideslope capture and track, and flare to touchdown. Results of a detailed nonlinear simulation of the digital control laws, actuator systems, and aircraft aerodynamics are presented.

Infinite sets of conservation laws for linear and nonlinear field equations

International Nuclear Information System (INIS)

Mickelsson, J.

1984-01-01

The relation between an infinite set of conservation laws of a linear field equation and the enveloping algebra of the space-time symmetry group is established. It is shown that each symmetric element of the enveloping algebra of the space-time symmetry group of a linear field equation generates a one-parameter group of symmetries of the field equation. The cases of the Maxwell and Dirac equations are studied in detail. Then it is shown that (at least in the sense of a power series in the 'coupling constant') the conservation laws of the linear case can be deformed to conservation laws of a nonlinear field equation which is obtained from the linear one by adding a nonlinear term invariant under the group of space-time symmetries. As an example, our method is applied to the Korteweg-de Vries equation and to the massless Thirring model. (orig.)

Disturbance attenuation of nonlinear control systems using an observer-based fuzzy feedback linearization control

International Nuclear Information System (INIS)

Chen, C.-C.; Hsu, C.-H.; Chen, Y.-J.; Lin, Y.-F.

2007-01-01

The almost disturbance decoupling and trajectory tracking of nonlinear control systems using an observer-based fuzzy feedback linearization control (FLC) is developed. Because not all of the state variables of the nonlinear dynamic equations are available, a nonlinear state observer is employed to estimate the state variables. The feedback linearization control guarantees the almost disturbance decoupling performance and the uniform ultimate bounded stability of the tracking error system. Once the tracking errors are driven to touch the global final attractor with the desired radius, the fuzzy logic control is immediately applied via human expert's knowledge to improve the convergence rate. One example, which cannot be solved by the first paper on the almost disturbance decoupling problem, is proposed in this paper to exploit the fact that the tracking and the almost disturbance decoupling performances are easily achieved by our proposed approach. In order to demonstrate the practical applicability, the study has investigated a pendulum control system

Chaos synchronization of uncertain chaotic systems using composite nonlinear feedback based integral sliding mode control.

Science.gov (United States)

Mobayen, Saleh

2018-06-01

This paper proposes a combination of composite nonlinear feedback and integral sliding mode techniques for fast and accurate chaos synchronization of uncertain chaotic systems with Lipschitz nonlinear functions, time-varying delays and disturbances. The composite nonlinear feedback method allows accurate following of the master chaotic system and the integral sliding mode control provides invariance property which rejects the perturbations and preserves the stability of the closed-loop system. Based on the Lyapunov- Krasovskii stability theory and linear matrix inequalities, a novel sufficient condition is offered for the chaos synchronization of uncertain chaotic systems. This method not only guarantees the robustness against perturbations and time-delays, but also eliminates reaching phase and avoids chattering problem. Simulation results demonstrate that the suggested procedure leads to a great control performance. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities (vol 24, pg 2752, 2007)

DEFF Research Database (Denmark)

Bache, Morten; Moses, J.; Wise, F.W.

2010-01-01

Erratum for [M. Bache, J. Moses, and F. W. Wise, "Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities," J. Opt. Soc. Am. B 24, 2752-2762 (2007)].......Erratum for [M. Bache, J. Moses, and F. W. Wise, "Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities," J. Opt. Soc. Am. B 24, 2752-2762 (2007)]....

Globally Asymptotic Stability of Stochastic Nonlinear Systems with Time-Varying Delays via Output Feedback Control

Directory of Open Access Journals (Sweden)

Mingzhu Song

2016-01-01

Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.

Fuzzy combination of fuzzy and switching state-feedback controllers for nonlinear systems subject to parameter uncertainties.

Science.gov (United States)

Lam, H K; Leung, Frank H F

2005-04-01

This paper presents a fuzzy controller, which involves a fuzzy combination of local fuzzy and global switching state-feedback controllers, for nonlinear systems subject to parameter uncertainties with known bounds. The nonlinear system is represented by a fuzzy combined Takagi-Sugeno-Kang model, which is a fuzzy combination of the global and local fuzzy plant models. By combining the local fuzzy and global switching state-feedback controllers using fuzzy logic techniques, the advantages of both controllers can be retained and the undesirable chattering effect introduced by the global switching state-feedback controller can be eliminated. The steady-state error introduced by the global switching state-feedback controller when a saturation function is used can also be removed. Stability conditions, which are related to the system matrices of the local and global closed-loop systems, are derived to guarantee the closed-loop system stability. An application example will be given to demonstrate the merits of the proposed approach.

Nonlinear Power-Level Control of the MHTGR Only with the Feedback Loop of Helium Temperature

Directory of Open Access Journals (Sweden)

Zhe Dong

2013-02-01

Full Text Available Power-level control is a crucial technique for the safe, stable and efficient operation of modular high temperature gas-cooled nuclear reactors (MHTGRs, which have strong inherent safety features and high outlet temperatures. The current power-level controllers of the MHTGRs need measurements of both the nuclear power and the helium temperature, which cannot provide satisfactory control performance and can even induce large oscillations when the neutron sensors are in error. In order to improve the fault tolerance of the control system, it is important to develop a power-level control strategy that only requires the helium temperature. The basis for developing this kind of control law is to give a state-observer of the MHTGR a relationship that only needs the measurement of helium temperature. With this in mind, a novel nonlinear state observer which only needs the measurement of helium temperature is proposed. This observer is globally convergent if there is no disturbance, and has the L2 disturbance attenuation performance if the disturbance is nonzero. The separation principle of this observer is also proven, which denotes that this observer can recover the performance of both globally asymptotic stabilizers and L2 disturbance attenuators. Then, a new dynamic output feedback power-level control strategy is established, which is composed of this observer and the well-built static state-feedback power-level control based upon iterative dissipation assignment (IDA-PLC. Finally, numerical simulation results show the high performance and feasibility of this newly-built dynamic output feedback power-level controller.

Focus scanning with feedback control for fiber-optic nonlinear endomicroscopy (Conference Presentation)

Science.gov (United States)

Li, Ang; Liang, Wenxuan; Li, Xingde

2017-02-01

Fiber-optic nonlinear endomicroscopy represents a strong promise to enable translation of nonlinear microscopy technologies to in vivo applications, particularly imaging of internal organs. Two-dimensional imaging beam scanning has been accomplished by using fiber-optic scanners or MEMS scanners. Yet nonlinear endomicroscopy still cannot perform rapid and reliable depth or focus scanning while maintaining a small form factor. Shape memory alloy (SMA) wire had shown promise in extending 2D endoscopic imaging to the third dimension. By Joule heating, the SMA wire would contract and move the endomicroscope optics to change beam focus. However, this method suffered from hysteresis, and was susceptible to change in ambient temperature, making it difficult to achieve accurate and reliable depth scanning. Here we present a feedback-controlled SMA actuator which addressed these challenges. The core of the feedback loop was a Hall effect sensor. By measuring the magnetic flux density from a tiny magnet attached to the SMA wire, contraction distance of the SMA wire could be tracked in real time. The distance was then fed to the PID algorithm running in a microprocessor, which computed the error between the command position and the current position of the actuator. The current running through the SMA wire was adjusted accordingly. Our feedback-controlled SMA actuator had a tube-like shape with outer diameter of 5.5 mm and length of 25 mm, and was designed to house the endomicroscope inside. Initial test showed that it allowed more than 300 microns of travel distance, with an average positioning error of less than 2 microns. 3D imaging experiments with the endomicroscope is underway, and its imaging performance will be assessed and discussed.

Conservation laws for certain time fractional nonlinear systems of partial differential equations

Science.gov (United States)

Singla, Komal; Gupta, R. K.

2017-12-01

In this study, an extension of the concept of nonlinear self-adjointness and Noether operators is proposed for calculating conserved vectors of the time fractional nonlinear systems of partial differential equations. In our recent work (J Math Phys 2016; 57: 101504), by proposing the symmetry approach for time fractional systems, the Lie symmetries for some fractional nonlinear systems have been derived. In this paper, the obtained infinitesimal generators are used to find conservation laws for the corresponding fractional systems.

Sensorless Estimation and Nonlinear Control of a Rotational Energy Harvester

Science.gov (United States)

Nunna, Kameswarie; Toh, Tzern T.; Mitcheson, Paul D.; Astolfi, Alessandro

2013-12-01

It is important to perform sensorless monitoring of parameters in energy harvesting devices in order to determine the operating states of the system. However, physical measurements of these parameters is often a challenging task due to the unavailability of access points. This paper presents, as an example application, the design of a nonlinear observer and a nonlinear feedback controller for a rotational energy harvester. A dynamic model of a rotational energy harvester with its power electronic interface is derived and validated. This model is then used to design a nonlinear observer and a nonlinear feedback controller which yield a sensorless closed-loop system. The observer estimates the mechancial quantities from the measured electrical quantities while the control law sustains power generation across a range of source rotation speeds. The proposed scheme is assessed through simulations and experiments.

Nonlinear free vibration control of beams using acceleration delayed-feedback control

International Nuclear Information System (INIS)

Alhazza, Khaled A; Alajmi, Mohammed; Masoud, Ziyad N

2008-01-01

A single-mode delayed-feedback control strategy is developed to reduce the free vibrations of a flexible beam using a piezoelectric actuator. A nonlinear variational model of the beam based on the von Kàrmàn nonlinear type deformations is considered. Using Galerkin's method, the resulting governing partial differential equations of motion are reduced to a system of nonlinear ordinary differential equations. A linear model using the first mode is derived and is used to characterize the damping produced by the controller as a function of the controller's gain and delay. Three-dimensional figures showing the damping magnitude as a function of the controller gain and delay are presented. The characteristic damping of the controller as predicted by the linear model is compared to that calculated using direct long-time integration of a three-mode nonlinear model. Optimal values of the controller gain and delay using both methods are obtained, simulated and compared. To validate the single-mode approximation, numerical simulations are performed using a three-mode full nonlinear model. Results of the simulations demonstrate an excellent controller performance in mitigating the first-mode vibration

Robust Feedback Linearization-based Control Design for a Wheeled Mobile Robot

DEFF Research Database (Denmark)

Bendtsen, Jan Dimon; Andersen, Palle; Pedersen, Tom Søndergaard

This paper considers the trajectory tracking problem for a four-wheel driven, four-wheel steered mobile robot moving in outdoor terrain. The robot is modeled as a non-holonomic dynamic system subject to pure rolling, no-slip constraints. A nonlinear trajectory tracking feedback control law based...

Output Feedback Stabilization with Nonlinear Predictive Control: Asymptotic properties

Directory of Open Access Journals (Sweden)

Lars Imsland

2003-07-01

Full Text Available State space based nonlinear model predictive control (NM PC needs the state for the prediction of the system behaviour. Unfortunately, for most applications, not all states are directly measurable. To recover the unmeasured states, typically a stable state observer is used. However, this implies that the stability of the closed-loop should be examined carefully, since no general nonlinear separation principle exists. Recently semi-global practical stability results for output feedback NMPC using a high-gain observer for state estimation have been established. One drawback of this result is that (in general the observer gain must be increased, if the desired set the state should converge to is made smaller. We show that under slightly stronger assumptions, not only practical stability, but also convergence of the system states and observer error to the origin for a sufficiently large but bounded observer gain can be achieved.

Uncertainty Modeling and Robust Output Feedback Control of Nonlinear Discrete Systems: A Mathematical Programming Approach

Directory of Open Access Journals (Sweden)

Olav Slupphaug

2001-01-01

Full Text Available We present a mathematical programming approach to robust control of nonlinear systems with uncertain, possibly time-varying, parameters. The uncertain system is given by different local affine parameter dependent models in different parts of the state space. It is shown how this representation can be obtained from a nonlinear uncertain system by solving a set of continuous linear semi-infinite programming problems, and how each of these problems can be solved as a (finite series of ordinary linear programs. Additionally, the system representation includes control- and state constraints. The controller design method is derived from Lyapunov stability arguments and utilizes an affine parameter dependent quadratic Lyapunov function. The controller has a piecewise affine output feedback structure, and the design amounts to finding a feasible solution to a set of linear matrix inequalities combined with one spectral radius constraint on the product of two positive definite matrices. A local solution approach to this nonconvex feasibility problem is proposed. Complexity of the design method and some special cases such as state- feedback are discussed. Finally, an application of the results is given by proposing an on-line computationally feasible algorithm for constrained nonlinear state- feedback model predictive control with robust stability.

Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

International Nuclear Information System (INIS)

Jia Li-Xin; Dai Hao; Hui Meng

2010-01-01

This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method

Adaptive neural network output feedback control for stochastic nonlinear systems with unknown dead-zone and unmodeled dynamics.

Science.gov (United States)

Tong, Shaocheng; Wang, Tong; Li, Yongming; Zhang, Huaguang

2014-06-01

This paper discusses the problem of adaptive neural network output feedback control for a class of stochastic nonlinear strict-feedback systems. The concerned systems have certain characteristics, such as unknown nonlinear uncertainties, unknown dead-zones, unmodeled dynamics and without the direct measurements of state variables. In this paper, the neural networks (NNs) are employed to approximate the unknown nonlinear uncertainties, and then by representing the dead-zone as a time-varying system with a bounded disturbance. An NN state observer is designed to estimate the unmeasured states. Based on both backstepping design technique and a stochastic small-gain theorem, a robust adaptive NN output feedback control scheme is developed. It is proved that all the variables involved in the closed-loop system are input-state-practically stable in probability, and also have robustness to the unmodeled dynamics. Meanwhile, the observer errors and the output of the system can be regulated to a small neighborhood of the origin by selecting appropriate design parameters. Simulation examples are also provided to illustrate the effectiveness of the proposed approach.

A Note on the Invariance Properties and Conservation Laws of the Kadomstev—Petviashvili Equation with Power Law Nonlinearity

International Nuclear Information System (INIS)

Bokhari A H; Zaman F D; Fakhar K; Kara A H

2011-01-01

First, we studied the invariance properties of the Kadomstev—Petviashvili equation with power law nonlinearity. Then, we determined the complete class of conservation laws and stated the corresponding conserved densities which are useful in finding the conserved quantities of the equation. The point symmetry generators were also used to reduce the equation to an exact solution and to verify the invariance properties of the conserved flows. (general)

Effects of linear and nonlinear time-delayed feedback on the noise-enhanced stability phenomenon in a periodically driven bistable system

International Nuclear Information System (INIS)

Jia, Zheng-Lin; Mei, Dong-Cheng

2011-01-01

We investigate numerically the effects of time delay on the phenomenon of noise-enhanced stability (NES) in a periodically modulated bistable system. Three types of time-delayed feedback, including linear delayed feedback, nonlinear delayed feedback and global delayed feedback, are considered. We find a non-monotonic behaviour of the mean first-passage time (MFPT) as a function of the delay time τ, with a maximum in the case of linear delayed feedback and with a minimum in the case of nonlinear delayed feedback. There are two peculiar values of τ around which the NES phenomenon is enhanced or weakened. For the case of global delayed feedback, the increase of τ always weakens the NES phenomenon. Moreover, we also show that the amplitude A and the frequency Ω of the periodic forcing play an opposite role in the NES phenomenon, i.e. the increase of A weakens the NES effect while the increase of Ω enhances it. These observations demonstrate that the time-delayed feedback can be used as a feasible control scheme for the NES phenomenon

On the Internal Model Principle in the Coordination of Nonlinear Systems

NARCIS (Netherlands)

De Persis, C.; Jayawardhana, B.

2014-01-01

The role of the internal model principle is investigated in this paper for the coordination of relative-degree-one and relative-degree-two nonlinear systems. For relative-degree-one systems that are incrementally (output-feedback) passive, we propose internal-model-based distributed control laws

Neural feedback linearization adaptive control for affine nonlinear systems based on neural network estimator

Directory of Open Access Journals (Sweden)

Bahita Mohamed

2011-01-01

Full Text Available In this work, we introduce an adaptive neural network controller for a class of nonlinear systems. The approach uses two Radial Basis Functions, RBF networks. The first RBF network is used to approximate the ideal control law which cannot be implemented since the dynamics of the system are unknown. The second RBF network is used for on-line estimating the control gain which is a nonlinear and unknown function of the states. The updating laws for the combined estimator and controller are derived through Lyapunov analysis. Asymptotic stability is established with the tracking errors converging to a neighborhood of the origin. Finally, the proposed method is applied to control and stabilize the inverted pendulum system.

Some current topics on nonlinear conservation laws lectures at the morningside center of mathematics, 1

CERN Document Server

Hsiao, Ling

2000-01-01

This volume resulted from a year-long program at the Morningside Center of Mathematics at the Academia Sinica in Beijing. It presents an overview of nonlinear conversation laws and introduces developments in this expanding field. Xin's introductory overview of the subject is followed by lecture notes of leading experts who have made fundamental contributions to this field of research. A. Bressan's theory of L^1-well-posedness for entropy weak solutions to systems of nonlinear hyperbolic conversation laws in the class of viscosity solutions is one of the most important results in the past two decades; G. Chen discusses weak convergence methods and various applications to many problems; P. Degond details mathematical modelling of semi-conductor devices; B. Perthame describes the theory of asymptotic equivalence between conservation laws and singular kinetic equations; Z. Xin outlines the recent development of the vanishing viscosity problem and nonlinear stability of elementary wave-a major focus of research in...

Adaptive critic designs for optimal control of uncertain nonlinear systems with unmatched interconnections.

Science.gov (United States)

Yang, Xiong; He, Haibo

2018-05-26

In this paper, we develop a novel optimal control strategy for a class of uncertain nonlinear systems with unmatched interconnections. To begin with, we present a stabilizing feedback controller for the interconnected nonlinear systems by modifying an array of optimal control laws of auxiliary subsystems. We also prove that this feedback controller ensures a specified cost function to achieve optimality. Then, under the framework of adaptive critic designs, we use critic networks to solve the Hamilton-Jacobi-Bellman equations associated with auxiliary subsystem optimal control laws. The critic network weights are tuned through the gradient descent method combined with an additional stabilizing term. By using the newly established weight tuning rules, we no longer need the initial admissible control condition. In addition, we demonstrate that all signals in the closed-loop auxiliary subsystems are stable in the sense of uniform ultimate boundedness by using classic Lyapunov techniques. Finally, we provide an interconnected nonlinear plant to validate the present control scheme. Copyright © 2018 Elsevier Ltd. All rights reserved.

Analysis of the Symmetries and Conservation Laws of the Nonlinear Jaulent-Miodek Equation

Directory of Open Access Journals (Sweden)

Mehdi Nadjafikhah

2014-01-01

Full Text Available Lie symmetry method is performed for the nonlinear Jaulent-Miodek equation. We will find the symmetry group and optimal systems of Lie subalgebras. The Lie invariants associated with the symmetry generators as well as the corresponding similarity reduced equations are also pointed out. And conservation laws of the J-M equation are presented with two steps: firstly, finding multipliers for computation of conservation laws and, secondly, symbolic computation of conservation laws will be applied.

Nonlinear Conservation Laws and Finite Volume Methods

Science.gov (United States)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

Combined feedforward and feedback control of a redundant, nonlinear, dynamic musculoskeletal system.

Science.gov (United States)

Blana, Dimitra; Kirsch, Robert F; Chadwick, Edward K

2009-05-01

A functional electrical stimulation controller is presented that uses a combination of feedforward and feedback for arm control in high-level injury. The feedforward controller generates the muscle activations nominally required for desired movements, and the feedback controller corrects for errors caused by muscle fatigue and external disturbances. The feedforward controller is an artificial neural network (ANN) which approximates the inverse dynamics of the arm. The feedback loop includes a PID controller in series with a second ANN representing the nonlinear properties and biomechanical interactions of muscles and joints. The controller was designed and tested using a two-joint musculoskeletal model of the arm that includes four mono-articular and two bi-articular muscles. Its performance during goal-oriented movements of varying amplitudes and durations showed a tracking error of less than 4 degrees in ideal conditions, and less than 10 degrees even in the case of considerable fatigue and external disturbances.

Nonlinear Dynamic Inversion Baseline Control Law: Architecture and Performance Predictions

Science.gov (United States)

Miller, Christopher J.

2011-01-01

A model reference dynamic inversion control law has been developed to provide a baseline control law for research into adaptive elements and other advanced flight control law components. This controller has been implemented and tested in a hardware-in-the-loop simulation; the simulation results show excellent handling qualities throughout the limited flight envelope. A simple angular momentum formulation was chosen because it can be included in the stability proofs for many basic adaptive theories, such as model reference adaptive control. Many design choices and implementation details reflect the requirements placed on the system by the nonlinear flight environment and the desire to keep the system as basic as possible to simplify the addition of the adaptive elements. Those design choices are explained, along with their predicted impact on the handling qualities.

Lectures in feedback design for multivariable systems

CERN Document Server

Isidori, Alberto

2017-01-01

This book focuses on methods that relate, in one form or another, to the “small-gain theorem”. It is aimed at readers who are interested in learning methods for the design of feedback laws for linear and nonlinear multivariable systems in the presence of model uncertainties. With worked examples throughout, it includes both introductory material and more advanced topics. Divided into two parts, the first covers relevant aspects of linear-systems theory, the second, nonlinear theory. In order to deepen readers’ understanding, simpler single-input–single-output systems generally precede treatment of more complex multi-input–multi-output (MIMO) systems and linear systems precede nonlinear systems. This approach is used throughout, including in the final chapters, which explain the latest advanced ideas governing the stabilization, regulation, and tracking of nonlinear MIMO systems. Two major design problems are considered, both in the presence of model uncertainties: asymptotic stabilization with a “...

Frequency-domain and time-domain methods for feedback nonlinear systems and applications to chaos control

International Nuclear Information System (INIS)

Duan Zhisheng; Wang Jinzhi; Yang Ying; Huang Lin

2009-01-01

This paper surveys frequency-domain and time-domain methods for feedback nonlinear systems and their possible applications to chaos control, coupled systems and complex dynamical networks. The absolute stability of Lur'e systems with single equilibrium and global properties of a class of pendulum-like systems with multi-equilibria are discussed. Time-domain and frequency-domain criteria for the convergence of solutions are presented. Some latest results on analysis and control of nonlinear systems with multiple equilibria and applications to chaos control are reviewed. Finally, new chaotic oscillating phenomena are shown in a pendulum-like system and a new nonlinear system with an attraction/repulsion function.

Ship nonlinear-feedback course keeping algorithm based on MMG model driven by bipolar sigmoid function for berthing

Directory of Open Access Journals (Sweden)

Qiang Zhang

2017-09-01

Full Text Available Course keeping is hard to implement under the condition of the propeller stopping or reversing at slow speed for berthing due to the ship's dynamic motion becoming highly nonlinear. To solve this problem, a practical Maneuvering Modeling Group (MMG ship mathematic model with propeller reversing transverse forces and low speed correction is first discussed to be applied for the right-handed single-screw ship. Secondly, a novel PID-based nonlinear feedback algorithm driven by bipolar sigmoid function is proposed. The PID parameters are determined by a closed-loop gain shaping algorithm directly, while the closed-loop gain shaping theory was employed for effects analysis of this algorithm. Finally, simulation experiments were carried out on an LPG ship. It is shown that the energy consumption and the smoothness performance of the nonlinear feedback control are reduced by 4.2% and 14.6% with satisfactory control effects; the proposed algorithm has the advantages of robustness, energy saving and safety in berthing practice.

Adaptive Neural Output-Feedback Control for a Class of Nonlower Triangular Nonlinear Systems With Unmodeled Dynamics.

Science.gov (United States)

Wang, Huanqing; Liu, Peter Xiaoping; Li, Shuai; Wang, Ding

2017-08-29

This paper presents the development of an adaptive neural controller for a class of nonlinear systems with unmodeled dynamics and immeasurable states. An observer is designed to estimate system states. The structure consistency of virtual control signals and the variable partition technique are combined to overcome the difficulties appearing in a nonlower triangular form. An adaptive neural output-feedback controller is developed based on the backstepping technique and the universal approximation property of the radial basis function (RBF) neural networks. By using the Lyapunov stability analysis, the semiglobally and uniformly ultimate boundedness of all signals within the closed-loop system is guaranteed. The simulation results show that the controlled system converges quickly, and all the signals are bounded. This paper is novel at least in the two aspects: 1) an output-feedback control strategy is developed for a class of nonlower triangular nonlinear systems with unmodeled dynamics and 2) the nonlinear disturbances and their bounds are the functions of all states, which is in a more general form than existing results.

Feedback control systems for non-linear simulation of operational transients in LMFBRs

International Nuclear Information System (INIS)

Khatib-Rahbar, M.; Agrawal, A.K.; Srinivasan, E.S.

1979-01-01

Feedback control systems for non-linear simulation of operational transients in LMFBRs are developed. The models include (1) the reactor power control and rod drive mechanism, (2) sodium flow control and pump drive system, (3) steam generator flow control and valve actuator dynamics, and (4) the supervisory control. These models have been incorporated into the SSC code using a flexible approach, in order to accommodate some design dependent variations. The impact of system nonlinearity on the control dynamics is shown to be significant for severe perturbations. Representative result for a 10 cent and 25 cent step insertion of reactivity and a 10% ramp change in load in 40 seconds demonstrate the suitability of this model for study of operational transients without scram in LMFBRs

Quantum-mechanical Green's functions and nonlinear superposition law

International Nuclear Information System (INIS)

Nassar, A.B.; Bassalo, J.M.F.; Antunes Neto, H.S.; Alencar, P. de T.S.

1986-01-01

The quantum-mechanical Green's function is derived for the problem of a time-dependent variable mass particle subject to a time-dependent forced harmonic oscillator potential by taking direct recourse of the corresponding Schroedinger equation. Through the usage of the nonlinear superposition law of Ray and Reid, it is shown that such a Green's function can be obtained from that for the problem of a particle with unit (constant) mass subject to either a forced harmonic potential with constant frequency or only to a time-dependent linear field. (Author) [pt

Quantum-mechanical Green's function and nonlinear superposition law

International Nuclear Information System (INIS)

Nassar, A.B.; Bassalo, J.M.F.; Antunes Neto, H.S.; Alencar, P.T.S.

1986-01-01

It is derived the quantum-mechanical Green's function for the problem of a time-dependent variable mass particle subject to a time-dependent forced harmonic-oscillator potential by taking direct recourse of the corresponding Schroedinger equation. Through the usage of the nonlinear superposition law of Ray and Reid, it is shown that such a Green's function can be obtained from that for the problem of a particle with unit (constant) mass subject to either a forced harmonic potential with constant frequency or only to a time-dependent linear field

Nonlinear dynamic analysis of 2-DOF nonlinear vibration isolation floating raft systems with feedback control

International Nuclear Information System (INIS)

Li Yingli; Xu Daolin; Fu Yiming; Zhou Jiaxi

2012-01-01

In this paper, the average method is adopted to analysis dynamic characteristics of nonlinear vibration isolation floating raft system with feedback control. The analytic results show that the purposes of reducing amplitude of oscillation and complicating the motion can be achieved by adjusting properly the system parameters, exciting frequency and control gain. The conclusions can provide some available evidences for the design and improvement of both the passive and active control of the vibration isolation systems. By altering the exciting frequency and control gain, complex motion of the system can be obtained. Numerical simulations show the system exhibits period vibration, double period vibration and quasi-period motion.

Neural-Based Compensation of Nonlinearities in an Airplane Longitudinal Model with Dynamic-Inversion Control

Directory of Open Access Journals (Sweden)

YanBin Liu

2017-01-01

Full Text Available The inversion design approach is a very useful tool for the complex multiple-input-multiple-output nonlinear systems to implement the decoupling control goal, such as the airplane model and spacecraft model. In this work, the flight control law is proposed using the neural-based inversion design method associated with the nonlinear compensation for a general longitudinal model of the airplane. First, the nonlinear mathematic model is converted to the equivalent linear model based on the feedback linearization theory. Then, the flight control law integrated with this inversion model is developed to stabilize the nonlinear system and relieve the coupling effect. Afterwards, the inversion control combined with the neural network and nonlinear portion is presented to improve the transient performance and attenuate the uncertain effects on both external disturbances and model errors. Finally, the simulation results demonstrate the effectiveness of this controller.

Explicit Nonlinear Model Predictive Control Theory and Applications

CERN Document Server

Grancharova, Alexandra

2012-01-01

Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø  Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...

Nonlinear feedback control of chaotic pendulum in presence of saturation effect

Energy Technology Data Exchange (ETDEWEB)

Alasty, Aria [Center of Excellence in Design, Robotics, and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, Tehran 1458889694 (Iran, Islamic Republic of)]. E-mail: aalasti@sharif.edu; Salarieh, Hassan [Center of Excellence in Design, Robotics, and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, Tehran 1458889694 (Iran, Islamic Republic of)]. E-mail: salarieh@mehr.sharif.edu

2007-01-15

In present paper, a feedback linearization control is applied to control a chaotic pendulum system. Tracking the desired periodic orbits such as period-one, period-two, and period-four orbits is efficiently achieved. Due to the presence of saturation in real world control signals, the stability of controller is investigated in presence of saturation and sufficient stability conditions are obtained. At first feedback linearization control law is designed, then to avoid the singularity condition, a saturating constraint is applied to the control signal. The stability conditions are obtained analytically. These conditions must be investigated for each specific case numerically. Simulation results show the effectiveness and robustness of proposed controller. A major advantage of this method is its shorter chaotic transient time in compare to other methods such as OGY and Pyragas controllers.

Investigation on the effect of nonlinear processes on similarity law in high-pressure argon discharges

Science.gov (United States)

Fu, Yangyang; Parsey, Guy M.; Verboncoeur, John P.; Christlieb, Andrew J.

2017-11-01

In this paper, the effect of nonlinear processes (such as three-body collisions and stepwise ionizations) on the similarity law in high-pressure argon discharges has been studied by the use of the Kinetic Global Model framework. In the discharge model, the ground state argon atoms (Ar), electrons (e), atom ions (Ar+), molecular ions (Ar2+), and fourteen argon excited levels Ar*(4s and 4p) are considered. The steady-state electron and ion densities are obtained with nonlinear processes included and excluded in the designed models, respectively. It is found that in similar gas gaps, keeping the product of gas pressure and linear dimension unchanged, with the nonlinear processes included, the normalized density relations deviate from the similarity relations gradually as the scale-up factor decreases. Without the nonlinear processes, the parameter relations are in good agreement with the similarity law predictions. Furthermore, the pressure and the dimension effects are also investigated separately with and without the nonlinear processes. It is shown that the gas pressure effect on the results is less obvious than the dimension effect. Without the nonlinear processes, the pressure and the dimension effects could be estimated from one to the other based on the similarity relations.

Shaping Microwave Fields Using Nonlinear Unsolicited Feedback: Application to Enhance Energy Harvesting

Science.gov (United States)

del Hougne, Philipp; Fink, Mathias; Lerosey, Geoffroy

2017-12-01

Wave-front shaping has emerged over the past decade as a powerful tool to control wave propagation through complex media, initially in optics and more recently also in the microwave domain with important applications in telecommunication, imaging, and energy transfer. The crux of implementing wave-front shaping concepts in real life is often its need for (direct) feedback, requiring access to the target to focus on. Here, we present the shaping of a microwave field based on indirect, unsolicited, and blind feedback which may be the pivotal step towards practical implementations. With the example of a radio-frequency harvester in a metallic cavity, we demonstrate tenfold enhancement of the harvested power by wave-front shaping based on nonlinear signals detected at an arbitrary position away from the harvesting device.

Learning-Based Adaptive Optimal Tracking Control of Strict-Feedback Nonlinear Systems.

Science.gov (United States)

Gao, Weinan; Jiang, Zhong-Ping; Weinan Gao; Zhong-Ping Jiang; Gao, Weinan; Jiang, Zhong-Ping

2018-06-01

This paper proposes a novel data-driven control approach to address the problem of adaptive optimal tracking for a class of nonlinear systems taking the strict-feedback form. Adaptive dynamic programming (ADP) and nonlinear output regulation theories are integrated for the first time to compute an adaptive near-optimal tracker without any a priori knowledge of the system dynamics. Fundamentally different from adaptive optimal stabilization problems, the solution to a Hamilton-Jacobi-Bellman (HJB) equation, not necessarily a positive definite function, cannot be approximated through the existing iterative methods. This paper proposes a novel policy iteration technique for solving positive semidefinite HJB equations with rigorous convergence analysis. A two-phase data-driven learning method is developed and implemented online by ADP. The efficacy of the proposed adaptive optimal tracking control methodology is demonstrated via a Van der Pol oscillator with time-varying exogenous signals.

On a quantum version of conservation laws for derivative nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Sen, S.; Chowdhury, A.R.

1988-01-01

The authors derived the quantum mechanical versions of infinite number of conservation laws associated with Derivative Nonlinear Schrodinger equation with the help of a methodology used in string theory. The renormalised version of the conserved quantities are obtained with explicit forms of the counter terms

On the structure on non-local conservation laws in the two-dimensional non-linear sigma-model

International Nuclear Information System (INIS)

Zamolodchikov, Al.B.

1978-01-01

The non-local conserved charges are supposed to satisfy a special multiplicative law in the space of asymptotic states of the non-linear sigma-model. This supposition leads to factorization equations for two-particle scattering matrix elements and determines to some extent the action of these charges in the asymptotic space. Their conservation turns out to be consistent with the factorized S-matrix of the non-linear sigma-model. It is shown also that the factorized sine-Gordon S-matrix is consistent with a similar family of conservation laws

Exponential synchronization of the Genesio-Tesi chaotic system via a novel feedback control

International Nuclear Information System (INIS)

Park, Ju H

2007-01-01

A novel feedback control scheme is proposed for exponential synchronization of the Genesio-Tesi chaotic system. The feedback controller consists of two parts: a linear dynamic control law and a nonlinear control one. For exponential synchronization between the drive and response Genesio-Tesi systems, the Lyapunov stability analysis is used. Then an existence criterion for the stabilizing controller is presented in terms of linear matrix inequalities (LMIs). The LMIs can be solved easily by various convex optimization algorithms. Finally, a numerical simulation is illustrated to show the effectiveness of the proposed chaos synchronization scheme

Nonlinear Control of Marine Surface Vessels

Science.gov (United States)

Das, Swarup; Talole, S. E.

2018-03-01

In the present study, a robust yaw control law design derived from nonlinear extended state observer (NESO) based nonlinear state error feedback controller (NSEFC) in conjunction with nonlinear tracking differentiator (NTD) for marine surface vessels is presented. As marine vessel operates in an environment where significant uncertainties and disturbances are present, an NESO is used to estimate the effect of the uncertainties and disturbances along with the plant states leading to a robust design through disturbance estimation and compensation. Convergence of NESO and NTD is demonstrated. The notable feature of the formulation is that to achieve robustness, accurate plant model or any characterization of the uncertainties and disturbances is not needed. Efficacy of the design is illustrated by simulation. Further, performance of the proposed design is compared with some existing controllers to showcase the effectiveness of the proposed design.

Vibration isolation using nonlinear damping implemented by a feedback-controlled MR damper

International Nuclear Information System (INIS)

Ho, C; Lang, Z Q; Billings, S A; Sapiński, B

2013-01-01

The main problem of using a conventional linear damper on a vibration isolation system is that the reduction of the resonant peak in many cases inevitably results in the degradation of the high-frequency transmissibility. Instead of using active control methods which normally depend on the model of the controlled plant and where unmodelled dynamics may induce stability concerns, recent studies have revealed that optimal vibration isolation over a wide frequency range can be achieved by using nonlinear damping. The present study is concerned with the realization of the ideal nonlinear damping characteristic using a feedback-controlled MR damper. Both simulation and experimental studies are conducted to demonstrate the advantages of the simple but effective vibration control strategy. This research work has significant implications for the effective use of MR dampers in the vibration control of a wide range of engineering systems. (paper)

Qualitative analysis and traveling wave solutions for the perturbed nonlinear Schroedinger's equation with Kerr law nonlinearity

International Nuclear Information System (INIS)

Zhang Zaiyun; Liu Zhenhai; Miao Xiujin; Chen Yuezhong

2011-01-01

In this Letter, we investigate the perturbed nonlinear Schroedinger's equation (NLSE) with Kerr law nonlinearity. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded traveling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution.

Reactivity-induced time-dependencies of EBR-II linear and non-linear feedbacks

International Nuclear Information System (INIS)

Grimm, K.N.; Meneghetti, D.

1988-01-01

Time-dependent linear feedback reactivities are calculated for stereotypical subassemblies in the EBR-II reactor. These quantities are calculated from nodal reactivities obtained from a kinetic code analysis of an experiment in which the change in power resulted from the dropping of a control rod. Shown with these linear reactivities are the reactivity associated with the control-rod shaft contraction and also time-dependent non-linear (mainly bowing) component deduced from the inverse kinetics of the experimentally measured fission power and the calculated linear reactivities. (author)

Constrained quadratic stabilization of discrete-time uncertain nonlinear multi-model systems using piecewise affine state-feedback

Directory of Open Access Journals (Sweden)

Olav Slupphaug

1999-07-01

Full Text Available In this paper a method for nonlinear robust stabilization based on solving a bilinear matrix inequality (BMI feasibility problem is developed. Robustness against model uncertainty is handled. In different non-overlapping regions of the state-space called clusters the plant is assumed to be an element in a polytope which vertices (local models are affine systems. In the clusters containing the origin in their closure, the local models are restricted to be linear systems. The clusters cover the region of interest in the state-space. An affine state-feedback is associated with each cluster. By utilizing the affinity of the local models and the state-feedback, a set of linear matrix inequalities (LMIs combined with a single nonconvex BMI are obtained which, if feasible, guarantee quadratic stability of the origin of the closed-loop. The feasibility problem is attacked by a branch-and-bound based global approach. If the feasibility check is successful, the Liapunov matrix and the piecewise affine state-feedback are given directly by the feasible solution. Control constraints are shown to be representable by LMIs or BMIs, and an application of the control design method to robustify constrained nonlinear model predictive control is presented. Also, the control design method is applied to a simple example.

Output feedback control of a quadrotor UAV using neural networks.

Science.gov (United States)

Dierks, Travis; Jagannathan, Sarangapani

2010-01-01

In this paper, a new nonlinear controller for a quadrotor unmanned aerial vehicle (UAV) is proposed using neural networks (NNs) and output feedback. The assumption on the availability of UAV dynamics is not always practical, especially in an outdoor environment. Therefore, in this work, an NN is introduced to learn the complete dynamics of the UAV online, including uncertain nonlinear terms like aerodynamic friction and blade flapping. Although a quadrotor UAV is underactuated, a novel NN virtual control input scheme is proposed which allows all six degrees of freedom (DOF) of the UAV to be controlled using only four control inputs. Furthermore, an NN observer is introduced to estimate the translational and angular velocities of the UAV, and an output feedback control law is developed in which only the position and the attitude of the UAV are considered measurable. It is shown using Lyapunov theory that the position, orientation, and velocity tracking errors, the virtual control and observer estimation errors, and the NN weight estimation errors for each NN are all semiglobally uniformly ultimately bounded (SGUUB) in the presence of bounded disturbances and NN functional reconstruction errors while simultaneously relaxing the separation principle. The effectiveness of proposed output feedback control scheme is then demonstrated in the presence of unknown nonlinear dynamics and disturbances, and simulation results are included to demonstrate the theoretical conjecture.

Inferring Instantaneous, Multivariate and Nonlinear Sensitivities for the Analysis of Feedback Processes in a Dynamical System: Lorenz Model Case Study

Science.gov (United States)

Aires, Filipe; Rossow, William B.; Hansen, James E. (Technical Monitor)

2001-01-01

A new approach is presented for the analysis of feedback processes in a nonlinear dynamical system by observing its variations. The new methodology consists of statistical estimates of the sensitivities between all pairs of variables in the system based on a neural network modeling of the dynamical system. The model can then be used to estimate the instantaneous, multivariate and nonlinear sensitivities, which are shown to be essential for the analysis of the feedbacks processes involved in the dynamical system. The method is described and tested on synthetic data from the low-order Lorenz circulation model where the correct sensitivities can be evaluated analytically.

Fuzzy Adaptive Output Feedback Control of Uncertain Nonlinear Systems With Prescribed Performance.

Science.gov (United States)

Zhang, Jin-Xi; Yang, Guang-Hong

2018-05-01

This paper investigates the tracking control problem for a family of strict-feedback systems in the presence of unknown nonlinearities and immeasurable system states. A low-complexity adaptive fuzzy output feedback control scheme is proposed, based on a backstepping method. In the control design, a fuzzy adaptive state observer is first employed to estimate the unmeasured states. Then, a novel error transformation approach together with a new modification mechanism is introduced to guarantee the finite-time convergence of the output error to a predefined region and ensure the closed-loop stability. Compared with the existing methods, the main advantages of our approach are that: 1) without using extra command filters or auxiliary dynamic surface control techniques, the problem of explosion of complexity can still be addressed and 2) the design procedures are independent of the initial conditions. Finally, two practical examples are performed to further illustrate the above theoretic findings.

Feedback-linearization and feedback-feedforward decentralized control for multimachine power system

Energy Technology Data Exchange (ETDEWEB)

De Tuglie, Enrico [Dipartimento di Ingegneria dell' Ambiente, e per lo Sviluppo Sostenibile - DIASS, Politecnico di Bari, Viale del Turismo 8, 74100 Taranto (Italy); Iannone, Silvio Marcello; Torelli, Francesco [Dipartimento di Elettrotecnica, ed Elettronica - DEE, Politecnico di Bari, Via Re David 200, 70125 Bari (Italy)

2008-03-15

In this paper a decentralized nonlinear controller for large-scale power systems is investigated. The proposed controller design is based on the input-output feedback linearization methodology. In order to overcome computational difficulties in adopting such methodology, the overall interconnected nonlinear system, given as n-order, is analyzed as a cascade connection of an n{sub 1}-order nonlinear subsystem and an n{sub 2}-order linear subsystem. The controller design is obtained by applying input-output feedback linearization to the nonlinear subsystem and adopting a tracking control scheme, based on feedback-feedforward technique, for the linear subsystem. In the assumed system model, which is characterised by an interconnected structure between generating units, a decentralised adaptive controller is implemented by decentralizing these constraints. The use of a totally decentralised controller implies a system performance decay with respect to performance when the system is equipped with a centralised controller. Fortunately, the robustness of the proposed controller, based on input-output feedback procedure, guarantees good performance in terms of disturbance even when disturbances are caused by decentralization of interconnection constraints. Test results, provided on the IEEE 30 bus test system, demonstrate the effectiveness and practical applicability of proposed methodology. (author)

Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory

Science.gov (United States)

de Paor, A. M.

Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ɛ has the value 1 is proved via the Popov theorem from feedback system stability theory.

Robust wide-range control of nuclear reactors by using the feedforward-feedback concept

International Nuclear Information System (INIS)

Weng, C.K.; Edwards, R.M.; Ray, A.

1994-01-01

A robust feedforward-feedback controller is proposed for wide-range operations of nuclear reactors. This control structure provides (a) optimized performance over a wide operating range resulting form the feedforward element and (b) guaranteed robust stability and performance resulting from the feedback element. The feedforward control law is synthesized via nonlinear programming, which generates an optimal control sequence over a finite-time horizon under specified constraints. The feedback control is synthesized via the structured singular value μ approach to guarantee robustness in the presence of disturbances and modeling uncertainties. The results of simulation experiments are presented to demonstrate efficacy of the proposed control structure for a large rapid power reduction to avoid unnecessary plant trips

AKNS hierarchy, Darboux transformation and conservation laws of the 1D nonautonomous nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Zhao Dun; Zhang Yujuan; Lou Weiwei; Luo Honggang

2011-01-01

By constructing nonisospectral Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy, we investigate the nonautonomous nonlinear Schroedinger (NLS) equations which have been used to describe the Feshbach resonance management in matter-wave solitons in Bose-Einstein condensate and the dispersion and nonlinearity managements for optical solitons. It is found that these equations are some special cases of a new integrable model of nonlocal nonautonomous NLS equations. Based on the Lax pairs, the Darboux transformation and conservation laws are explored. It is shown that the local external potentials would break down the classical infinite number of conservation laws. The result indicates that the integrability of the nonautonomous NLS systems may be nontrivial in comparison to the conventional concept of integrability in the canonical case.

Propagation of multidimensional nonlinear waves and kinematical conservation laws

CERN Document Server

Prasad, Phoolan

2017-01-01

This book formulates the kinematical conservation laws (KCL), analyses them and presents their applications to various problems in physics. Finally, it addresses one of the most challenging problems in fluid dynamics: finding successive positions of a curved shock front. The topics discussed are the outcome of collaborative work that was carried out mainly at the Indian Institute of Science, Bengaluru, India. The theory presented in the book is supported by referring to extensive numerical results. The book is organised into ten chapters. Chapters 1–4 offer a summary of and briefly discuss the theory of hyperbolic partial differential equations and conservation laws. Formulation of equations of a weakly nonlinear wavefront and those of a shock front are briefly explained in Chapter 5, while Chapter 6 addresses KCL theory in space of arbitrary dimensions. The remaining chapters examine various analyses and applications of KCL equations ending in the ultimate goal-propagation of a three-dimensional curved sho...

Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory

Directory of Open Access Journals (Sweden)

A. M. de Paor

1998-01-01

Full Text Available Hide (Nonlinear Processes in Geophysics, 1998 has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ε has the value 1 is proved via the Popov theorem from feedback system stability theory.

Finite difference techniques for nonlinear hyperbolic conservation laws

International Nuclear Information System (INIS)

Sanders, R.

1985-01-01

The present study is concerned with numerical approximations to the initial value problem for nonlinear systems of conservative laws. Attention is given to the development of a class of conservation form finite difference schemes which are based on the finite volume method (i.e., the method of averages). These schemes do not fit into the classical framework of conservation form schemes discussed by Lax and Wendroff (1960). The finite volume schemes are specifically intended to approximate solutions of multidimensional problems in the absence of rectangular geometries. In addition, the development is reported of different schemes which utilize the finite volume approach for time discretization. Particular attention is given to local time discretization and moving spatial grids. 17 references

Chirp-free direct modulation of 550 nm emission in Er3+ -Doped Fluoroindate glass by nonlinear feedback control

Science.gov (United States)

Cai, Runyu; Thitsa, Makhin; Bluiett, Althea; Brown, Ei; Hommerich, Uwe

2017-06-01

We propose a direct modulation method with nonlinear feedback controller which can produce chirp-free modulation of the output pulse without bulky external modulators. This work reports the design of the controller which, via a feedback loop, varies and controls the pump rate in real time by automatically adjusting the pump power to precisely modulate the emission of 550 nm in Er3+ -doped Fluoroindate glass under 1.48 μm pumping. In this interdisciplinary paper, well established theoretical tools from nonlinear control theory are applied to the dynamical system of the laser material in order to produce the desired output of the laser. The controller is simulated in MATLAB Simulink and the simulation results show that our technique yields precise modulation of the output intensity without frequency chirping. Results on both theoretical analysis of the control methodology and simulation are presented.

Nonlinear and linear wave equations for propagation in media with frequency power law losses

Science.gov (United States)

Szabo, Thomas L.

2003-10-01

The Burgers, KZK, and Westervelt wave equations used for simulating wave propagation in nonlinear media are based on absorption that has a quadratic dependence on frequency. Unfortunately, most lossy media, such as tissue, follow a more general frequency power law. The authors first research involved measurements of loss and dispersion associated with a modification to Blackstock's solution to the linear thermoviscous wave equation [J. Acoust. Soc. Am. 41, 1312 (1967)]. A second paper by Blackstock [J. Acoust. Soc. Am. 77, 2050 (1985)] showed the loss term in the Burgers equation for plane waves could be modified for other known instances of loss. The authors' work eventually led to comprehensive time-domain convolutional operators that accounted for both dispersion and general frequency power law absorption [Szabo, J. Acoust. Soc. Am. 96, 491 (1994)]. Versions of appropriate loss terms were developed to extend the standard three nonlinear wave equations to these more general losses. Extensive experimental data has verified the predicted phase velocity dispersion for different power exponents for the linear case. Other groups are now working on methods suitable for solving wave equations numerically for these types of loss directly in the time domain for both linear and nonlinear media.

Robust nonlinear control design with application to a marine cooling system

DEFF Research Database (Denmark)

Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon

2012-01-01

. In this context, we apply a bilinear transformation to obtain a well-posed H-inf problem. The design procedure is applied to a marine cooling system with flow dependent delays and performance of the resulting control design is evaluated through a simulation example where a comparison is made to a linear control......In this paper we consider design of control laws for a class of nonlinear systems with time-varying state delays by use of principles from feedback linearization. To deal with model uncertainties and delay mismatches, a robust linear H-inf controller is designed for the feedback linearized system...

Passivation and control of partially known SISO nonlinear systems via dynamic neural networks

Directory of Open Access Journals (Sweden)

Reyes-Reyes J.

2000-01-01

Full Text Available In this paper, an adaptive technique is suggested to provide the passivity property for a class of partially known SISO nonlinear systems. A simple Dynamic Neural Network (DNN, containing only two neurons and without any hidden-layers, is used to identify the unknown nonlinear system. By means of a Lyapunov-like analysis the new learning law for this DNN, guarantying both successful identification and passivation effects, is derived. Based on this adaptive DNN model, an adaptive feedback controller, serving for wide class of nonlinear systems with an a priori incomplete model description, is designed. Two typical examples illustrate the effectiveness of the suggested approach.

Adaptive nonlinear control using input normalized neural networks

International Nuclear Information System (INIS)

Leeghim, Henzeh; Seo, In Ho; Bang, Hyo Choong

2008-01-01

An adaptive feedback linearization technique combined with the neural network is addressed to control uncertain nonlinear systems. The neural network-based adaptive control theory has been widely studied. However, the stability analysis of the closed-loop system with the neural network is rather complicated and difficult to understand, and sometimes unnecessary assumptions are involved. As a result, unnecessary assumptions for stability analysis are avoided by using the neural network with input normalization technique. The ultimate boundedness of the tracking error is simply proved by the Lyapunov stability theory. A new simple update law as an adaptive nonlinear control is derived by the simplification of the input normalized neural network assuming the variation of the uncertain term is sufficiently small

Dynamic behaviors for a perturbed nonlinear Schrödinger equation with the power-law nonlinearity in a non-Kerr medium

Science.gov (United States)

Chai, Jun; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong; Liu, De-Yin

2017-04-01

Effects of quantic nonlinearity on the propagation of the ultrashort optical pulses in a non-Kerr medium, like an optical fiber, can be described by a perturbed nonlinear Schrödinger equation with the power law nonlinearity, which is studied in this paper from a planar-dynamic-system view point. We obtain the equivalent two-dimensional planar dynamic system of such an equation, for which, according to the bifurcation theory and qualitative theory, phase portraits are given. Through the analysis of those phase portraits, we present the relations among the Hamiltonian, orbits of the dynamic system and types of the analytic solutions. Analytic expressions of the periodic-wave solutions, kink- and bell-shaped solitary-wave solutions are derived, and we find that the periodic-wave solutions can be reduced to the kink- and bell-shaped solitary-wave solutions.

Stabilization of exact nonlinear Timoshenko beams in space by boundary feedback

Science.gov (United States)

Do, K. D.

2018-05-01

Boundary feedback controllers are designed to stabilize Timoshenko beams with large translational and rotational motions in space under external disturbances. The exact nonlinear partial differential equations governing motion of the beams are derived and used in the control design. The designed controllers guarantee globally practically asymptotically (and locally practically exponentially) stability of the beam motions at the reference state. The control design, well-posedness and stability analysis are based on various relationships between the earth-fixed and body-fixed coordinates, Sobolev embeddings, and a Lyapunov-type theorem developed to study well-posedness and stability for a class of evolution systems in Hilbert space. Simulation results are included to illustrate the effectiveness of the proposed control design.

Helicity coherence in binary neutron star mergers and nonlinear feedback

Science.gov (United States)

Chatelain, Amélie; Volpe, Cristina

2017-02-01

Neutrino flavor conversion studies based on astrophysical environments usually implement neutrino mixings, neutrino interactions with matter, and neutrino self-interactions. In anisotropic media, the most general mean-field treatment includes neutrino mass contributions as well, which introduce a coupling between neutrinos and antineutrinos termed helicity or spin coherence. We discuss resonance conditions for helicity coherence for Dirac and Majorana neutrinos. We explore the role of these mean-field contributions on flavor evolution in the context of a binary neutron star merger remnant. We find that resonance conditions can be satisfied in neutron star merger scenarios while adiabaticity is not sufficient for efficient flavor conversion. We analyze our numerical findings by discussing general conditions to have multiple Mikheyev-Smirnov-Wolfenstein-like resonances, in the presence of nonlinear feedback, in astrophysical environments.

BRIEF COMMUNICATIONS: Strong reflection of a series of pulses from a four-wave mirror with thermal nonlinearity under parametric feedback conditions

Science.gov (United States)

Barashkov, M. S.; Bel'dyugin, Igor'M.; Zolotarev, M. V.; Kruzhilin, Yu I.; Krymskiĭ, M. I.; Oshkin, S. P.; Starkov, G. S.; Umnov, A. F.; Kharchenko, M. A.

1989-04-01

A four-wave mirror exhibiting a thermal nonlinearity was used in a study of the interaction of concurrent waves under parametric feedback conditions in the presence of a nonreciprocal element. Strong reflection of a series of pulses of ~ 300 ns duration from a neodymium glass laser was demonstrated: the maximum reflection coefficient was in excess of 30. An analysis was made of the quality of the radiation reflected from this four-mirror parametric feedback system. A considerable reduction was observed in the steady-state threshold for the operation of this mirror with a thermal nonlinearity when the angles of convergence of the interacting beams were small compared with the case of head-on collision of the waves.

On the treatment of nonlinear local feedbacks within advanced nodal generalized perturbation theory

International Nuclear Information System (INIS)

Maldonado, G.I.; Turinsky, P.J.; Kropaczek, D.J.

1993-01-01

Recent efforts to upgrade the underlying neutronics formulations within the in-core nuclear fuel management optimization code FORMOSA (Ref. 1) have produced two important developments; first, a computationally efficient and second-order-accurate advanced nodal generalized perturbation theory (GPT) model [derived from the nonlinear iterative nodal expansion method (NEM)] for evaluating core attributes (i.e., k eff and power distribution versus cycle burnup), and second, an equally efficient and accurate treatment of local thermal-hydraulic and fission product feedbacks embedded within NEM GPT. The latter development is the focus of this paper

Coherent-feedback-induced controllable optical bistability and photon blockade

International Nuclear Information System (INIS)

Liu, Yu-Long; Liu, Zhong-Peng; Zhang, Jing

2015-01-01

It is well known that some nonlinear phenomena such as strong photon blockade are difficult to observe in optomechanical systems with current experimental technology. Here we present a coherent feedback control strategy in which a linear cavity is coherently controlled by an optomechanical controller in a feedback manner. The coherent feedback loop transfers quantum nonlinearity from the controller to the controlled cavity causing destructive quantum interference to occur, and making it possible to observe strong nonlinear effects. With the help of the coherent feedback loop, large and tunable bistability and strong photon blockade of the cavity modes can be achieved even in the optomechanical weak coupling regime. Additionally, the coherent feedback loop leads to two-photon and multiphoton tunnelings for the controlled linear cavity, which are also typical quantum nonlinear phenomena. We hope that our work can give new perspectives on engineering nonlinear interactions in quantum systems. (paper)

The effective reflection of a pulse sequence from a four-wave mirror with thermal nonlinearity under parametric feedback

Science.gov (United States)

Barashkov, M. S.; Bel'Diugin, I. M.; Zolotarev, M. V.; Kruzhilin, Iu. I.; Krymskii, M. I.

1989-04-01

A four-wave mirror with thermal nonlinearity has been experimentally realized with the interaction of corunning waves under parametric feedback with a nonreciprocal element. The effective reflection of a sequence of pulses with duration of about 300 ns from a neodymium-glass laser with maximal reflection coefficients greater than 30 has been demonstrated. The quality of the radiation reflected from the mirror is studied. A significant reduction in the steady-state lasing threshold has been shown with thermal nonlinearity at small angles of the interacting beam convergence, compared to the case of counterrunning convergence.

The simplex method for nonlinear sliding mode control

Directory of Open Access Journals (Sweden)

Bartolini G.

1998-01-01

Full Text Available General nonlinear control systems described by ordinary differential equations with a prescribed sliding manifold are considered. A method of designing a feedback control law such that the state variable fulfills the sliding condition in finite time is based on the construction of a suitable simplex of vectors in the tangent space of the manifold. The convergence of the method is proved under an obtuse angle condition and a way to build the required simplex is indicated. An example of engineering interest is presented.

Nonlinear decentralized robust governor control for hydroturbine-generator sets in multi-machine power systems

Energy Technology Data Exchange (ETDEWEB)

Qiang Lu; Yusong Sun; Yuanzhang Sun [Tsinghua University, Beijing (China). Dept. of Electrical Engineering; Felix F Wu; Yixin Ni [University of Hong Kong (China). Dept. of Electrical and Electronic Engineering; Yokoyama, Akihiko [University of Tokyo (Japan). Dept. of Electrical Engineering; Goto, Masuo; Konishi, Hiroo [Hitachi Ltd., Tokyo (Japan). Power System Div.

2004-06-01

A novel nonlinear decentralized robust governor control for hydroturbine-generator sets in multi-machine power systems is suggested in this paper. The nonelastic water hammer effect and disturbances are considered in the modeling. The advanced differential geometry theory, nonlinear robust control theory and the dynamic feedback method are combined to solve the problem. The nonlinear decentralized robust control law for the speed governor of hydroturbine-generators has been derived. The input signals to the proposed controller are all local measurements and independent to the system parameters. The derived control law guarantees the integrated system stability with disturbance attenuation, which is significant to the real power system application. Computer tests on an 8-machine, 36-bus power system show clearly the effectiveness of the new control strategy in transient stability enhancement and disturbance attenuation. The computer test results based on the suggested controller are compared favorably with those based on the conventional linear governor control. (author)

A high-order relaxation method with projective integration for solving nonlinear systems of hyperbolic conservation laws

Science.gov (United States)

Lafitte, Pauline; Melis, Ward; Samaey, Giovanni

2017-07-01

We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the nonlinear hyperbolic conservation law is approximated by a kinetic equation with stiff BGK source term. Then, this kinetic equation is integrated in time using a projective integration method. After taking a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution, the time derivative is estimated and used in an (outer) Runge-Kutta method of arbitrary order. We show that, with an appropriate choice of inner step size, the time step restriction on the outer time step is similar to the CFL condition for the hyperbolic conservation law. Moreover, the number of inner time steps is also independent of the stiffness of the BGK source term. We discuss stability and consistency, and illustrate with numerical results (linear advection, Burgers' equation and the shallow water and Euler equations) in one and two spatial dimensions.

Observer-based adaptive control of chaos in nonlinear discrete-time systems using time-delayed state feedback

International Nuclear Information System (INIS)

Goharrizi, Amin Yazdanpanah; Khaki-Sedigh, Ali; Sepehri, Nariman

2009-01-01

A new approach to adaptive control of chaos in a class of nonlinear discrete-time-varying systems, using a delayed state feedback scheme, is presented. It is discussed that such systems can show chaotic behavior as their parameters change. A strategy is employed for on-line calculation of the Lyapunov exponents that will be used within an adaptive scheme that decides on the control effort to suppress the chaotic behavior once detected. The scheme is further augmented with a nonlinear observer for estimation of the states that are required by the controller but are hard to measure. Simulation results for chaotic control problem of Jin map are provided to show the effectiveness of the proposed scheme.

Feedback Linearization Based Arc Length Control for Gas Metal Arc Welding

DEFF Research Database (Denmark)

Thomsen, Jesper Sandberg

2005-01-01

a linear system to be controlled by linear state feedback control. The advantage of using a nonlinear approach as feedback linearization is the ability of this method to cope with nonlinearities and different operating points. However, the model describing the GMAW process is not exact, and therefore......In this paper a feedback linearization based arc length controller for gas metal arc welding (GMAW) is described. A nonlinear model describing the dynamic arc length is transformed into a system where nonlinearities can be cancelled by a nonlinear state feedback control part, and thus, leaving only......, the cancellation of nonlinear terms might give rise to problems with respect to robustness. Robustness of the closed loop system is therefore nvestigated by simulation....

Bayesian feedback versus Markovian feedback in a two-level atom

International Nuclear Information System (INIS)

Wiseman, H.M.; Mancini, Stefano; Wang Jin

2002-01-01

We compare two different approaches to the control of the dynamics of a continuously monitored open quantum system. The first is Markovian feedback, as introduced in quantum optics by Wiseman and Milburn [Phys. Rev. Lett. 70, 548 (1993)]. The second is feedback based on an estimate of the system state, developed recently by Doherty and Jacobs [Phys. Rev. A 60, 2700 (1999)]. Here we choose to call it, for brevity, Bayesian feedback. For systems with nonlinear dynamics, we expect these two methods of feedback control to give markedly different results. The simplest possible nonlinear system is a driven and damped two-level atom, so we choose this as our model system. The monitoring is taken to be homodyne detection of the atomic fluorescence, and the control is by modulating the driving. The aim of the feedback in both cases is to stabilize the internal state of the atom as close as possible to an arbitrarily chosen pure state, in the presence of inefficient detection and other forms of decoherence. Our results (obtained without recourse to stochastic simulations) prove that Bayesian feedback is never inferior, and is usually superior, to Markovian feedback. However, it would be far more difficult to implement than Markovian feedback and it loses its superiority when obvious simplifying approximations are made. It is thus not clear which form of feedback would be better in the face of inevitable experimental imperfections

Conservation Laws and Traveling Wave Solutions of a Generalized Nonlinear ZK-BBM Equation

Directory of Open Access Journals (Sweden)

Khadijo Rashid Adem

2014-01-01

Full Text Available We study a generalized two-dimensional nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM equation, which is in fact Benjamin-Bona-Mahony equation formulated in the ZK sense. Conservation laws for this equation are constructed by using the new conservation theorem due to Ibragimov and the multiplier method. Furthermore, traveling wave solutions are obtained by employing the (G'/G-expansion method.

Enzymatic Synthesis of Ampicillin: Nonlinear Modeling, Kinetics Estimation, and Adaptive Control

Directory of Open Access Journals (Sweden)

Monica Roman

2012-01-01

Full Text Available Nowadays, the use of advanced control strategies in biotechnology is quite low. A main reason is the lack of quality of the data, and the fact that more sophisticated control strategies must be based on a model of the dynamics of bioprocesses. The nonlinearity of the bioprocesses and the absence of cheap and reliable instrumentation require an enhanced modeling effort and identification strategies for the kinetics. The present work approaches modeling and control strategies for the enzymatic synthesis of ampicillin that is carried out inside a fed-batch bioreactor. First, a nonlinear dynamical model of this bioprocess is obtained by using a novel modeling procedure for biotechnology: the bond graph methodology. Second, a high gain observer is designed for the estimation of the imprecisely known kinetics of the synthesis process. Third, by combining an exact linearizing control law with the on-line estimation kinetics algorithm, a nonlinear adaptive control law is designed. The case study discussed shows that a nonlinear feedback control strategy applied to the ampicillin synthesis bioprocess can cope with disturbances, noisy measurements, and parametric uncertainties. Numerical simulations performed with MATLAB environment are included in order to test the behavior and the performances of the proposed estimation and control strategies.

Finite-time generalized function matrix projective lag synchronization of coupled dynamical networks with different dimensions via the double power function nonlinear feedback control method

International Nuclear Information System (INIS)

Dai, Hao; Si, Gangquan; Jia, Lixin; Zhang, Yanbin

2014-01-01

This paper investigates the problem of finite-time generalized function matrix projective lag synchronization between two different coupled dynamical networks with different dimensions of network nodes. The double power function nonlinear feedback control method is proposed in this paper to guarantee that the state trajectories of the response network converge to the state trajectories of the drive network according to a function matrix in a given finite time. Furthermore, in comparison with the traditional nonlinear feedback control method, the new method improves the synchronization efficiency, and shortens the finite synchronization time. Numerical simulation results are presented to illustrate the effectiveness of this method. (papers)

Painleve analysis, conservation laws, and symmetry of perturbed nonlinear equations

International Nuclear Information System (INIS)

Basak, S.; Chowdhury, A.R.

1987-01-01

The authors consider the Lie-Backlund symmetries and conservation laws of a perturbed KdV equation and NLS equation. The arbitrary coefficients of the perturbing terms can be related to the condition of existence of nontrivial LB symmetry generators. When the perturbed KdV equation is subjected to Painleve analysis a la Weiss, it is found that the resonance position changes compared to the unperturbed one. They prove the compatibility of the overdetermined set of equations obtained at the different stages of recursion relations, at least for one branch. All other branches are also indicated and difficulties associated them are discussed considering the perturbation parameter epsilon to be small. They determine the Lax pair for the aforesaid branch through the use of Schwarzian derivative. For the perturbed NLS equation they determine the conservation laws following the approach of Chen and Liu. From the recurrence of these conservation laws a Lax pair is constructed. But the Painleve analysis does not produce a positive answer for the perturbed NLS equation. So here they have two contrasting examples of perturbed nonlinear equations: one passes the Painleve test and its Lax pair can be found from the analysis itself, but the other equation does not meet the criterion of the Painleve test, though its Lax pair is found in another way

An open-closed-loop iterative learning control approach for nonlinear switched systems with application to freeway traffic control

Science.gov (United States)

Sun, Shu-Ting; Li, Xiao-Dong; Zhong, Ren-Xin

2017-10-01

For nonlinear switched discrete-time systems with input constraints, this paper presents an open-closed-loop iterative learning control (ILC) approach, which includes a feedforward ILC part and a feedback control part. Under a given switching rule, the mathematical induction is used to prove the convergence of ILC tracking error in each subsystem. It is demonstrated that the convergence of ILC tracking error is dependent on the feedforward control gain, but the feedback control can speed up the convergence process of ILC by a suitable selection of feedback control gain. A switched freeway traffic system is used to illustrate the effectiveness of the proposed ILC law.

A nonlinear adaptive backstepping approach applied to a three phase PWM AC-DC converter feeding induction heating

Science.gov (United States)

Hadri-Hamida, A.; Allag, A.; Hammoudi, M. Y.; Mimoune, S. M.; Zerouali, S.; Ayad, M. Y.; Becherif, M.; Miliani, E.; Miraoui, A.

2009-04-01

This paper presents a new control strategy for a three phase PWM converter, which consists of applying an adaptive nonlinear control. The input-output feedback linearization approach is based on the exact cancellation of the nonlinearity, for this reason, this technique is not efficient, because system parameters can vary. First a nonlinear system modelling is derived with state variables of the input current and the output voltage by using power balance of the input and output, the nonlinear adaptive backstepping control can compensate the nonlinearities in the nominal system and the uncertainties. Simulation results are obtained using Matlab/Simulink. These results show how the adaptive backstepping law updates the system parameters and provide an efficient control design both for tracking and regulation in order to improve the power factor.

Linear feedback control, adaptive feedback control and their combination for chaos (lag) synchronization of LC chaotic systems

International Nuclear Information System (INIS)

Yan Zhenya; Yu Pei

2007-01-01

In this paper, we study chaos (lag) synchronization of a new LC chaotic system, which can exhibit not only a two-scroll attractor but also two double-scroll attractors for different parameter values, via three types of state feedback controls: (i) linear feedback control; (ii) adaptive feedback control; and (iii) a combination of linear feedback and adaptive feedback controls. As a consequence, ten families of new feedback control laws are designed to obtain global chaos lag synchronization for τ < 0 and global chaos synchronization for τ = 0 of the LC system. Numerical simulations are used to illustrate these theoretical results. Each family of these obtained feedback control laws, including two linear (adaptive) functions or one linear function and one adaptive function, is added to two equations of the LC system. This is simpler than the known synchronization controllers, which apply controllers to all equations of the LC system. Moreover, based on the obtained results of the LC system, we also derive the control laws for chaos (lag) synchronization of another new type of chaotic system

A strain-hardening bi-power law for the nonlinear behaviour of biological soft tissues.

Science.gov (United States)

Nicolle, S; Vezin, P; Palierne, J-F

2010-03-22

Biological soft tissues exhibit a strongly nonlinear viscoelastic behaviour. Among parenchymous tissues, kidney and liver remain less studied than brain, and a first goal of this study is to report additional material properties of kidney and liver tissues in oscillatory shear and constant shear rate tests. Results show that the liver tissue is more compliant but more strain hardening than kidney. A wealth of multi-parameter mathematical models has been proposed for describing the mechanical behaviour of soft tissues. A second purpose of this work is to develop a new constitutive law capable of predicting our experimental data in the both linear and nonlinear viscoelastic regime with as few parameters as possible. We propose a nonlinear strain-hardening fractional derivative model in which six parameters allow fitting the viscoelastic behaviour of kidney and liver tissues for strains ranging from 0.01 to 1 and strain rates from 0.0151 s(-1) to 0.7s(-1). Copyright (c) 2009 Elsevier Ltd. All rights reserved.

Adaptive estimation for control of uncertain nonlinear systems with applications to target tracking

Science.gov (United States)

Madyastha, Venkatesh Kattigari

2005-08-01

Design of nonlinear observers has received considerable attention since the early development of methods for linear state estimation. The most popular approach is the extended Kalman filter (EKF), that goes through significant degradation in the presence of nonlinearities, particularly if unmodeled dynamics are coupled to the process and the measurement. For uncertain nonlinear systems, adaptive observers have been introduced to estimate the unknown state variables where no priori information about the unknown parameters is available. While establishing global results, these approaches are applicable only to systems transformable to output feedback form. Over the recent years, neural network (NN) based identification and estimation schemes have been proposed that relax the assumptions on the system at the price of sacrificing on the global nature of the results. However, most of the NN based adaptive observer approaches in the literature require knowledge of the full dimension of the system, therefore may not be suitable for systems with unmodeled dynamics. We first propose a novel approach to nonlinear state estimation from the perspective of augmenting a linear time invariant observer with an adaptive element. The class of nonlinear systems treated here are finite but of otherwise unknown dimension. The objective is to improve the performance of the linear observer when applied to a nonlinear system. The approach relies on the ability of the NNs to approximate the unknown dynamics from finite time histories of available measurements. Next we investigate nonlinear state estimation from the perspective of adaptively augmenting an existing time varying observer, such as an EKF. EKFs find their applications mostly in target tracking problems. The proposed approaches are robust to unmodeled dynamics, including unmodeled disturbances. Lastly, we consider the problem of adaptive estimation in the presence of feedback control for a class of uncertain nonlinear systems

Direct Adaptive Tracking Control for a Class of Pure-Feedback Stochastic Nonlinear Systems Based on Fuzzy-Approximation

Directory of Open Access Journals (Sweden)

Huanqing Wang

2014-01-01

Full Text Available The problem of fuzzy-based direct adaptive tracking control is considered for a class of pure-feedback stochastic nonlinear systems. During the controller design, fuzzy logic systems are used to approximate the packaged unknown nonlinearities, and then a novel direct adaptive controller is constructed via backstepping technique. It is shown that the proposed controller guarantees that all the signals in the closed-loop system are bounded in probability and the tracking error eventually converges to a small neighborhood around the origin in the sense of mean quartic value. The main advantages lie in that the proposed controller structure is simpler and only one adaptive parameter needs to be updated online. Simulation results are used to illustrate the effectiveness of the proposed approach.

Enhancing a slow and weak optomechanical nonlinearity with delayed quantum feedback

Science.gov (United States)

Wang, Zhaoyou; Safavi-Naeini, Amir H.

2017-07-01

A central goal of quantum optics is to generate large interactions between single photons so that one photon can strongly modify the state of another one. In cavity optomechanics, photons interact with the motional degrees of freedom of an optical resonator, for example, by imparting radiation pressure forces on a movable mirror or sensing minute fluctuations in the position of the mirror. Here, we show that the optical nonlinearity arising from these effects, typically too small to operate on single photons, can be sufficiently enhanced with feedback to generate large interactions between single photons. We propose a protocol that allows photons propagating in a waveguide to interact with each other through multiple bounces off an optomechanical system. The protocol is analysed by evolving the full many-body quantum state of the waveguide-coupled system, illustrating that large photon-photon interactions mediated by mechanical motion may be within experimental reach.

On Mixed Data and Event Driven Design for Adaptive-Critic-Based Nonlinear $H_{\\infty}$ Control.

Science.gov (United States)

Wang, Ding; Mu, Chaoxu; Liu, Derong; Ma, Hongwen

2018-04-01

In this paper, based on the adaptive critic learning technique, the control for a class of unknown nonlinear dynamic systems is investigated by adopting a mixed data and event driven design approach. The nonlinear control problem is formulated as a two-player zero-sum differential game and the adaptive critic method is employed to cope with the data-based optimization. The novelty lies in that the data driven learning identifier is combined with the event driven design formulation, in order to develop the adaptive critic controller, thereby accomplishing the nonlinear control. The event driven optimal control law and the time driven worst case disturbance law are approximated by constructing and tuning a critic neural network. Applying the event driven feedback control, the closed-loop system is built with stability analysis. Simulation studies are conducted to verify the theoretical results and illustrate the control performance. It is significant to observe that the present research provides a new avenue of integrating data-based control and event-triggering mechanism into establishing advanced adaptive critic systems.

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models.

Science.gov (United States)

Pozo, Carlos; Marín-Sanguino, Alberto; Alves, Rui; Guillén-Gosálbez, Gonzalo; Jiménez, Laureano; Sorribas, Albert

2011-08-25

Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

Directory of Open Access Journals (Sweden)

Sorribas Albert

2011-08-01

Full Text Available Abstract Background Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

Non-linear flow law of rockglacier creep determined from geomorphological observations: A case study from the Murtèl rockglacier (Engadin, SE Switzerland)

Science.gov (United States)

Frehner, Marcel; Amschwand, Dominik; Gärtner-Roer, Isabelle

2016-04-01

Rockglaciers consist of unconsolidated rock fragments (silt/sand-rock boulders) with interstitial ice; hence their creep behavior (i.e., rheology) may deviate from the simple and well-known flow-laws for pure ice. Here we constrain the non-linear viscous flow law that governs rockglacier creep based on geomorphological observations. We use the Murtèl rockglacier (upper Engadin valley, SE Switzerland) as a case study, for which high-resolution digital elevation models (DEM), time-lapse borehole deformation data, and geophysical soundings exist that reveal the exterior and interior architecture and dynamics of the landform. Rockglaciers often feature a prominent furrow-and-ridge topography. For the Murtèl rockglacier, Frehner et al. (2015) reproduced the wavelength, amplitude, and distribution of the furrow-and-ridge morphology using a linear viscous (Newtonian) flow model. Arenson et al. (2002) presented borehole deformation data, which highlight the basal shear zone at about 30 m depth and a curved deformation profile above the shear zone. Similarly, the furrow-and-ridge morphology also exhibits a curved geometry in map view. Hence, the surface morphology and the borehole deformation data together describe a curved 3D geometry, which is close to, but not quite parabolic. We use a high-resolution DEM to quantify the curved geometry of the Murtèl furrow-and-ridge morphology. We then calculate theoretical 3D flow geometries using different non-linear viscous flow laws. By comparing them to the measured curved 3D geometry (i.e., both surface morphology and borehole deformation data), we can determine the most adequate flow-law that fits the natural data best. Linear viscous models result in perfectly parabolic flow geometries; non-linear creep leads to localized deformation at the sides and bottom of the rockglacier while the deformation in the interior and top are less intense. In other words, non-linear creep results in non-parabolic flow geometries. Both the

Complex fluid network optimization and control integrative design based on nonlinear dynamic model

International Nuclear Information System (INIS)

Sui, Jinxue; Yang, Li; Hu, Yunan

2016-01-01

In view of distribution according to complex fluid network’s needs, this paper proposed one optimization computation method of the nonlinear programming mathematical model based on genetic algorithm. The simulation result shows that the overall energy consumption of the optimized fluid network has a decrease obviously. The control model of the fluid network is established based on nonlinear dynamics. We design the control law based on feedback linearization, take the optimal value by genetic algorithm as the simulation data, can also solve the branch resistance under the optimal value. These resistances can provide technical support and reference for fluid network design and construction, so can realize complex fluid network optimization and control integration design.

Robust output synchronization of heterogeneous nonlinear agents in uncertain networks.

Science.gov (United States)

Yang, Xi; Wan, Fuhua; Tu, Mengchuan; Shen, Guojiang

2017-11-01

This paper investigates the global robust output synchronization problem for a class of nonlinear multi-agent systems. In the considered setup, the controlled agents are heterogeneous and with both dynamic and parametric uncertainties, the controllers are incapable of exchanging their internal states with the neighbors, and the communication network among agents is defined by an uncertain simple digraph. The problem is pursued via nonlinear output regulation theory and internal model based design. For each agent, the input-driven filter and the internal model compose the controller, and the decentralized dynamic output feedback control law is derived by using backstepping method and the modified dynamic high-gain technique. The theoretical result is applied to output synchronization problem for uncertain network of Lorenz-type agents. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Control of an atom laser using feedback

International Nuclear Information System (INIS)

Haine, S.A.; Ferris, A.J.; Close, J.D.; Hope, J.J.

2004-01-01

A generalized method of using feedback to control multimode behavior in Bose-Einstein condensates is introduced. We show that for any available control, there is an associated moment of the atomic density and a feedback scheme that will remove energy from the system while there are oscillations in that moment. We demonstrate these schemes by considering a condensate trapped in a harmonic potential that can be modulated in strength and position. The formalism of our feedback scheme also allows the inclusion of certain types of nonlinear controls. If the nonlinear interaction between the atoms can be controlled via a Feshbach resonance, we show that the feedback process can operate with a much higher efficiency

Exact Solution of a Faraday's Law Problem that Includes a Nonlinear Term and Its Implication for Perturbation Theory.

Science.gov (United States)

Fulcher, Lewis P.

1979-01-01

Presents an exact solution to the nonlinear Faraday's law problem of a rod sliding on frictionless rails with resistance. Compares the results with perturbation calculations based on the methods of Poisson and Pincare and of Kryloff and Bogoliuboff. (Author/GA)

Conservation Laws in Biochemical Reaction Networks

DEFF Research Database (Denmark)

Mahdi, Adam; Ferragut, Antoni; Valls, Claudia

2017-01-01

We study the existence of linear and nonlinear conservation laws in biochemical reaction networks with mass-action kinetics. It is straightforward to compute the linear conservation laws as they are related to the left null-space of the stoichiometry matrix. The nonlinear conservation laws...... are difficult to identify and have rarely been considered in the context of mass-action reaction networks. Here, using the Darboux theory of integrability, we provide necessary structural (i.e., parameterindependent) conditions on a reaction network to guarantee the existence of nonlinear conservation laws...

Toward high-speed 3D nonlinear soft tissue deformation simulations using Abaqus software.

Science.gov (United States)

Idkaidek, Ashraf; Jasiuk, Iwona

2015-12-01

We aim to achieve a fast and accurate three-dimensional (3D) simulation of a porcine liver deformation under a surgical tool pressure using the commercial finite element software Abaqus. The liver geometry is obtained using magnetic resonance imaging, and a nonlinear constitutive law is employed to capture large deformations of the tissue. Effects of implicit versus explicit analysis schemes, element type, and mesh density on computation time are studied. We find that Abaqus explicit and implicit solvers are capable of simulating nonlinear soft tissue deformations accurately using first-order tetrahedral elements in a relatively short time by optimizing the element size. This study provides new insights and guidance on accurate and relatively fast nonlinear soft tissue simulations. Such simulations can provide force feedback during robotic surgery and allow visualization of tissue deformations for surgery planning and training of surgical residents.

ANCON, Space-Independent Reactor Kinetics with Linear or Nonlinear Thermal Feedback

International Nuclear Information System (INIS)

Vigil, John C.; Dugan, E.T.

1988-01-01

1 - Description of problem or function: ANCON solves the point-reactor kinetic equations including thermal feedback. Lump-type heat balance equations are used to represent the thermodynamics, and the heat capacity of each lump can vary with temperature. Thermal feedback can be either a linear or a non-linear function of lump temperature, and the impressed reactivity can be either a polynomial or sinusoidal function. 2 - Method of solution: In ANCON the system of coupled first-order differential equations is solved by a method based on continuous analytic continuation (references 2 and 3). The basic procedure consists of expanding all the dependent variables except reactivity in Taylor series, with a truncation error criterion, over successive intervals on the time axis. Variations of the basic procedure are used to increase the efficiency of the method in special situations. Automatic switching from the basic procedure to one of its variations (and vice-versa) may occur during the course of a transient. The method yields an analytic criterion for the magnitude of the time-step at any point in the transient. 3 - Restrictions on the complexity of the problem: The program is currently restricted to a maximum of six delayed neutron groups and a maximum of 56 lumps. Larger problems can be accommodated on a 65 K computer by increasing the dimensions of a few subscripted variables. Also, the code is currently restricted to a constant external transport delays, only the open-loop response of a reactor can be computed with ANCON

Investigation and Development of Control Laws for the NASA Langley Research Center Cockpit Motion Facility

Science.gov (United States)

Coon, Craig R.; Cardullo, Frank M.; Zaychik, Kirill B.

2014-01-01

The ability to develop highly advanced simulators is a critical need that has the ability to significantly impact the aerospace industry. The aerospace industry is advancing at an ever increasing pace and flight simulators must match this development with ever increasing urgency. In order to address both current problems and potential advancements with flight simulator techniques, several aspects of current control law technology of the National Aeronautics and Space Administration (NASA) Langley Research Center's Cockpit Motion Facility (CMF) motion base simulator were examined. Preliminary investigation of linear models based upon hardware data were examined to ensure that the most accurate models are used. This research identified both system improvements in the bandwidth and more reliable linear models. Advancements in the compensator design were developed and verified through multiple techniques. The position error rate feedback, the acceleration feedback and the force feedback were all analyzed in the heave direction using the nonlinear model of the hardware. Improvements were made using the position error rate feedback technique. The acceleration feedback compensator also provided noteworthy improvement, while attempts at implementing a force feedback compensator proved unsuccessful.

High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

Science.gov (United States)

Fisher, Travis C.; Carpenter, Mark H.

2013-01-01

Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.

Predictor feedback for delay systems implementations and approximations

CERN Document Server

Karafyllis, Iasson

2017-01-01

This monograph bridges the gap between the nonlinear predictor as a concept and as a practical tool, presenting a complete theory of the application of predictor feedback to time-invariant, uncertain systems with constant input delays and/or measurement delays. It supplies several methods for generating the necessary real-time solutions to the systems’ nonlinear differential equations, which the authors refer to as approximate predictors. Predictor feedback for linear time-invariant (LTI) systems is presented in Part I to provide a solid foundation on the necessary concepts, as LTI systems pose fewer technical difficulties than nonlinear systems. Part II extends all of the concepts to nonlinear time-invariant systems. Finally, Part III explores extensions of predictor feedback to systems described by integral delay equations and to discrete-time systems. The book’s core is the design of control and observer algorithms with which global stabilization, guaranteed in the previous literature with idealized (b...

SOS based robust H(∞) fuzzy dynamic output feedback control of nonlinear networked control systems.

Science.gov (United States)

Chae, Seunghwan; Nguang, Sing Kiong

2014-07-01

In this paper, a methodology for designing a fuzzy dynamic output feedback controller for discrete-time nonlinear networked control systems is presented where the nonlinear plant is modelled by a Takagi-Sugeno fuzzy model and the network-induced delays by a finite state Markov process. The transition probability matrix for the Markov process is allowed to be partially known, providing a more practical consideration of the real world. Furthermore, the fuzzy controller's membership functions and premise variables are not assumed to be the same as the plant's membership functions and premise variables, that is, the proposed approach can handle the case, when the premise of the plant are not measurable or delayed. The membership functions of the plant and the controller are approximated as polynomial functions, then incorporated into the controller design. Sufficient conditions for the existence of the controller are derived in terms of sum of square inequalities, which are then solved by YALMIP. Finally, a numerical example is used to demonstrate the validity of the proposed methodology.

Lie symmetry analysis, explicit solutions and conservation laws for the space-time fractional nonlinear evolution equations

Science.gov (United States)

Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru

2018-04-01

This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.

Nonlinear chaos control and synchronization

NARCIS (Netherlands)

Huijberts, H.J.C.; Nijmeijer, H.; Schöll, E.; Schuster, H.G.

2007-01-01

This chapter contains sections titled: Introduction Nonlinear Geometric Control Some Differential Geometric Concepts Nonlinear Controllability Chaos Control Through Feedback Linearization Chaos Control Through Input-Output Linearization Lyapunov Design Lyapunov Stability and Lyapunov's First Method

Global Harmonic Current Rejection of Nonlinear Backstepping Control with Multivariable Adaptive Internal Model Principle for Grid-Connected Inverter under Distorted Grid Voltage

Directory of Open Access Journals (Sweden)

Yang Yu

2013-01-01

Full Text Available Based on a brief review on current harmonics generation mechanism for grid-connected inverter under distorted grid voltage, the harmonic disturbances and uncertain items are immersed into the original state-space differential equation of grid-connected inverter. A new algorithm of global current harmonic rejection based on nonlinear backstepping control with multivariable internal model principle is proposed for grid-connected inverter with exogenous disturbances and uncertainties. A type of multivariable internal model for a class of nonlinear harmonic disturbances is constructed. Based on application of backstepping control law of the nominal system, a multivariable adaptive state feedback controller combined with multivariable internal model and adaptive control law is designed to guarantee the closed-loop system globally uniformly bounded, which is proved by a constructed Lyapunov function. The presented algorithm extends rejection of nonlinear single-input systems to multivariable globally defined normal form, the correctness and effectiveness of which are verified by the simulation results.

Dynamic bounds for power and efficiency of non-ideal energy converters under nonlinear transfer laws

International Nuclear Information System (INIS)

Sieniutycz, Stanislaw

2009-01-01

We present a thermodynamic approach to simulation and modeling of nonlinear energy converters, in particular radiation engines. Novel results are obtained especially for dynamical engines when the temperature of the propelling medium decreases in time due to a continual decrease of the medium's internal energy caused by the power production. Basic thermodynamic principles determine the converter's efficiency and work limits in terms of the entropy production. The real work is a cumulative effect obtained in a system of a resource fluid, a sequence of engines, and an infinite bath. Nonlinear modeling involves dynamic optimization in which the classical expression for efficiency at maximum power is generalized to endoirreversible machines and nonlinear transfer laws. The primary result is a finite-rate generalization of the classical, reversible work potential (exergy). The generalized work function depends on thermal coordinates and a dissipation index, h, i.e. a Hamiltonian of the minimum entropy production problem. This generalized work function implies stronger bounds on work delivered or supplied than the reversible work potential. The role of the nonlinear analyses and dynamic optimization is shown especially for radiation engines. As an example of the kinetic work limit, generalized exergy of radiation fluid is estimated in terms of finite rates, quantified by the Hamiltonian h

Topological approximation of the nonlinear Anderson model

Science.gov (United States)

Milovanov, Alexander V.; Iomin, Alexander

2014-06-01

We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the

Numerical investigation of the nonlinear dynamics of a hybrid acousto-optic Bragg cell with a variable feedback gain

Science.gov (United States)

Chatterjee, Monish R.; Zhou, Hao

2014-09-01

Since around 1979, the operation of an acousto-optic Bragg cell under positive first-order feedback via amplification and delay in the loop has been studied extensively by several groups [1-3]. In recent work, the analysis of the nonlinear dynamics (NLD) of the system was extended to include bistable maps and Lyapunov exponents, and application of the chaos for signal encryption and decryption for uniform plane waves. The present work originated with the problem of a variable photodetector aperture opening relative to the first-order light. This potentially complex problem is simplified by assuming instead a variable feedback gain ( β ~ (t)), which leads to considerably different NLD. This paper examines initially the NLD versus the (DC) bias voltage for different variable- β ~ conditions, including slow and fast rates of change of the gain with time in relation to the feedback delay. It is found that the response depends critically on the rate of rise of the feedback gain, and also that the resulting chaotic regimes are generally significantly different from those for fixed values of β ~ . We have generated constant feedback gain and the variable feedback gain (t) chaos characteristics of the hybrid A-O network. Chaos as an equivalent carrier has been used to encrypt messages for both fixed and variable β ~ . The transmitted signal is detected from the encrypted carrier using a heterodyne method, using a slave Bragg cell with matched keys to generate local chaos followed by a low pass filter and a phase inverter. Results between variable- and fixed-gain systems are compared in terms of advantages and disadvantages.

Feedback control linear, nonlinear and robust techniques and design with industrial applications

CERN Document Server

Dodds, Stephen J

2015-01-01

This book develops the understanding and skills needed to be able to tackle original control problems. The general approach to a given control problem is to try the simplest tentative solution first and, when this is insufficient, to explain why and use a more sophisticated alternative to remedy the deficiency and achieve satisfactory performance. This pattern of working gives readers a full understanding of different controllers and teaches them to make an informed choice between traditional controllers and more advanced modern alternatives in meeting the needs of a particular plant. Attention is focused on the time domain, covering model-based linear and nonlinear forms of control together with robust control based on sliding modes and the use of state observers such as disturbance estimation. Feedback Control is self-contained, paying much attention to explanations of underlying concepts, with detailed mathematical derivations being employed where necessary. Ample use is made of diagrams to aid these conce...

Differential Neural Networks for Identification and Filtering in Nonlinear Dynamic Games

Directory of Open Access Journals (Sweden)

Emmanuel García

2014-01-01

Full Text Available This paper deals with the problem of identifying and filtering a class of continuous-time nonlinear dynamic games (nonlinear differential games subject to additive and undesired deterministic perturbations. Moreover, the mathematical model of this class is completely unknown with the exception of the control actions of each player, and even though the deterministic noises are known, their power (or their effect is not. Therefore, two differential neural networks are designed in order to obtain a feedback (perfect state information pattern for the mentioned class of games. In this way, the stability conditions for two state identification errors and for a filtering error are established, the upper bounds of these errors are obtained, and two new learning laws for each neural network are suggested. Finally, an illustrating example shows the applicability of this approach.

Noninteracting control of nonlinear systems based on relaxed control

NARCIS (Netherlands)

Jayawardhana, B.

2010-01-01

In this paper, we propose methodology to solve noninteracting control problem for general nonlinear systems based on the relaxed control technique proposed by Artstein. For a class of nonlinear systems which cannot be stabilized by smooth feedback, a state-feedback relaxed control can be designed to

Operation of the transverse feedback system at the CERN SPS

International Nuclear Information System (INIS)

Bossart, R.; Louwerse, R.; Mourier, J.; Vos, L.

1987-01-01

To prevent transverse instabilities at high beam intensity in the SPS, the transverse feedback system for damping the betatron oscillations has been upgraded for larger damping decrements and for increased system's bandwidth. The feedback loop now contains a digital delay line cancellor, so that the damper works with a velocity feedback Δx/Δt, unaffected by the closed orbit position x at the pick-up station. The digital processing of the feedback signal facilitates nonlinear feedback techniques such as antidamping and ''band-bang'' feedback. The ''bang-bang'' feedback provides the maximum possible damping rate of the injection oscillations in the SPS-collider, in order to minimize the emittance increase caused by filamentation. The antidamping nonlinearity provides small continuous beam oscillations of 50 μm amplitude for tracking the machine tune Q with a phase locked loop

Nonlinearity and disorder: Classification and stability of nonlinear impurity modes

DEFF Research Database (Denmark)

Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole

2001-01-01

We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of no...... the case of a power-law nonlinearity in detail. We discuss several scenarios of the instability-induced dynamics of the nonlinear impurity modes, including the mode decay or switching to a new stable state, and collapse at the impurity site....

Nonlinear Time Series Prediction Using Chaotic Neural Networks

Science.gov (United States)

Li, Ke-Ping; Chen, Tian-Lun

2001-06-01

A nonlinear feedback term is introduced into the evaluation equation of weights of the backpropagation algorithm for neural network, the network becomes a chaotic one. For the purpose of that we can investigate how the different feedback terms affect the process of learning and forecasting, we use the model to forecast the nonlinear time series which is produced by Makey-Glass equation. By selecting the suitable feedback term, the system can escape from the local minima and converge to the global minimum or its approximate solutions, and the forecasting results are better than those of backpropagation algorithm. The project supported by National Basic Research Project "Nonlinear Science" and National Natural Science Foundation of China under Grant No. 60074020

Stabilization of nonlinear systems using sampled-data output-feedback fuzzy controller based on polynomial-fuzzy-model-based control approach.

Science.gov (United States)

Lam, H K

2012-02-01

This paper investigates the stability of sampled-data output-feedback (SDOF) polynomial-fuzzy-model-based control systems. Representing the nonlinear plant using a polynomial fuzzy model, an SDOF fuzzy controller is proposed to perform the control process using the system output information. As only the system output is available for feedback compensation, it is more challenging for the controller design and system analysis compared to the full-state-feedback case. Furthermore, because of the sampling activity, the control signal is kept constant by the zero-order hold during the sampling period, which complicates the system dynamics and makes the stability analysis more difficult. In this paper, two cases of SDOF fuzzy controllers, which either share the same number of fuzzy rules or not, are considered. The system stability is investigated based on the Lyapunov stability theory using the sum-of-squares (SOS) approach. SOS-based stability conditions are obtained to guarantee the system stability and synthesize the SDOF fuzzy controller. Simulation examples are given to demonstrate the merits of the proposed SDOF fuzzy control approach.

Dynamics of the flood response to slow-fast landscape-climate feedbacks

Directory of Open Access Journals (Sweden)

R. A. P. Perdigão

2015-06-01

Full Text Available The dynamical evolution of the flood response to landscape-climate feedbacks is evaluated in a joint nonlinear statistical-dynamical approach. For that purpose, a spatiotemporal sensitivity analysis is conducted on hydrological data from 1976–2008 over 804 catchments throughout Austria, and a general, data-independent nonlinear dynamical model is built linking floods with climate (via precipitation, landscape (via elevation and their feedbacks. These involve nonlinear scale interactions, with landform evolution processes taking place at the millennial scale (slow dynamics, and climate adjusting in years to decades (fast dynamics. The results show that floods are more responsive to spatial (regional than to temporal (decadal variability. Catchments from dry lowlands and high wetlands exhibit similarity between the spatial and temporal sensitivities (spatiotemporal symmetry and low landscape-climate codependence, suggesting they are not coevolving significantly. However, intermediate regions show differences between those sensitivities (symmetry breaks and higher landscape-climate codependence, suggesting undergoing coevolution. The break of symmetry is an emergent behaviour from nonlinear feedbacks within the system. A new coevolution index is introduced relating spatiotemporal symmetry with relative characteristic celerities, which need to be taken into account in hydrological space-time trading. Coevolution is expressed here by the interplay between slow and fast dynamics, represented respectively by spatial and temporal characteristics. The dynamical model captures emerging features of the flood dynamics and nonlinear landscape-climate feedbacks, supporting the nonlinear statistical assessment of spatiotemporally asymmetric flood change. Moreover, it enables the dynamical estimation of flood changes in space and time from the given knowledge at different spatiotemporal conditions. This study ultimately brings to light emerging signatures of

Output feedback dissipation control for the power-level of modular high-temperature gas-cooled reactors

International Nuclear Information System (INIS)

Dong, Z.

2011-01-01

Because of its strong inherent safety features and the high outlet temperature, the modular high temperature gas-cooled nuclear reactor (MHTGR) is the chosen technology for a new generation of nuclear power plants. Such power plants are being considered for industrial applications with a wide range of power levels, thus power-level regulation is very important for their efficient and stable operation. Exploiting the large scale asymptotic closed-loop stability provided by nonlinear controllers, a nonlinear power-level regulator is presented in this paper that is based upon both the techniques of feedback dissipation and well-established backstepping. The virtue of this control strategy, i.e., the ability of globally asymptotic stabilization, is that it takes advantage of the inherent zero-state detectability property of the MHTGR dynamics. Moreover, this newly built power-level regulator is also robust towards modeling uncertainty in the control rod dynamics. If modeling uncertainty of the control rod dynamics is small enough to be omitted, then this control law can be simplified to a classical proportional feedback controller. The comparison of the control performance between the newly-built power controller and the simplified controller is also given through numerical study and theoretical analysis. (author)

New numerical methods for open-loop and feedback solutions to dynamic optimization problems

Science.gov (United States)

Ghosh, Pradipto

The topic of the first part of this research is trajectory optimization of dynamical systems via computational swarm intelligence. Particle swarm optimization is a nature-inspired heuristic search method that relies on a group of potential solutions to explore the fitness landscape. Conceptually, each particle in the swarm uses its own memory as well as the knowledge accumulated by the entire swarm to iteratively converge on an optimal or near-optimal solution. It is relatively straightforward to implement and unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, is still relatively new. In the first half of this thesis particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems including thrust programming for minimum fuel, multi-burn spacecraft orbit transfer, and computing minimum-time rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of constrained nonlinear mixed-integer programming problems with the swarming technique. For each solved optimal programming problem, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy. The second half of this research develops a new extremal-field approach for synthesizing nearly optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general nonlinear differential equations. A notable revelation from this development

Helmholtz solitons in power-law optical materials

International Nuclear Information System (INIS)

Christian, J. M.; McDonald, G. S.; Potton, R. J.; Chamorro-Posada, P.

2007-01-01

A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures the evolution of broad beams at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses, and liquid crystals. Exact analytical soliton solutions are presented for a generic nonlinearity, within which known Kerr solitons comprise a subset. Three general conservation laws are also reported. Analysis and numerical simulations examine the stability of the Helmholtz power-law solitons. A propagation feature, associated with spatial solitons in power-law media, constituting a class of oscillatory solution, is identified

Global output feedback control for a class of high-order feedforward nonlinear systems with input delay.

Science.gov (United States)

Zha, Wenting; Zhai, Junyong; Fei, Shumin

2013-07-01

This paper investigates the problem of output feedback stabilization for a class of high-order feedforward nonlinear systems with time-varying input delay. First, a scaling gain is introduced into the system under a set of coordinate transformations. Then, the authors construct an observer and controller to make the nominal system globally asymptotically stable. Based on homogeneous domination approach and Lyapunov-Krasovskii functional, it is shown that the closed-loop system can be rendered globally asymptotically stable by the scaling gain. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed scheme. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

LMI-based stability and performance conditions for continuous-time nonlinear systems in Takagi-Sugeno's form.

Science.gov (United States)

Lam, H K; Leung, Frank H F

2007-10-01

This correspondence presents the stability analysis and performance design of the continuous-time fuzzy-model-based control systems. The idea of the nonparallel-distributed-compensation (non-PDC) control laws is extended to the continuous-time fuzzy-model-based control systems. A nonlinear controller with non-PDC control laws is proposed to stabilize the continuous-time nonlinear systems in Takagi-Sugeno's form. To produce the stability-analysis result, a parameter-dependent Lyapunov function (PDLF) is employed. However, two difficulties are usually encountered: 1) the time-derivative terms produced by the PDLF will complicate the stability analysis and 2) the stability conditions are not in the form of linear-matrix inequalities (LMIs) that aid the design of feedback gains. To tackle the first difficulty, the time-derivative terms are represented by some weighted-sum terms in some existing approaches, which will increase the number of stability conditions significantly. In view of the second difficulty, some positive-definitive terms are added in order to cast the stability conditions into LMIs. In this correspondence, the favorable properties of the membership functions and nonlinear control laws, which allow the introduction of some free matrices, are employed to alleviate the two difficulties while retaining the favorable properties of PDLF-based approach. LMI-based stability conditions are derived to ensure the system stability. Furthermore, based on a common scalar performance index, LMI-based performance conditions are derived to guarantee the system performance. Simulation examples are given to illustrate the effectiveness of the proposed approach.

Nonlinear adaptive robust back stepping force control of hydraulic load simulator: Theory and experiments

International Nuclear Information System (INIS)

Yao, Jianyong; Jiao, Zongxia; Yao, Bin

2014-01-01

High performance robust force control of hydraulic load simulator with constant but unknown hydraulic parameters is considered. In contrast to the linear control based on hydraulic linearization equations, hydraulic inherent nonlinear properties and uncertainties make the conventional feedback proportional-integral-derivative (PID) control not yield to high performance requirements. Furthermore, the hydraulic system may be subjected to non-smooth and discontinuous nonlinearities due to the directional change of valve opening. In this paper, based on a nonlinear system model of hydraulic load simulator, a discontinuous projection-based nonlinear adaptive robust back stepping controller is developed with servo valve dynamics. The proposed controller constructs a novel stable adaptive controller and adaptation laws with additional pressure dynamic related unknown parameters, which can compensate for the system nonlinearities and uncertain parameters, meanwhile a well-designed robust controller is also synthesized to dominate the model uncertainties coming from both parametric uncertainties and uncertain nonlinearities including unmodeled and ignored system dynamics. The controller theoretically guarantee a prescribed transient performance and final tracking accuracy in presence of both parametric uncertainties and uncertain nonlinearities; while achieving asymptotic output tracking in the absence of unstructured uncertainties. The implementation issues are also discussed for controller simplification. Some comparative results are obtained to verify the high-performance nature of the proposed controller.

Nonlinear adaptive robust back stepping force control of hydraulic load simulator: Theory and experiments

Energy Technology Data Exchange (ETDEWEB)

Yao, Jianyong [Nanjing University of Science and Technology, Nanjing (China); Jiao, Zongxia [Beihang University, Beijing (China); Yao, Bin [Purdue University, West Lafayette (United States)

2014-04-15

High performance robust force control of hydraulic load simulator with constant but unknown hydraulic parameters is considered. In contrast to the linear control based on hydraulic linearization equations, hydraulic inherent nonlinear properties and uncertainties make the conventional feedback proportional-integral-derivative (PID) control not yield to high performance requirements. Furthermore, the hydraulic system may be subjected to non-smooth and discontinuous nonlinearities due to the directional change of valve opening. In this paper, based on a nonlinear system model of hydraulic load simulator, a discontinuous projection-based nonlinear adaptive robust back stepping controller is developed with servo valve dynamics. The proposed controller constructs a novel stable adaptive controller and adaptation laws with additional pressure dynamic related unknown parameters, which can compensate for the system nonlinearities and uncertain parameters, meanwhile a well-designed robust controller is also synthesized to dominate the model uncertainties coming from both parametric uncertainties and uncertain nonlinearities including unmodeled and ignored system dynamics. The controller theoretically guarantee a prescribed transient performance and final tracking accuracy in presence of both parametric uncertainties and uncertain nonlinearities; while achieving asymptotic output tracking in the absence of unstructured uncertainties. The implementation issues are also discussed for controller simplification. Some comparative results are obtained to verify the high-performance nature of the proposed controller.

Neural cryptography with feedback.

Science.gov (United States)

Ruttor, Andreas; Kinzel, Wolfgang; Shacham, Lanir; Kanter, Ido

2004-04-01

Neural cryptography is based on a competition between attractive and repulsive stochastic forces. A feedback mechanism is added to neural cryptography which increases the repulsive forces. Using numerical simulations and an analytic approach, the probability of a successful attack is calculated for different model parameters. Scaling laws are derived which show that feedback improves the security of the system. In addition, a network with feedback generates a pseudorandom bit sequence which can be used to encrypt and decrypt a secret message.

Nonlinear Tracking Control of a Conductive Supercoiled Polymer Actuator.

Science.gov (United States)

Luong, Tuan Anh; Cho, Kyeong Ho; Song, Min Geun; Koo, Ja Choon; Choi, Hyouk Ryeol; Moon, Hyungpil

2018-04-01

Artificial muscle actuators made from commercial nylon fishing lines have been recently introduced and shown as a new type of actuator with high performance. However, the actuators also exhibit significant nonlinearities, which make them difficult to control, especially in precise trajectory-tracking applications. In this article, we present a nonlinear mathematical model of a conductive supercoiled polymer (SCP) actuator driven by Joule heating for model-based feedback controls. Our efforts include modeling of the hysteresis behavior of the actuator. Based on nonlinear modeling, we design a sliding mode controller for SCP actuator-driven manipulators. The system with proposed control law is proven to be asymptotically stable using the Lyapunov theory. The control performance of the proposed method is evaluated experimentally and compared with that of a proportional-integral-derivative (PID) controller through one-degree-of-freedom SCP actuator-driven manipulators. Experimental results show that the proposed controller's performance is superior to that of a PID controller, such as the tracking errors are nearly 10 times smaller compared with those of a PID controller, and it is more robust to external disturbances such as sensor noise and actuator modeling error.

Feedback options in nonlinear numerical finance

DEFF Research Database (Denmark)

Hugger, Jens; Mashayekhi, Sima

2012-01-01

on an infinite slab is presented and boundary values on a bounded domain are derived. This bounded, nonlinear, 2 dimensional initial-boundary value problem is solved numerically using a number of standard finite difference schemes and the methods incorporated in the symbolic software Maple™....

Rotating and standing waves in a diffractive nonlinear optical system with delayed feedback under O(2) Hopf bifurcation

Science.gov (United States)

Budzinskiy, S. S.; Razgulin, A. V.

2017-08-01

In this paper we study one-dimensional rotating and standing waves in a model of an O(2)-symmetric nonlinear optical system with diffraction and delay in the feedback loop whose dynamics is governed by a system of coupled delayed parabolic equation and linear Schrodinger-type equation. We elaborate a two-step approach: transition to a rotating coordinate system to obtain the profiles of the waves as small parameter expansions and the normal form technique to study their qualitative dynamic behavior and stability. Theoretical results stand in a good agreement with direct computer simulations presented.

Nonlinear Dynamic Inversion Baseline Control Law: Flight-Test Results for the Full-scale Advanced Systems Testbed F/A-18 Airplane

Science.gov (United States)

Miller, Christopher J.

2011-01-01

A model reference nonlinear dynamic inversion control law has been developed to provide a baseline controller for research into simple adaptive elements for advanced flight control laws. This controller has been implemented and tested in a hardware-in-the-loop simulation and in flight. The flight results agree well with the simulation predictions and show good handling qualities throughout the tested flight envelope with some noteworthy deficiencies highlighted both by handling qualities metrics and pilot comments. Many design choices and implementation details reflect the requirements placed on the system by the nonlinear flight environment and the desire to keep the system as simple as possible to easily allow the addition of the adaptive elements. The flight-test results and how they compare to the simulation predictions are discussed, along with a discussion about how each element affected pilot opinions. Additionally, aspects of the design that performed better than expected are presented, as well as some simple improvements that will be suggested for follow-on work.

Control and diagnostic uses of feedback

International Nuclear Information System (INIS)

Sen, A. K.

2000-01-01

Recent results on multimode feedback control of magnetohydrodynamic (MHD) modes and a variety of diagnostic uses of feedback are summarized. First, is the report on reduction and scaling of transport under feedback. By controlling the fluctuation amplitudes and consequently the transport via feedback, it is found that the scaling of the diffusion coefficient is linear with root-mean-square rms fluctuation level. The scaling appears not to agree with any generic theory. A variety of other diagnostic uses of feedback have been developed. The primary goal is an experimental methodology for the determination of dynamic models of plasma turbulence, both for better transport understanding and more credible feedback controller designs. A specific motivation is to search for a low-order dynamic model, suitable for the convenient study of both transport and feedback. First, the time series analysis method is used for the determination of chaotic attractor dimension of plasma fluctuations. For ExB rotational flute modes it is found to be close to three, indicating that a low-order dynamic model may be adequate for transport prediction and feedback controller design. Second, a new method for direct experimental determination of nonlinear dynamical models of plasma turbulence using feedback has been developed. Specifically, the process begins with a standard three-wave coupling model and introduces a variable feedback gain. The power spectrum, delayed power spectrum, and bispectrum of fluctuations are then experimentally obtained. By varying the feedback gain continuously, an arbitrary number of numerical equations for a fixed number of unknowns can be generated. Their numerical solution yields the linear dispersion, as well as nonlinear coupling coefficients. This method has been successfully applied for ExB rotationally driven flute modes. (c) 2000 American Institute of Physics

RF feedback simulation for the PEP-II B Factory

International Nuclear Information System (INIS)

Tighe, R.

1994-06-01

A model, of the beam and RF system for PEP-11 has been developed to allow both time-domain simulation and frequency-domain analysis of the complete system. The model includes the full set of feedback loops and nonlinear elements such as the beam and klystron. The model may be used to predict beam and feedback stability in the presence of nonlinearities through time-domain simulation as well as system frequency response about a given operating point

Hamiltonian structures of some non-linear evolution equations

International Nuclear Information System (INIS)

Tu, G.Z.

1983-06-01

The Hamiltonian structure of the O(2,1) non-linear sigma model, generalized AKNS equations, are discussed. By reducing the O(2,1) non-linear sigma model to its Hamiltonian form some new conservation laws are derived. A new hierarchy of non-linear evolution equations is proposed and shown to be generalized Hamiltonian equations with an infinite number of conservation laws. (author)

Time skewing and amplitude nonlinearity mitigation by feedback equalization for 56 Gbps VCSEL-based PAM-4 links

Science.gov (United States)

You, Yue; Zhang, Wenjia; Sun, Lin; Du, Jiangbing; Liang, Chenyu; Yang, Fan; He, Zuyuan

2018-03-01

The vertical cavity surface emitting laser (VCSEL)-based multimode optical transceivers enabled by pulse amplitude modulation (PAM)-4 will be commercialized in near future to meet the 400-Gbps standard short reach optical interconnects. It is still challenging to achieve over 56/112-Gbps with the multilevel signaling as the multimode property of the device and link would introduce the nonlinear temporal response for the different levels. In this work, we scrutinize the distortions that relates to the multilevel feature of PAM-4 modulation, and propose an effective feedback equalization scheme for 56-Gbps VCSEL-based PAM-4 optical interconnects system to mitigate the distortions caused by eye timing-skew and nonlinear power-dependent noise. Level redistribution at Tx side is theoretically modeled and constructed to achieve equivalent symbol error ratios (SERs) of four levels and improved BER performance. The cause of the eye skewing and the mitigation approach are also simulated at 100-Gbps and experimentally investigated at 56-Gbps. The results indicate more than 2-dB power penalty improvement has been achieved by using such a distortion aware equalizer.

Nonlinearity, Conservation Law and Shocks

Indian Academy of Sciences (India)

However, genuine nonlinearity is always present in an ideal gas. The conservation form of the equation (25) brings in shocks which cut off the growing part of the amplitUde as shown in. Figure 15. Acknowledgements. The author sincerely thanks the two referees whose valuable comments led to an improvement of the ...

Nonlinear feedback in a six-dimensional Lorenz model: impact of an additional heating term

Science.gov (United States)

Shen, B.-W.

2015-12-01

In this study, a six-dimensional Lorenz model (6DLM) is derived, based on a recent study using a five-dimensional (5-D) Lorenz model (LM), in order to examine the impact of an additional mode and its accompanying heating term on solution stability. The new mode added to improve the representation of the streamfunction is referred to as a secondary streamfunction mode, while the two additional modes, which appear in both the 6DLM and 5DLM but not in the original LM, are referred to as secondary temperature modes. Two energy conservation relationships of the 6DLM are first derived in the dissipationless limit. The impact of three additional modes on solution stability is examined by comparing numerical solutions and ensemble Lyapunov exponents of the 6DLM and 5DLM as well as the original LM. For the onset of chaos, the critical value of the normalized Rayleigh number (rc) is determined to be 41.1. The critical value is larger than that in the 3DLM (rc ~ 24.74), but slightly smaller than the one in the 5DLM (rc ~ 42.9). A stability analysis and numerical experiments obtained using generalized LMs, with or without simplifications, suggest the following: (1) negative nonlinear feedback in association with the secondary temperature modes, as first identified using the 5DLM, plays a dominant role in providing feedback for improving the solution's stability of the 6DLM, (2) the additional heating term in association with the secondary streamfunction mode may destabilize the solution, and (3) overall feedback due to the secondary streamfunction mode is much smaller than the feedback due to the secondary temperature modes; therefore, the critical Rayleigh number of the 6DLM is comparable to that of the 5DLM. The 5DLM and 6DLM collectively suggest different roles for small-scale processes (i.e., stabilization vs. destabilization), consistent with the following statement by Lorenz (1972): "If the flap of a butterfly's wings can be instrumental in generating a tornado, it can

RF feedback simulation results for PEP-II

International Nuclear Information System (INIS)

Tighe, R.; Corredoura, P.

1995-06-01

A model of the RF feedback system for PEP-II has been developed to provide time-domain simulation and frequency-domain analysis of the complete system. The model includes the longitudinal beam dynamics, cavity fundamental resonance, feedback loops, and the nonlinear klystron operating near saturation. Transients from an ion clearing gap and a reference phase modulation from the longitudinal feedback system are also studied. Growth rates are predicted and overall system stability examined

Feedback control of edge turbulence in a tokamak

International Nuclear Information System (INIS)

Kan, Zhai; Yi-zhi, Wen; Chang-xuan, Yu; Wan-dong, Liu; Chao, Wang; Ge, Zhuang; Kan, Zhai; Zhi-Zhan, Yu

1997-01-01

An experiment on feedback control of edge turbulence has been undertaken on the KT-5C tokamak. The results indicate that the edge turbulence could be suppressed or enhanced depending on the phase shift of the feedback network. In a typical case of 90 degree phase shift feedback, the turbulence amplitudes of both T e and n e were reduced by about 25% when the gain of the feedback network was 15. Correspondingly the radial particle flux decreased to about 75% level of the background. Through bispectral analysis it is found that there exists a substantial nonlinear coupling between various modes comprised in edge turbulence, especially in the frequency range from about 10 kHz to 100 kHz, which contains the large part of the edge turbulence energy in KT-5C tokamak. In particular, by actively controlling the turbulence amplitude using feedback, a direct experimental evidence of the link between the nonlinear wave-wave coupling over the whole spectrum in turbulence, the saturated turbulence amplitude, and the radial particle flux was provided. copyright 1997 The American Physical Society

Robust Speed Tracking Control for a Micro Turbine as a Distributed Energy Resource via Feedback Domination and Disturbance Observer

Directory of Open Access Journals (Sweden)

Ancheng Xu

2017-01-01

Full Text Available Micro turbine (MT is characterized with complex dynamics, parameter uncertainties, and variable working conditions. In this paper, a novel robust controller is investigated for a single-shaft micro turbine as a distributed energy resource by integrating a feedback domination control technique and a feedforward disturbance compensation. An active estimation process of the mismatched disturbances is firstly enabled by constructing a disturbance observer. Secondly, we adopt a feedback domination technique, rather than popularly used feedback linearization methods, to handle the system nonlinearities. In an explicit way, the composite controllers are then derived by recursive design based on Lyapunov theory while a global input-to-state stability can be guaranteed. Abundant comparison simulation results are provided to demonstrate the effectiveness of the proposed scheme, which not only perform an improved closed-loop control performance comparing to all existing results, but also render a simple control law which will ease its practical implementation.

Output Feedback Dissipation Control for the Power-Level of Modular High-Temperature Gas-Cooled Reactors

Directory of Open Access Journals (Sweden)

Zhe Dong

2011-11-01

Full Text Available Because of its strong inherent safety features and the high outlet temperature, the modular high temperature gas-cooled nuclear reactor (MHTGR is the chosen technology for a new generation of nuclear power plants. Such power plants are being considered for industrial applications with a wide range of power levels, thus power-level regulation is very important for their efficient and stable operation. Exploiting the large scale asymptotic closed-loop stability provided by nonlinear controllers, a nonlinear power-level regulator is presented in this paper that is based upon both the techniques of feedback dissipation and well-established backstepping. The virtue of this control strategy, i.e., the ability of globally asymptotic stabilization, is that it takes advantage of the inherent zero-state detectability property of the MHTGR dynamics. Moreover, this newly built power-level regulator is also robust towards modeling uncertainty in the control rod dynamics. If modeling uncertainty of the control rod dynamics is small enough to be omitted, then this control law can be simplified to a classical proportional feedback controller. The comparison of the control performance between the newly-built power controller and the simplified controller is also given through numerical study and theoretical analysis.

Output Feedback Tracking Control of an Underactuated Quad-Rotor UAV

National Research Council Canada - National Science Library

Lee, DongBin; Burg, Timothy; Xian, Bin; Dawson, Darren

2006-01-01

...) using output feedback (OFB). Specifically, an observer is designed to estimate the velocities and an output feedback controller is designed for a nonlinear UAV system in which only position and angles are measurable...

Mobile robot nonlinear feedback control based on Elman neural network observer

Directory of Open Access Journals (Sweden)

Khaled Al-Mutib

2015-12-01

Full Text Available This article presents a new approach to control a wheeled mobile robot without velocity measurement. The controller developed is based on kinematic model as well as dynamics model to take into account parameters of dynamics. These parameters related to dynamic equations are identified using a proposed methodology. Input–output feedback linearization is considered with a slight modification in the mathematical expressions to implement the dynamic controller and analyze the nonlinear internal behavior. The developed controllers require sensors to obtain the states needed for the closed-loop system. However, some states may not be available due to the absence of the sensors because of the cost, the weight limitation, reliability, induction of errors, failure, and so on. Particularly, for the velocity measurements, the required accuracy may not be achieved in practical applications due to the existence of significant errors induced by stochastic or cyclical noise. In this article, Elman neural network is proposed to work as an observer to estimate the velocity needed to complete the full state required for the closed-loop control and account for all the disturbances and model parameter uncertainties. Different simulations are carried out to demonstrate the feasibility of the approach in tracking different reference trajectories in comparison with other paradigms.

Constructing and analysis of soliton-like solutions of (1 + 1), (2 + 1), (3 + 1)-dimensional Schrodinger equations with the third power nonlinearity law

International Nuclear Information System (INIS)

Zhestkov, S.V.; Romanenko, A.A.

2009-01-01

The problem of existence of soliton-like solutions of (1+1), (2+1), (3+1)-dimensional Schrodinger equations with the third power nonlinearity law is investigated. The numerical-analytical method of constructing solitons is developed. (authors)

Model Based Control of Single-Phase Marine Cooling Systems

DEFF Research Database (Denmark)

Hansen, Michael

2014-01-01

in this work is on the development of a nonlinear robust control design. The design is based on principles from feedback. linearization to compensate for nonlinearities as well as transport delays by including a delay estimate in the feedback law. To deal with the uncertainties that emerged from the feedback...

Model-Free Adaptive Control for Unknown Nonlinear Zero-Sum Differential Game.

Science.gov (United States)

Zhong, Xiangnan; He, Haibo; Wang, Ding; Ni, Zhen

2018-05-01

In this paper, we present a new model-free globalized dual heuristic dynamic programming (GDHP) approach for the discrete-time nonlinear zero-sum game problems. First, the online learning algorithm is proposed based on the GDHP method to solve the Hamilton-Jacobi-Isaacs equation associated with optimal regulation control problem. By setting backward one step of the definition of performance index, the requirement of system dynamics, or an identifier is relaxed in the proposed method. Then, three neural networks are established to approximate the optimal saddle point feedback control law, the disturbance law, and the performance index, respectively. The explicit updating rules for these three neural networks are provided based on the data generated during the online learning along the system trajectories. The stability analysis in terms of the neural network approximation errors is discussed based on the Lyapunov approach. Finally, two simulation examples are provided to show the effectiveness of the proposed method.

Distributed Cooperative Control of Nonlinear and Non-identical Multi-agent Systems

DEFF Research Database (Denmark)

Bidram, Ali; Lewis, Frank; Davoudi, Ali

2013-01-01

This paper exploits input-output feedback linearization technique to implement distributed cooperative control of multi-agent systems with nonlinear and non-identical dynamics. Feedback linearization transforms the synchronization problem for a nonlinear and heterogeneous multi-agent system...... for electric power microgrids. The effectiveness of the proposed control is verified by simulating a microgrid test system....

Nonlinear hyperbolic waves in multidimensions

CERN Document Server

Prasad, Phoolan

2001-01-01

The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts.Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts...

Discrete- and finite-bandwidth-frequency distributions in nonlinear stability applications

Science.gov (United States)

Kuehl, Joseph J.

2017-02-01

A new "wave packet" formulation of the parabolized stability equations method is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a "nonlinear coupling coefficient." It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening, and results in disturbance representation more consistent with the experiment than traditional formulations. A Mach 6 flared-cone example is presented.

Finite-time stabilisation of a class of switched nonlinear systems with state constraints

Science.gov (United States)

Huang, Shipei; Xiang, Zhengrong

2018-06-01

This paper investigates the finite-time stabilisation for a class of switched nonlinear systems with state constraints. Some power orders of the system are allowed to be ratios of positive even integers over odd integers. A Barrier Lyapunov function is introduced to guarantee that the state constraint is not violated at any time. Using the convex combination method and a recursive design approach, a state-dependent switching law and state feedback controllers of individual subsystems are constructed such that the closed-loop system is finite-time stable without violation of the state constraint. Two examples are provided to show the effectiveness of the proposed method.

Nonlinear H-infinity State Feedback Controllers: Computation of Valid Region

DEFF Research Database (Denmark)

Pedersen, Michael; Møller-Pedersen, J.; Pagh Petersen, M.

1996-01-01

"From a general point of view the state feedback QTR H-infinitysuboptimal control probelm is reasonable well-understood. Inportantproblems remain with regard to a priori information of the size of theneighbourhood where the local state feedback QTR H-infinityproblem is solvable, and with regard t...

Bryan's effect and anisotropic nonlinear damping

Science.gov (United States)

Joubert, Stephan V.; Shatalov, Michael Y.; Fay, Temple H.; Manzhirov, Alexander V.

2018-03-01

In 1890, G. H. Bryan discovered the following: "The vibration pattern of a revolving cylinder or bell revolves at a rate proportional to the inertial rotation rate of the cylinder or bell." We call this phenomenon Bryan's law or Bryan's effect. It is well known that any imperfections in a vibratory gyroscope (VG) affect Bryan's law and this affects the accuracy of the VG. Consequently, in this paper, we assume that all such imperfections are either minimised or eliminated by some known control method and that only damping is present within the VG. If the damping is isotropic (linear or nonlinear), then it has been recently demonstrated in this journal, using symbolic analysis, that Bryan's law remains invariant. However, it is known that linear anisotropic damping does affect Bryan's law. In this paper, we generalise Rayleigh's dissipation function so that anisotropic nonlinear damping may be introduced into the equations of motion. Using a mixture of numeric and symbolic analysis on the ODEs of motion of the VG, for anisotropic light nonlinear damping, we demonstrate (up to an approximate average), that Bryan's law is affected by any form of such damping, causing pattern drift, compromising the accuracy of the VG.

Adaptive control of Parkinson's state based on a nonlinear computational model with unknown parameters.

Science.gov (United States)

Su, Fei; Wang, Jiang; Deng, Bin; Wei, Xi-Le; Chen, Ying-Yuan; Liu, Chen; Li, Hui-Yan

2015-02-01

The objective here is to explore the use of adaptive input-output feedback linearization method to achieve an improved deep brain stimulation (DBS) algorithm for closed-loop control of Parkinson's state. The control law is based on a highly nonlinear computational model of Parkinson's disease (PD) with unknown parameters. The restoration of thalamic relay reliability is formulated as the desired outcome of the adaptive control methodology, and the DBS waveform is the control input. The control input is adjusted in real time according to estimates of unknown parameters as well as the feedback signal. Simulation results show that the proposed adaptive control algorithm succeeds in restoring the relay reliability of the thalamus, and at the same time achieves accurate estimation of unknown parameters. Our findings point to the potential value of adaptive control approach that could be used to regulate DBS waveform in more effective treatment of PD.

STABLE ADAPTIVE CONTROL FOR A CLASS OF NONLINEAR SYSTEMS WITHOUT USE OF A SUPERVISORY TERM IN THE CONTROL LAW

Directory of Open Access Journals (Sweden)

MOHAMED BAHITA

2012-02-01

Full Text Available In this paper, a direct adaptive control scheme for a class of nonlinear systems is proposed. The architecture employs a Gaussian radial basis function (RBF network to construct an adaptive controller. The parameters of the adaptive controller are adapted and changed according to a law derived using Lyapunov stability theory. The centres of the RBF network are adapted on line using the k-means algorithm. Asymptotic Lyapunov stability is established without the use of a supervisory (compensatory term in the control law and with the tracking errors converging to a neighbourhood of the origin. Finally, a simulation is provided to explore the feasibility of the proposed neuronal controller design method.

Testing the Law of One Price under Nonlinearity for Egg Market of Selected Provinces of Iran

Directory of Open Access Journals (Sweden)

M. Ghahremanzadeh

2016-05-01

Full Text Available Introduction: Regarding to the ever-increasing consumption of egg and consequently enhancement of its production during recent years, consideration to this output's market integration has special importance. Considering the fact that information on market integration may provide specific evidence as to the competitiveness of market, the effectiveness of arbitrage and the efficiency of pricing could be, likewise, useful to guide subsequent interventions aimed at improving the performance of market. In this context, in present study, validity of Law of One Price (LOP will be tested in the egg market and among selected provinces. Materials and Methods: Nonlinearity naturally extracted from local market due to existence of transportation and other transaction costs, so common cointegration test results are not suitable for market integration. In this study, at first, for being sure that series follow nonlinear behavior, Luukkonen et al. (1988 and BDS nonlinearity tests were used. Then for testing Law of One price in the egg market, nonlinear unit root test proposed by Emmanouilides and Fousekis (2012, which is an auxiliary regression for ESTAR model, was used. The data are daily retail prices of egg with the sample period ranging from April 2006 to march 2014 for north-west provinces of Iran including West Azerbaijan, East Azerbaijan, Ardebil, Tehran and Zanjan, which were obtained from State Live Stock Affairs Logistics Incorporated Company. Results and Discussion: Based on the DF-GLS unit root test, the null hypothesis of unit root for egg price differentials was rejected. So, all series of price differentials are stationary. In the next step nonlinearity of price differentials of egg between two provinces was examined. In BDS test, at the beginning, an ARMA model was estimated then the test was carried out to the residual of estimated model with embedding dimension (m 2-8 and the dimensional distance (ε chosen equals to 0.5 and 2 times of

Semi-discrete approximations to nonlinear systems of conservation laws; consistency and L(infinity)-stability imply convergence. Final report

International Nuclear Information System (INIS)

Tadmor, E.

1988-07-01

A convergence theory for semi-discrete approximations to nonlinear systems of conservation laws is developed. It is shown, by a series of scalar counter-examples, that consistency with the conservation law alone does not guarantee convergence. Instead, a notion of consistency which takes into account both the conservation law and its augmenting entropy condition is introduced. In this context it is concluded that consistency and L(infinity)-stability guarantee for a relevant class of admissible entropy functions, that their entropy production rate belongs to a compact subset of H(loc)sup -1 (x,t). One can now use compensated compactness arguments in order to turn this conclusion into a convergence proof. The current state of the art for these arguments includes the scalar and a wide class of 2 x 2 systems of conservation laws. The general framework of the vanishing viscosity method is studied as an effective way to meet the consistency and L(infinity)-stability requirements. How this method is utilized to enforce consistency and stability for scalar conservation laws is shown. In this context we prove, under the appropriate assumptions, the convergence of finite difference approximations (e.g., the high resolution TVD and UNO methods), finite element approximations (e.g., the Streamline-Diffusion methods) and spectral and pseudospectral approximations (e.g., the Spectral Viscosity methods)

Should Principals Know More about Law?

Science.gov (United States)

Doctor, Tyrus L.

2013-01-01

Educational law is a critical piece of the education conundrum. Principals reference law books on a daily basis in order to address the wide range of complex problems in the school system. A principal's knowledge of law issues and legal decision-making are essential to provide effective feedback for a successful school.

On nonlinear dynamics and control of a robotic arm with chaos

Directory of Open Access Journals (Sweden)

Felix J. L. P.

2014-01-01

Full Text Available In this paper a robotic arm is modelled by a double pendulum excited in its base by a DC motor of limited power via crank mechanism and elastic connector. In the mathematical model, a chaotic motion was identified, for a wide range of parameters. Controlling of the chaotic behaviour of the system, were implemented using, two control techniques, the nonlinear saturation control (NSC and the optimal linear feedback control (OLFC. The actuator and sensor of the device are allowed in the pivot and joints of the double pendulum. The nonlinear saturation control (NSC is based in the order second differential equations and its action in the pivot/joint of the robotic arm is through of quadratic nonlinearities feedback signals. The optimal linear feedback control (OLFC involves the application of two control signals, a nonlinear feedforward control to maintain the controlled system to a desired periodic orbit, and control a feedback control to bring the trajectory of the system to the desired orbit. Simulation results, including of uncertainties show the feasibility of the both methods, for chaos control of the considered system.

Nonlinear Synergetic Governor Controllers for Steam Turbine Generators to Enhance Power System Stability

Directory of Open Access Journals (Sweden)

Xingbao Ju

2017-07-01

Full Text Available This paper proposes a decentralized nonlinear synergetic governor controller (NSGC for turbine generators to enhance power system stability by using synergetic control theory and the feedback linearization technique. The precise feedback linearization model of a turbine-generator with a steam valve control is obtained, at first, by using a feedback linearization technique. Then based on this model, a manifold is defined as a linear combination of the deviation of the rotor angle, speed deviation, and speed derivative. The control law of the proposed NSGC is deduced and the stability condition of the whole closed-loop system is subsequently analyzed. According to the requirement of the primary frequency regulation, an additional proportional integral (PI controller is designed to dynamically track the steady-state value of the rotor angle. Case studies are undertaken based on a single-machine infinite-bus system and the New England system, respectively. Simulation results show that the proposed NSGC can suppress the power oscillations and improve transient stability more effectively in comparison with the conventional proportional-integral-derivative (PID governor controller. Moreover, the proposed NSGC is robust to the variations of the system operating conditions.

A reliable treatment for nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Khani, F.; Hamedi-Nezhad, S.; Molabahrami, A.

2007-01-01

Exp-function method is used to find a unified solution of nonlinear wave equation. Nonlinear Schroedinger equations with cubic and power law nonlinearity are selected to illustrate the effectiveness and simplicity of the method. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear equation

Modeling of long-range memory processes with inverse cubic distributions by the nonlinear stochastic differential equations

Science.gov (United States)

Kaulakys, B.; Alaburda, M.; Ruseckas, J.

2016-05-01

A well-known fact in the financial markets is the so-called ‘inverse cubic law’ of the cumulative distributions of the long-range memory fluctuations of market indicators such as a number of events of trades, trading volume and the logarithmic price change. We propose the nonlinear stochastic differential equation (SDE) giving both the power-law behavior of the power spectral density and the long-range dependent inverse cubic law of the cumulative distribution. This is achieved using the suggestion that when the market evolves from calm to violent behavior there is a decrease of the delay time of multiplicative feedback of the system in comparison to the driving noise correlation time. This results in a transition from the Itô to the Stratonovich sense of the SDE and yields a long-range memory process.

Nonlinear control of ships minimizing the position tracking errors

Directory of Open Access Journals (Sweden)

Svein P. Berge

1999-07-01

Full Text Available In this paper, a nonlinear tracking controller with integral action for ships is presented. The controller is based on state feedback linearization. Exponential convergence of the vessel-fixed position and velocity errors are proven by using Lyapunov stability theory. Since we only have two control devices, a rudder and a propeller, we choose to control the longship and the sideship position errors to zero while the heading is stabilized indirectly. A Virtual Reference Point (VRP is defined at the bow or ahead of the ship. The VRP is used for tracking control. It is shown that the distance from the center of rotation to the VRP will influence on the stability of the zero dynamics. By selecting the VRP at the bow or even ahead of the bow, the damping in yaw can be increased and the zero dynamics is stabilized. Hence, the heading angle will be less sensitive to wind, currents and waves. The control law is simulated by using a nonlinear model of the Japanese training ship Shiojimaru with excellent results. Wind forces are added to demonstrate the robustness and performance of the integral controller.

Multi-Body Ski Jumper Model with Nonlinear Dynamic Inversion Muscle Control for Trajectory Optimization

Directory of Open Access Journals (Sweden)

Patrick Piprek

2018-02-01

Full Text Available This paper presents an approach to model a ski jumper as a multi-body system for an optimal control application. The modeling is based on the constrained Newton-Euler-Equations. Within this paper the complete multi-body modeling methodology as well as the musculoskeletal modeling is considered. For the musculoskeletal modeling and its incorporation in the optimization model, we choose a nonlinear dynamic inversion control approach. This approach uses the muscle models as nonlinear reference models and links them to the ski jumper movement by a control law. This strategy yields a linearized input-output behavior, which makes the optimal control problem easier to solve. The resulting model of the ski jumper can then be used for trajectory optimization whose results are compared to literature jumps. Ultimately, this enables the jumper to get a very detailed feedback of the flight. To achieve the maximal jump length, exact positioning of his body with respect to the air can be displayed.

Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems.

Science.gov (United States)

Wang, Fang; Chen, Bing; Lin, Chong; Li, Xuehua

2016-11-14

In this paper, a consensus tracking problem of nonlinear multiagent systems is investigated under a directed communication topology. All the followers are modeled by stochastic nonlinear systems in nonstrict feedback form, where nonlinearities and stochastic disturbance terms are totally unknown. Based on the structural characteristic of neural networks (in Lemma 4), a novel distributed adaptive neural control scheme is put forward. The raised control method not only effectively handles unknown nonlinearities in nonstrict feedback systems, but also copes with the interactions among agents and coupling terms. Based on the stochastic Lyapunov functional method, it is indicated that all the signals of the closed-loop system are bounded in probability and all followers' outputs are convergent to a neighborhood of the output of leader. At last, the efficiency of the control method is testified by a numerical example.

A feedback linearization approach to spacecraft control using momentum exchange devices. Ph.D. Thesis

Science.gov (United States)

Dzielski, John Edward

1988-01-01

Recent developments in the area of nonlinear control theory have shown how coordiante changes in the state and input spaces can be used with nonlinear feedback to transform certain nonlinear ordinary differential equations into equivalent linear equations. These feedback linearization techniques are applied to resolve two problems arising in the control of spacecraft equipped with control moment gyroscopes (CMGs). The first application involves the computation of rate commands for the gimbals that rotate the individual gyroscopes to produce commanded torques on the spacecraft. The second application is to the long-term management of stored momentum in the system of control moment gyroscopes using environmental torques acting on the vehicle. An approach to distributing control effort among a group of redundant actuators is described that uses feedback linearization techniques to parameterize sets of controls which influence a specified subsystem in a desired way. The approach is adapted for use in spacecraft control with double-gimballed gyroscopes to produce an algorithm that avoids problematic gimbal configurations by approximating sets of gimbal rates that drive CMG rotors into desirable configurations. The momentum management problem is stated as a trajectory optimization problem with a nonlinear dynamical constraint. Feedback linearization and collocation are used to transform this problem into an unconstrainted nonlinear program. The approach to trajectory optimization is fast and robust. A number of examples are presented showing applications to the proposed NASA space station.

Feedback control of nonlinear quantum systems: a rule of thumb.

Science.gov (United States)

Jacobs, Kurt; Lund, Austin P

2007-07-13

We show that in the regime in which feedback control is most effective - when measurements are relatively efficient, and feedback is relatively strong - then, in the absence of any sharp inhomogeneity in the noise, it is always best to measure in a basis that does not commute with the system density matrix than one that does. That is, it is optimal to make measurements that disturb the state one is attempting to stabilize.

Robust flight control using incremental nonlinear dynamic inversion and angular acceleration prediction

NARCIS (Netherlands)

Sieberling, S.; Chu, Q.P.; Mulder, J.A.

2010-01-01

This paper presents a flight control strategy based on nonlinear dynamic inversion. The approach presented, called incremental nonlinear dynamic inversion, uses properties of general mechanical systems and nonlinear dynamic inversion by feeding back angular accelerations. Theoretically, feedback of

Robust model predictive control for constrained continuous-time nonlinear systems

Science.gov (United States)

Sun, Tairen; Pan, Yongping; Zhang, Jun; Yu, Haoyong

2018-02-01

In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.

FEEDBACK LINEARISATION APPLIED ON A HYDRAULIC

DEFF Research Database (Denmark)

Andersen, Torben Ole; Hansen, Michael Rygaard; Pedersen, Henrik C.

2005-01-01

is on developing and applying several different feedback linearisation (FL) controllers to the individual servo actuators in a hydraulically driven servo robot to evaluate and compare their possiblities and limitations. This is done based on both simulation and experimental results.......Generally most hydraulic systems are intrensically non-linear, why applying linear control techniques typically results in conservatively dimensioned controllers to obtain stable performance. Non-linear control techniques have the potential of overcoming these problems, and in this paper the focus...

Advantages of coherent feedback for cooling quantum oscillators.

Science.gov (United States)

Hamerly, Ryan; Mabuchi, Hideo

2012-10-26

We model the cooling of open optical and optomechanical resonators via optical feedback in the linear quadratic Gaussian setting of stochastic control theory. We show that coherent feedback control schemes, in which the resonator is embedded in an interferometer to achieve all-optical feedback, can outperform the best possible linear quadratic Gaussian measurement-based schemes in the quantum regime of low steady-state excitation number. Such performance gains are attributed to the coherent controller's ability to process noncommuting output field quadratures simultaneously without loss of fidelity, and may provide important clues for the design of coherent feedback schemes for more general problems of nonlinear and robust control.

Adaptive Optimizing Nonlinear Control Design for an Over-actuated Aircraft Model

NARCIS (Netherlands)

Van Oort, E.R.; Sonneveldt, L.; Chu, Q.P.; Mulder, J.A.

2011-01-01

In this paper nonlinear adaptive flight control laws based on the backstepping approach are proposed which are applicable to over-actuated nonlinear systems. Instead of solving the control allocation exactly, update laws for the desired control effector signals are defined such that they converge to

Collapse of nonlinear Langmuir waves

International Nuclear Information System (INIS)

Malkin, V.M.

1986-01-01

The dispersion of sufficiently intensive Langmuir waves is determined by intrinsic (electron) nonlinearity. During Langmuir collapse the wave energy density required for the appearance of electron nonlinearity is attained, generally speaking, prior to the development of dissipative processes. Up to now, the effect of electron nonlinearity on the collapse dynamics and spectrum of strong Langmuir turbulence ( which may be very appreciable ) has not been studied extensively because of the difficulty of describing nonlinear Langmuir waves. In the present paper the positive determinacy of the electron nonlinear hamiltonian is proven, the increment of modulation instability of a nonlinear Langmuir wave cluster localized in a cavity is calculated, and the universal law of their collapse is found

Traders' strategy with price feedbacks in financial market

OpenAIRE

Mizuno, Takayuki; Nakano, Tohur; Takayasu, Misako; Takayasu, Hideki

2003-01-01

We introduce an autoregressive-type model of prices in financial market taking into account the self-modulation effect. We find that traders are mainly using strategies with weighted feedbacks of past prices. These feedbacks are responsible for the slow diffusion in short times, apparent trends and power law distribution of price changes.

Adaptive nonlinear control for a research reactor

International Nuclear Information System (INIS)

Benitez R, J.S.

1994-01-01

Linearization by feedback of states is based on the idea of transform the nonlinear dynamic equation of a system in a linear form. This linear behavior can be achieve well in a complete way (input state) or in partial way (input output). This can be applied to systems of single or multiple inputs, and can be used to solve problems of stabilization and tracking of references trajectories. Comparing this method with conventional ones, linearization by feedback of states is exact in certain region of the space of state, instead of linear approximations of the equations in a certain point of the operation. In the presence of parametric uncertainties in the model of the system, the introduction of adaptive schemes provide a type toughness to the control system by nonlinear feedback, which gives as result the eventual cancellation of the nonlinear terms in the dynamic relationship between the output and the input of the auxiliary control. In the same way, it has been presented the design of a nonlinearizing control for the non lineal model of a TRIGA Mark III type reactor, with the aim of tracking a predetermined power profile. The asymptotic tracking of such profile is, at the present moment, in the stage of verification by computerized simulation the relative easiness in the design of auxiliary variable of control, as well as the decoupling action of the output variable, make very attractive the utilization of the method herein presented. (Author)

Solutions and conservation laws of Benjamin–Bona–Mahony ...

Indian Academy of Sciences (India)

obtained with power-law and dual power-law nonlinearities. The Lie group analysis as ... The notion of conservation laws plays an important role in the solution process of differential ... For the theory and applications of Lie group analysis the ...

Edge turbulence control on the KT-5C tokamak by feedback using electrostatic probes

International Nuclear Information System (INIS)

Zhai Kan; Wang Cheng; Wen Yizi; Yu Changxuan; Wan Shude; Liu Wandong; Xu Zhizhan

1998-01-01

Experiments on edge turbulence control have been performed on the KT-5C tokamak by feedback using two sets of electrostatic probes as the driving probe and detective probe. The results indicate that the feedback can enhance or reduce the turbulence amplitude depending upon the phase shift and gain of the feedback network. When the feedback with 90 degree phase shift and with certain loop gain is applied, the spectrum component of turbulence is reduced obviously and the fluctuation amplitude of the electron density and electron temperature become lower by about 25%. consistently the particle flux across the magnetic field induced by the electrostatic fluctuation also decreases by about 25%. On the other hand, the feedback with 0 degree or 180 degree or -90 degree phase shift can enhance the amplitude of the edge turbulence. These results indicate a nonlinear mechanism of the influence of feedback on the edge turbulence, which to some extent also reflect a specific nonlinear characteristic of the edge turbulence

Convergence Guaranteed Nonlinear Constraint Model Predictive Control via I/O Linearization

Directory of Open Access Journals (Sweden)

Xiaobing Kong

2013-01-01

Full Text Available Constituting reliable optimal solution is a key issue for the nonlinear constrained model predictive control. Input-output feedback linearization is a popular method in nonlinear control. By using an input-output feedback linearizing controller, the original linear input constraints will change to nonlinear constraints and sometimes the constraints are state dependent. This paper presents an iterative quadratic program (IQP routine on the continuous-time system. To guarantee its convergence, another iterative approach is incorporated. The proposed algorithm can reach a feasible solution over the entire prediction horizon. Simulation results on both a numerical example and the continuous stirred tank reactors (CSTR demonstrate the effectiveness of the proposed method.

Robust receding horizon control for networked and distributed nonlinear systems

CERN Document Server

Li, Huiping

2017-01-01

This book offers a comprehensive, easy-to-understand overview of receding-horizon control for nonlinear networks. It presents novel general strategies that can simultaneously handle general nonlinear dynamics, system constraints, and disturbances arising in networked and large-scale systems and which can be widely applied. These receding-horizon-control-based strategies can achieve sub-optimal control performance while ensuring closed-loop stability: a feature attractive to engineers. The authors address the problems of networked and distributed control step-by-step, gradually increasing the level of challenge presented. The book first introduces the state-feedback control problems of nonlinear networked systems and then studies output feedback control problems. For large-scale nonlinear systems, disturbance is considered first, then communication delay separately, and lastly the simultaneous combination of delays and disturbances. Each chapter of this easy-to-follow book not only proposes and analyzes novel ...

A Fourier transform method for Vsin i estimations under nonlinear Limb-Darkening laws

Energy Technology Data Exchange (ETDEWEB)

Levenhagen, R. S., E-mail: ronaldo.levenhagen@gmail.com [Universidade Federal de São Paulo, Depto. Ciências Exatas e da Terra, Rua Prof. Arthur Riedel, 275, Jd. Eldorado, CEP 09972-270 Diadema, SP (Brazil)

2014-12-10

Star rotation offers us a large horizon for the study of many important physical issues pertaining to stellar evolution. Currently, four methods are widely used to infer rotation velocities, namely those related to line width calibrations, on the fitting of synthetic spectra, interferometry, and on Fourier transforms (FTs) of line profiles. Almost all of the estimations of stellar projected rotation velocities using the Fourier method in the literature have been addressed with the use of linear limb-darkening (LD) approximations during the evaluation of rotation profiles and their cosine FTs, which in certain cases, lead to discrepant velocity estimates. In this work, we introduce new mathematical expressions of rotation profiles and their Fourier cosine transforms assuming three nonlinear LD laws—quadratic, square-root, and logarithmic—and study their applications with and without gravity-darkening (GD) and geometrical flattening (GF) effects. Through an analysis of He I models in the visible range accounting for both limb and GD, we find out that, for classical models without rotationally driven effects, all the Vsin i values are too close to each other. On the other hand, taking into account GD and GF, the Vsin i obtained with the linear law result in Vsin i values that are systematically smaller than those obtained with the other laws. As a rule of thumb, we apply these expressions to the FT method to evaluate the projected rotation velocity of the emission B-type star Achernar (α Eri).

Fitts’ Law in the Control of Isometric Grip Force With Naturalistic Targets

Directory of Open Access Journals (Sweden)

Zachary C. Thumser

2018-04-01

Full Text Available Fitts’ law models the relationship between amplitude, precision, and speed of rapid movements. It is widely used to quantify performance in pointing tasks, study human-computer interaction, and generally to understand perceptual-motor information processes, including research to model performance in isometric force production tasks. Applying Fitts’ law to an isometric grip force task would allow for quantifying grasp performance in rehabilitative medicine and may aid research on prosthetic control and design. We examined whether Fitts’ law would hold when participants attempted to accurately produce their intended force output while grasping a manipulandum when presented with images of various everyday objects (we termed this the implicit task. Although our main interest was the implicit task, to benchmark it and establish validity, we examined performance against a more standard visual feedback condition via a digital force-feedback meter on a video monitor (explicit task. Next, we progressed from visual force feedback with force meter targets to the same targets without visual force feedback (operating largely on feedforward control with tactile feedback. This provided an opportunity to see if Fitts’ law would hold without vision, and allowed us to progress toward the more naturalistic implicit task (which does not include visual feedback. Finally, we changed the nature of the targets from requiring explicit force values presented as arrows on a force-feedback meter (explicit targets to the more naturalistic and intuitive target forces implied by images of objects (implicit targets. With visual force feedback the relation between task difficulty and the time to produce the target grip force was predicted by Fitts’ law (average r2 = 0.82. Without vision, average grip force scaled accurately although force variability was insensitive to the target presented. In contrast, images of everyday objects generated more reliable grip forces

Fitts' Law in the Control of Isometric Grip Force With Naturalistic Targets.

Science.gov (United States)

Thumser, Zachary C; Slifkin, Andrew B; Beckler, Dylan T; Marasco, Paul D

2018-01-01

Fitts' law models the relationship between amplitude, precision, and speed of rapid movements. It is widely used to quantify performance in pointing tasks, study human-computer interaction, and generally to understand perceptual-motor information processes, including research to model performance in isometric force production tasks. Applying Fitts' law to an isometric grip force task would allow for quantifying grasp performance in rehabilitative medicine and may aid research on prosthetic control and design. We examined whether Fitts' law would hold when participants attempted to accurately produce their intended force output while grasping a manipulandum when presented with images of various everyday objects (we termed this the implicit task). Although our main interest was the implicit task, to benchmark it and establish validity, we examined performance against a more standard visual feedback condition via a digital force-feedback meter on a video monitor (explicit task). Next, we progressed from visual force feedback with force meter targets to the same targets without visual force feedback (operating largely on feedforward control with tactile feedback). This provided an opportunity to see if Fitts' law would hold without vision, and allowed us to progress toward the more naturalistic implicit task (which does not include visual feedback). Finally, we changed the nature of the targets from requiring explicit force values presented as arrows on a force-feedback meter (explicit targets) to the more naturalistic and intuitive target forces implied by images of objects (implicit targets). With visual force feedback the relation between task difficulty and the time to produce the target grip force was predicted by Fitts' law (average r 2 = 0.82). Without vision, average grip force scaled accurately although force variability was insensitive to the target presented. In contrast, images of everyday objects generated more reliable grip forces without the visualized

Nonlinear waves in waveguides with stratification

CERN Document Server

Leble, Sergei B

1991-01-01

S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.

Improving the Critic Learning for Event-Based Nonlinear $H_{\\infty }$ Control Design.

Science.gov (United States)

Wang, Ding; He, Haibo; Liu, Derong

2017-10-01

In this paper, we aim at improving the critic learning criterion to cope with the event-based nonlinear H ∞ state feedback control design. First of all, the H ∞ control problem is regarded as a two-player zero-sum game and the adaptive critic mechanism is used to achieve the minimax optimization under event-based environment. Then, based on an improved updating rule, the event-based optimal control law and the time-based worst-case disturbance law are obtained approximately by training a single critic neural network. The initial stabilizing control is no longer required during the implementation process of the new algorithm. Next, the closed-loop system is formulated as an impulsive model and its stability issue is handled by incorporating the improved learning criterion. The infamous Zeno behavior of the present event-based design is also avoided through theoretical analysis on the lower bound of the minimal intersample time. Finally, the applications to an aircraft dynamics and a robot arm plant are carried out to verify the efficient performance of the present novel design method.

Effect of feedback and noise on fast ion instability

International Nuclear Information System (INIS)

Chao, A.W.; Stupakov, G.V.

1997-07-01

One can use a feedback system to suppress the fast ion instability. However, the feedback noise (and also other sources of noise in the machine) continuously excites the transient oscillations in the electron beam that are amplified through the electron interaction with the ions. We calculate the equilibrium level of these oscillations under the influence of the feedback and show how they grow exponentially from the head to the tail of the bunch train in a linear theory. Nonlinear saturation effects are assume negligible

Bayesian integration and non-linear feedback control in a full-body motor task.

Science.gov (United States)

Stevenson, Ian H; Fernandes, Hugo L; Vilares, Iris; Wei, Kunlin; Körding, Konrad P

2009-12-01

A large number of experiments have asked to what degree human reaching movements can be understood as being close to optimal in a statistical sense. However, little is known about whether these principles are relevant for other classes of movements. Here we analyzed movement in a task that is similar to surfing or snowboarding. Human subjects stand on a force plate that measures their center of pressure. This center of pressure affects the acceleration of a cursor that is displayed in a noisy fashion (as a cloud of dots) on a projection screen while the subject is incentivized to keep the cursor close to a fixed position. We find that salient aspects of observed behavior are well-described by optimal control models where a Bayesian estimation model (Kalman filter) is combined with an optimal controller (either a Linear-Quadratic-Regulator or Bang-bang controller). We find evidence that subjects integrate information over time taking into account uncertainty. However, behavior in this continuous steering task appears to be a highly non-linear function of the visual feedback. While the nervous system appears to implement Bayes-like mechanisms for a full-body, dynamic task, it may additionally take into account the specific costs and constraints of the task.

Bayesian integration and non-linear feedback control in a full-body motor task.

Directory of Open Access Journals (Sweden)

Ian H Stevenson

2009-12-01

Full Text Available A large number of experiments have asked to what degree human reaching movements can be understood as being close to optimal in a statistical sense. However, little is known about whether these principles are relevant for other classes of movements. Here we analyzed movement in a task that is similar to surfing or snowboarding. Human subjects stand on a force plate that measures their center of pressure. This center of pressure affects the acceleration of a cursor that is displayed in a noisy fashion (as a cloud of dots on a projection screen while the subject is incentivized to keep the cursor close to a fixed position. We find that salient aspects of observed behavior are well-described by optimal control models where a Bayesian estimation model (Kalman filter is combined with an optimal controller (either a Linear-Quadratic-Regulator or Bang-bang controller. We find evidence that subjects integrate information over time taking into account uncertainty. However, behavior in this continuous steering task appears to be a highly non-linear function of the visual feedback. While the nervous system appears to implement Bayes-like mechanisms for a full-body, dynamic task, it may additionally take into account the specific costs and constraints of the task.

Adaptive nonlinear robust relative pose control of spacecraft autonomous rendezvous and proximity operations.

Science.gov (United States)

Sun, Liang; Huo, Wei; Jiao, Zongxia

2017-03-01

This paper studies relative pose control for a rigid spacecraft with parametric uncertainties approaching to an unknown tumbling target in disturbed space environment. State feedback controllers for relative translation and relative rotation are designed in an adaptive nonlinear robust control framework. The element-wise and norm-wise adaptive laws are utilized to compensate the parametric uncertainties of chaser and target spacecraft, respectively. External disturbances acting on two spacecraft are treated as a lumped and bounded perturbation input for system. To achieve the prescribed disturbance attenuation performance index, feedback gains of controllers are designed by solving linear matrix inequality problems so that lumped disturbance attenuation with respect to the controlled output is ensured in the L 2 -gain sense. Moreover, in the absence of lumped disturbance input, asymptotical convergence of relative pose are proved by using the Lyapunov method. Numerical simulations are performed to show that position tracking and attitude synchronization are accomplished in spite of the presence of couplings and uncertainties. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Nonlinear Feedback Control of the Rotary Inverted Pendulum

Science.gov (United States)

2017-06-01

Feedback linearization has advantages over linearized control because of the ability to operate over a wider range of motion than the small...1sin 2 sin 2 sin 02 2 sin( )1 sin 2 2 xb J x J x x m Ll x x x D x gm l xJ x b f f x

Numerical Feedback Stabilization with Applications to Networks

Directory of Open Access Journals (Sweden)

Simone Göttlich

2017-01-01

Full Text Available The focus is on the numerical consideration of feedback boundary control problems for linear systems of conservation laws including source terms. We explain under which conditions the numerical discretization can be used to design feedback boundary values for network applications such as electric transmission lines or traffic flow systems. Several numerical examples illustrate the properties of the results for different types of networks.

Passivity based nonlinear attitude control of the Rømer satellite

DEFF Research Database (Denmark)

Quottrup, Michael Melholt; Krogh-Sørensen, J.; Wisniewski, Rafal

This paper suggests nonlinear attitude control of the Danish satellite Rømer. This satellite will be designed to fulfil two scientific objectives: The observation of stellar oscillations and the detection and localisation of gamma-ray bursts. The satellite will be equipped with a tetrahedron...... configuration of Wide Angle Telescopes for Cosmic Hard x-rays (WATCH), that server the dual purpose of X-ray detectors and momentum wheels. By employing passivity theory it is shown, that the satellite is a passive system. This paper shows, that global asymptotic can be obtained with a passive and an imput...... and output strictly passive system in a feedback interconnection. It is demonstrated in a simulation study that the resultant control has a potential for on-board implementation in the acquistion phase, where global stabillity of the control law is vital...

Nonlinear generalization of special relativity

International Nuclear Information System (INIS)

Winterberg, F.

1985-01-01

In Poincares axiomatic formulation special relativity is a derived consequence of a true Lorentz contraction, for a rod in absolute motion through a substratum. Furthermore, Lorentz had shown that the rod contraction can be understood by an inverse square law interaction and therefore special relativity derived from more fundamental principles. The derivation by Lorentz shows that the root of the divergence problems is the singular inverse square law. By replacing the inverse square law with a regular one through the introduction of a finite length, the author has succeeded in deriving a nonlinear generalization of special relativity which eliminates all infinities. Besides the relative velocities, these nonlinear transformation equations also contain absolute velocities against a substratum, but in the limit of small energies they go over into the linear Lorentz transformations. Depending on the smallness of the fundamental length, departures from special relativity can be observed only at very high energies. The theorem that the velocity of light is the same in all reference systems still holds and likewise the conservation laws for energy and momentum

Development of a Model Following Control Law for Inflight Simulation and Flight Controls Research

Science.gov (United States)

Takahashi, Mark; Fletcher, Jay; Aiken, Edwin W. (Technical Monitor)

1994-01-01

quality models that include rotor dynamics in a physically meaningful context must be available. A non-physical accounting of the rotor, such as lumping the effect as a time delay, is not likely to produce the desired results. High order simulation models based on first principals are satisfactory for the initial design phase in order to work out the control law design concept and get an initial set of gains. These models, however, have known deficiencies, which must be resolved in the final control law design. The error in the pitch-roll cross coupling is one notable deficiency that even sophisticated rotorcraft models including complex wake aerodynamics have yet to capture successfully. This error must be accounted for to achieve the desired decoupling. The approach to design the proposed inflight simulation control law is based on using a combination of simulation and identified models. The linear and nonlinear higher order models were used to develop an explicit model following control structure. This structure was developed to accommodate the design of control laws compliant to many of the quantitative requirements in ADS-33C. Furthermore, it also allows for control law research using rotor-state feedback and other design methodologies such as Quantitative Feedback and H-Infinity. Final gain selection will be based on higher order identified models which include rotor degrees of freedom.

Time-delayed feedback control of diffusion in random walkers

Science.gov (United States)

Ando, Hiroyasu; Takehara, Kohta; Kobayashi, Miki U.

2017-07-01

Time delay in general leads to instability in some systems, while specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a stochastic process, i.e., a random walk, and observe its diffusion phenomenon with time-delayed feedback. As a result, the diffusion coefficient decreases with increasing delay time. We analytically illustrate this suppression of diffusion by using stochastic delay differential equations and justify the feasibility of this suppression by applying time-delayed feedback to a molecular dynamics model.

Nonlinear Dot Plots.

Science.gov (United States)

Rodrigues, Nils; Weiskopf, Daniel

2018-01-01

Conventional dot plots use a constant dot size and are typically applied to show the frequency distribution of small data sets. Unfortunately, they are not designed for a high dynamic range of frequencies. We address this problem by introducing nonlinear dot plots. Adopting the idea of nonlinear scaling from logarithmic bar charts, our plots allow for dots of varying size so that columns with a large number of samples are reduced in height. For the construction of these diagrams, we introduce an efficient two-way sweep algorithm that leads to a dense and symmetrical layout. We compensate aliasing artifacts at high dot densities by a specifically designed low-pass filtering method. Examples of nonlinear dot plots are compared to conventional dot plots as well as linear and logarithmic histograms. Finally, we include feedback from an expert review.

How Are Feedbacks Represented in Land Models?

Directory of Open Access Journals (Sweden)

Yang Chen

2016-09-01

Full Text Available Land systems are characterised by many feedbacks that can result in complex system behaviour. We defined feedbacks as the two-way influences between the land use system and a related system (e.g., climate, soils and markets, both of which are encompassed by the land system. Land models that include feedbacks thus probably more accurately mimic how land systems respond to, e.g., policy or climate change. However, representing feedbacks in land models is a challenge. We reviewed articles incorporating feedbacks into land models and analysed each with predefined indicators. We found that (1 most modelled feedbacks couple land use systems with transport, soil and market systems, while only a few include feedbacks between land use and social systems or climate systems; (2 equation-based land use models that follow a top-down approach prevail; and (3 feedbacks’ effects on system behaviour remain relatively unexplored. We recommend that land system modellers (1 consider feedbacks between land use systems and social systems; (2 adopt (bottom-up approaches suited to incorporating spatial heterogeneity and better representing land use decision-making; and (3 pay more attention to nonlinear system behaviour and its implications for land system management and policy.

Convexity and Weighted Integral Inequalities for Energy Decay Rates of Nonlinear Dissipative Hyperbolic Systems

International Nuclear Information System (INIS)

Alabau-Boussouira, Fatiha

2005-01-01

This work is concerned with the stabilization of hyperbolic systems by a nonlinear feedback which can be localized on a part of the boundary or locally distributed. We show that general weighted integral inequalities together with convexity arguments allow us to produce a general semi-explicit formula which leads to decay rates of the energy in terms of the behavior of the nonlinear feedback close to the origin. This formula allows us to unify for instance the cases where the feedback has a polynomial growth at the origin, with the cases where it goes exponentially fast to zero at the origin. We also give three other significant examples of nonpolynomial growth at the origin. We also prove the optimality of our results for the one-dimensional wave equation with nonlinear boundary dissipation. The key property for obtaining our general energy decay formula is the understanding between convexity properties of an explicit function connected to the feedback and the dissipation of energy

Limitations of Feedback, Feedforward and IMC Controller for a First Order Non-Linear Process with Dead Time

Directory of Open Access Journals (Sweden)

Maruthai Suresh

2010-10-01

Full Text Available A nonlinear process, the heat exchanger whose parameters vary with respect to the process variable, is considered. The time constant and gain of the chosen process vary as a function of temperature. The limitations of the conventional feedback controller tuned using Ziegler-Nichols settings for the chosen process are brought out. The servo and regulatory responses through simulation and experimentation for various magnitudes of set-point changes and load changes at various operating points with the controller tuned only at a chosen nominal operating point are obtained and analyzed. Regulatory responses for output load changes are studied. The efficiency of feedforward controller and the effects of modeling error have been brought out. An IMC based system is presented to understand clearly how variations of system parameters affect the performance of the controller. The present work illustrates the effectiveness of Feedforward and IMC controller.

Nonlinear resonance in Duffing oscillator with fixed and integrative ...

Indian Academy of Sciences (India)

We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Duffing oscillator with two types of time-delayed feedbacks, namely, fixed and integrative. Particularly, we analyse the effect of the time-delay parameter and the strength of the ...

Nonlinear resonance in Duffing oscillator with fixed and integrative ...

Indian Academy of Sciences (India)

2012-03-02

Mar 2, 2012 ... Abstract. We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Duffing oscillator with two types of time-delayed feedbacks, namely, fixed and integrative. Particularly, we analyse the effect of the time-delay parameter α and the ...

A stochastic optimal feedforward and feedback control methodology for superagility

Science.gov (United States)

Halyo, Nesim; Direskeneli, Haldun; Taylor, Deborah B.

1992-01-01

A new control design methodology is developed: Stochastic Optimal Feedforward and Feedback Technology (SOFFT). Traditional design techniques optimize a single cost function (which expresses the design objectives) to obtain both the feedforward and feedback control laws. This approach places conflicting demands on the control law such as fast tracking versus noise atttenuation/disturbance rejection. In the SOFFT approach, two cost functions are defined. The feedforward control law is designed to optimize one cost function, the feedback optimizes the other. By separating the design objectives and decoupling the feedforward and feedback design processes, both objectives can be achieved fully. A new measure of command tracking performance, Z-plots, is also developed. By analyzing these plots at off-nominal conditions, the sensitivity or robustness of the system in tracking commands can be predicted. Z-plots provide an important tool for designing robust control systems. The Variable-Gain SOFFT methodology was used to design a flight control system for the F/A-18 aircraft. It is shown that SOFFT can be used to expand the operating regime and provide greater performance (flying/handling qualities) throughout the extended flight regime. This work was performed under the NASA SBIR program. ICS plans to market the software developed as a new module in its commercial CACSD software package: ACET.

Feedback control of thermal instability by compression and decompression

International Nuclear Information System (INIS)

Okamoto, M.; Hirano, K.; Amano, T.; Ohnishi, M.

1983-01-01

Active feedback control of the fusion output power by means of plasma compression-decompression is considered with the purpose of achieving steady-state plasma ignition in a tokamak. A simple but realistic feedback control system is modelled and zero-dimensional energy balance equations are solved numerically by taking into account the errors in the measurements, a procedure that is necessary for the feedback control. It is shown that the control can stabilize the thermal runaway completely and maintain steady-state operation without any significant change in major radius or thermal output power. Linear stability is analysed for a general type of scaling law, and the dependence of the stability conditions on the scaling law is studied. The possibility of load-following operation is considered. Finally, a one-dimensional analysis is applied to the large-aspect-ratio case. (author)

Taylor's series method for solving the nonlinear point kinetics equations

International Nuclear Information System (INIS)

Nahla, Abdallah A.

2011-01-01

Highlights: → Taylor's series method for nonlinear point kinetics equations is applied. → The general order of derivatives are derived for this system. → Stability of Taylor's series method is studied. → Taylor's series method is A-stable for negative reactivity. → Taylor's series method is an accurate computational technique. - Abstract: Taylor's series method for solving the point reactor kinetics equations with multi-group of delayed neutrons in the presence of Newtonian temperature feedback reactivity is applied and programmed by FORTRAN. This system is the couples of the stiff nonlinear ordinary differential equations. This numerical method is based on the different order derivatives of the neutron density, the precursor concentrations of i-group of delayed neutrons and the reactivity. The r th order of derivatives are derived. The stability of Taylor's series method is discussed. Three sets of applications: step, ramp and temperature feedback reactivities are computed. Taylor's series method is an accurate computational technique and stable for negative step, negative ramp and temperature feedback reactivities. This method is useful than the traditional methods for solving the nonlinear point kinetics equations.

Dynamical control of chaos by slave-master feedback

International Nuclear Information System (INIS)

Behnia, S.; Akhshani, A.

2009-01-01

Techniques for stabilizing unstable state in nonlinear dynamical systems using small perturbations fall into three general categories: feedback, non-feedback schemes, and a combination of feedback and non-feedback. However, the general problem of finding conditions for creation or suppression of chaos still remains open. We describe a method for dynamical control of chaos. This method is based on a definition of the hierarchy of solvable chaotic maps with dynamical parameter as a control parameter. In order to study the new mechanism of control of chaotic process, Kolmogorov-Sinai entropy of the chaotic map with dynamical parameter based on discussion the properties of invariant measure have been calculated and confirmed by calculation of Lyapunov exponents. The introduced chaotic maps can be used as dynamical control.

Pramana – Journal of Physics | Indian Academy of Sciences

Indian Academy of Sciences (India)

Proportional, adaptive proportional and discontinuous non-linear (DNL) control methods were used to derive the control laws. The first method employed occasional proportional feedback. The adaptive method used spatio-temporal feedback control. The DNL method used a discontinuous feedback linearization procedure, ...

Robust nonlinear control of nuclear reactors under model uncertainty

International Nuclear Information System (INIS)

Park, Moon Ghu

1993-02-01

A nonlinear model-based control method is developed for the robust control of a nuclear reactor. The nonlinear plant model is used to design a unique control law which covers a wide operating range. The robustness is a crucial factor for the fully automatic control of reactor power due to time-varying, uncertain parameters, and state estimation error, or unmodeled dynamics. A variable structure control (VSC) method is introduced which consists of an adaptive performance specification (fime control) after the tracking error reaches the narrow boundary-layer by a time-optimal control (coarse control). Variable structure control is a powerful method for nonlinear system controller design which has inherent robustness to parameter variations or external disturbances using the known uncertainty bounds, and it requires very low computational efforts. In spite of its desirable properties, conventional VSC presents several important drawbacks that limit its practical applicability. One of the most undesirable phenomena is chattering, which implies extremely high control activity and may excite high-frequency unmodeled dynamics. This problem is due to the neglected actuator time-delay or sampling effects. The problem was partially remedied by replacing chattering control by a smooth control inter-polation in a boundary layer neighnboring a time-varying sliding surface. But, for the nuclear reactor systems which has very fast dynamic response, the sampling effect may destroy the narrow boundary layer when a large uncertainty bound is used. Due to the very short neutron life time, large uncertainty bound leads to the high gain in feedback control. To resolve this problem, a derivative feedback is introduced that gives excellent performance by reducing the uncertainty bound. The stability of tracking error dynamics is guaranteed by the second method of Lyapunov using the two-level uncertainty bounds that are obtained from the knowledge of uncertainty bound and the estimated

Nonlinear Control of Heartbeat Models

Directory of Open Access Journals (Sweden)

Witt Thanom

2011-02-01

Full Text Available This paper presents a novel application of nonlinear control theory to heartbeat models. Existing heartbeat models are investigated and modified by incorporating the control input as a pacemaker to provide the control channel. A nonlinear feedback linearization technique is applied to force the output of the systems to generate artificial electrocardiogram (ECG signal using discrete data as the reference inputs. The synthetic ECG may serve as a flexible signal source to assess the effectiveness of a diagnostic ECG signal-processing device.

Tutorial on nonlinear backstepping: Applications to ship control

Directory of Open Access Journals (Sweden)

Thor I. Fossen

1999-04-01

Full Text Available The theoretical foundation of nonlinear backstepping designs is presented in a tutorial setting. This includes a brief review of integral backstepping, extensions to SISO and MIMO systems in strict feedback form and physical motivated case studies. Parallels and differences to feedback linearization where it is shown how so-called "good nonlincarities" can be exploited in the design are also made.

Generalized non-linear Schroedinger hierarchy

International Nuclear Information System (INIS)

Aratyn, H.; Gomes, J.F.; Zimerman, A.H.

1994-01-01

The importance in studying the completely integrable models have became evident in the last years due to the fact that those models present an algebraic structure extremely rich, providing the natural scenery for solitons description. Those models can be described through non-linear differential equations, pseudo-linear operators (Lax formulation), or a matrix formulation. The integrability implies in the existence of a conservation law associated to each of degree of freedom. Each conserved charge Q i can be associated to a Hamiltonian, defining a time evolution related to to a time t i through the Hamilton equation ∂A/∂t i =[A,Q i ]. Particularly, for a two-dimensions field theory, infinite degree of freedom exist, and consequently infinite conservation laws describing the time evolution in space of infinite times. The Hamilton equation defines a hierarchy of models which present a infinite set of conservation laws. This paper studies the generalized non-linear Schroedinger hierarchy

PEP-II RF feedback system simulation

Energy Technology Data Exchange (ETDEWEB)

Tighe, R [Stanford Linear Accelerator Center, Menlo Park, CA (United States)

1996-08-01

A model containing the fundamental impedance of the PEP-II cavity along with the longitudinal beam dynamics and RF feedback system components is in use. It is prepared in a format allowing time-domain as well as frequency-domain analysis and full graphics capability. Matlab and Simulink are control system design and analysis programs (widely available) with many built-in tools. The model allows the use of compiled C-code modules for compute intensive portions. We desire to represent as nearly as possible the components of the feedback system including all delays, sample rates and applicable nonlinearities. (author)

Periodic feedback stabilization for linear periodic evolution equations

CERN Document Server

Wang, Gengsheng

2016-01-01

This book introduces a number of recent advances regarding periodic feedback stabilization for linear and time periodic evolution equations. First, it presents selected connections between linear quadratic optimal control theory and feedback stabilization theory for linear periodic evolution equations. Secondly, it identifies several criteria for the periodic feedback stabilization from the perspective of geometry, algebra and analyses respectively. Next, it describes several ways to design periodic feedback laws. Lastly, the book introduces readers to key methods for designing the control machines. Given its coverage and scope, it offers a helpful guide for graduate students and researchers in the areas of control theory and applied mathematics.

Fuzzy robust nonlinear control approach for electro-hydraulic flight motion simulator

Directory of Open Access Journals (Sweden)

Han Songshan

2015-02-01

Full Text Available A fuzzy robust nonlinear controller for hydraulic rotary actuators in flight motion simulators is proposed. Compared with other three-order models of hydraulic rotary actuators, the proposed controller based on first-order nonlinear model is more easily applied in practice, whose control law is relatively simple. It not only does not need high-order derivative of desired command, but also does not require the feedback signals of velocity, acceleration and jerk of hydraulic rotary actuators. Another advantage is that it does not rely on any information of friction, inertia force and external disturbing force/torque, which are always difficult to resolve in flight motion simulators. Due to the special composite vane seals of rectangular cross-section and goalpost shape used in hydraulic rotary actuators, the leakage model is more complicated than that of traditional linear hydraulic cylinders. Adaptive multi-input single-output (MISO fuzzy compensators are introduced to estimate nonlinear uncertain functions about leakage and bulk modulus. Meanwhile, the decomposition of the uncertainties is used to reduce the total number of fuzzy rules. Different from other adaptive fuzzy compensators, a discontinuous projection mapping is employed to guarantee the estimation process to be bounded. Furthermore, with a sufficient number of fuzzy rules, the controller theoretically can guarantee asymptotic tracking performance in the presence of the above uncertainties, which is very important for high-accuracy tracking control of flight motion simulators. Comparative experimental results demonstrate the effectiveness of the proposed algorithm, which can guarantee transient performance and better final accurate tracking in the presence of uncertain nonlinearities and parametric uncertainties.

Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits

KAUST Repository

Ge, Xiaoqing

2010-12-01

Hassan Khalil’s research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building blocks in digital systems. The paper first investigates local and global stability properties of an n-stage ring oscillator by making use of its cyclic structure. It next studies global stability properties of a class of cross-coupled oscillators which admit the representation of a dynamic system in feedback with a static nonlinearity, and presents su cient conditions for almost global convergence of the solutions to a limit cycle when the feedback gain is in the vicinity of a bifurcation point. The result are also extended to the synchronization of interconnected identical oscillator circuits.

Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits

KAUST Repository

Ge, Xiaoqing; Arcak, Murat; Salama, Khaled N.

2010-01-01

Hassan Khalil’s research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building blocks in digital systems. The paper first investigates local and global stability properties of an n-stage ring oscillator by making use of its cyclic structure. It next studies global stability properties of a class of cross-coupled oscillators which admit the representation of a dynamic system in feedback with a static nonlinearity, and presents su cient conditions for almost global convergence of the solutions to a limit cycle when the feedback gain is in the vicinity of a bifurcation point. The result are also extended to the synchronization of interconnected identical oscillator circuits.

Quantifying the ice-albedo feedback through decoupling

Science.gov (United States)

Kravitz, B.; Rasch, P. J.

2017-12-01

The ice-albedo feedback involves numerous individual components, whereby warming induces sea ice melt, inducing reduced surface albedo, inducing increased surface shortwave absorption, causing further warming. Here we attempt to quantify the sea ice albedo feedback using an analogue of the "partial radiative perturbation" method, but where the governing mechanisms are directly decoupled in a climate model. As an example, we can isolate the insulating effects of sea ice on surface energy and moisture fluxes by allowing sea ice thickness to change but fixing Arctic surface albedo, or vice versa. Here we present results from such idealized simulations using the Community Earth System Model in which individual components are successively fixed, effectively decoupling the ice-albedo feedback loop. We isolate the different components of this feedback, including temperature change, sea ice extent/thickness, and air-sea exchange of heat and moisture. We explore the interactions between these different components, as well as the strengths of the total feedback in the decoupled feedback loop, to quantify contributions from individual pieces. We also quantify the non-additivity of the effects of the components as a means of investigating the dominant sources of nonlinearity in the ice-albedo feedback.

Nonlinear saturation controller for vibration supersession of a nonlinear composite beam

Energy Technology Data Exchange (ETDEWEB)

Hamed, Y. S. [Menofia University, Menouf (Egypt); Amer, Y. A. [Zagazig University, Zagazig (Egypt)

2014-08-15

In this paper, a study for nonlinear saturation controller (NSC) is presented that used to suppress the vibration amplitude of a structural dynamic model simulating nonlinear composite beam at simultaneous sub-harmonic and internal resonance excitation. The absorber exploits the saturation phenomenon that is known to occur in dynamical systems with quadratic non-linearities of the feedback gain and a two-to-one internal resonance. The analytical solution for the system and the nonlinear saturation controller are obtained using method of multiple time scales perturbation up to the second order approximation. All possible resonance cases were extracted at this approximation order and studied numerically. The stability of the system at the worst resonance case (Ω = 2ω{sub s} and ω{sub s} =2ω{sub C}) is investigated using both frequency response equations and phase-plane trajectories. The effects of different parameters on the system and the controller are studied numerically. The effect of some types of controller on the system is investigated numerically. The simulation results are achieved using Matlab and Maple programs.

Distributed Cooperative Current-Sharing Control of Parallel Chargers Using Feedback Linearization

Directory of Open Access Journals (Sweden)

Jiangang Liu

2014-01-01

Full Text Available We propose a distributed current-sharing scheme to address the output current imbalance problem for the parallel chargers in the energy storage type light rail vehicle system. By treating the parallel chargers as a group of agents with output information sharing through communication network, the current-sharing control problem is recast as the consensus tracking problem of multiagents. To facilitate the design, input-output feedback linearization is first applied to transform the nonidentical nonlinear charging system model into the first-order integrator. Then, a general saturation function is introduced to design the cooperative current-sharing control law which can guarantee the boundedness of the proposed control. The cooperative stability of the closed-loop system under fixed and dynamic communication topologies is rigorously proved with the aid of Lyapunov function and LaSalle invariant principle. Simulation using a multicharging test system further illustrates that the output currents of parallel chargers are balanced using the proposed control.

Nonlinear GARCH model and 1 / f noise

Science.gov (United States)

Kononovicius, A.; Ruseckas, J.

2015-06-01

Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1,1) process and its nonlinear modifications, reminiscent of NGARCH model. We investigate the possibility to reproduce power law statistics, probability density function and power spectral density, using ARCH family models. For this purpose we derive stochastic differential equations from the GARCH processes in consideration. We find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics. We show that linear GARCH(1,1) process has power law distribution, but its power spectral density is Brownian noise-like. However, the nonlinear modifications exhibit both power law distribution and power spectral density of the 1 /fβ form, including 1 / f noise.

Dynamics and control of a financial system with time-delayed feedbacks

International Nuclear Information System (INIS)

Chen, W.-C.

2008-01-01

Complex behaviors in a financial system with time-delayed feedbacks are discussed in this study via numerical modeling. The system shows complex dynamics such as periodic, quasi-periodic, and chaotic behaviors. Both period doubling and inverse period doubling routes were found in this system. This paper also shows that the attractor merging crisis is a fundamental feature of nonlinear financial systems with time-delayed feedbacks. Control of the deterministic chaos in the financial system can be realized using Pyragas feedbacks

Nonlinear analysis and control of a continuous fermentation process

DEFF Research Database (Denmark)

Szederkényi, G.; Kristensen, Niels Rode; Hangos, K.M

2002-01-01

Different types of nonlinear controllers are designed and compared for a simple continuous bioreactor operating near optimal productivity. This operating point is located close to a fold bifurcation point. Nonlinear analysis of stability, controllability and zero dynamics is used to investigate o...... are recommended for the simple fermenter. Passivity based controllers have been found to be globally stable, not very sensitive to the uncertainties in the reaction rate and controller parameter but they require full nonlinear state feedback....

Energy harvesting with stacked dielectric elastomer transducers: Nonlinear theory, optimization, and linearized scaling law

Science.gov (United States)

Tutcuoglu, A.; Majidi, C.

2014-12-01

Using principles of damped harmonic oscillation with continuous media, we examine electrostatic energy harvesting with a "soft-matter" array of dielectric elastomer (DE) transducers. The array is composed of infinitely thin and deformable electrodes separated by layers of insulating elastomer. During vibration, it deforms longitudinally, resulting in a change in the capacitance and electrical enthalpy of the charged electrodes. Depending on the phase of electrostatic loading, the DE array can function as either an actuator that amplifies small vibrations or a generator that converts these external excitations into electrical power. Both cases are addressed with a comprehensive theory that accounts for the influence of viscoelasticity, dielectric breakdown, and electromechanical coupling induced by Maxwell stress. In the case of a linearized Kelvin-Voigt model of the dielectric, we obtain a closed-form estimate for the electrical power output and a scaling law for DE generator design. For the complete nonlinear model, we obtain the optimal electrostatic voltage input for maximum electrical power output.

A Nonlinear Fuel Optimal Reaction Jet Control Law

National Research Council Canada - National Science Library

Breitfeller, Eric

2002-01-01

We derive a nonlinear fuel optimal attitude control system (ACS) that drives the final state to the desired state according to a cost function that weights the final state angular error relative to the angular rate error...

Nonlinear Control of Induction Motors: A Performance Study

DEFF Research Database (Denmark)

Rasmussen, Henrik; Vadstrup, P.; Børsting, H.

1998-01-01

A novel approach to control of induction motors based on nonlinear state feedback has previously been presented by the authors. The resulting scheme gives a linearized input-output decoupling of the torque and the amplitude of the field. The proposed approach is used to design controllers for the...... for the field amplitude and the motor torque. The method is compared with the traditional Rotor Field Oriented Control method as regards variations in rotor resistance an magnetizing inductance......A novel approach to control of induction motors based on nonlinear state feedback has previously been presented by the authors. The resulting scheme gives a linearized input-output decoupling of the torque and the amplitude of the field. The proposed approach is used to design controllers...

Hadron–Quark Combustion as a Nonlinear, Dynamical System

Science.gov (United States)

Ouyed, Amir; Ouyed, Rachid; Jaikumar, Prashanth

2018-03-01

The hadron-quark combustion front is a system that couples various processes, such as chemical reactions, hydrodynamics, diffusion, and neutrino transport. Previous numerical work has shown that this system is very nonlinear, and can be very sensitive to some of these processes. In these proceedings, we contextualize the hadron-quark combustion as a nonlinear system, subject to dramatic feedback triggered by leptonic weak decays and neutrino transport.

Fractional analysis for nonlinear electrical transmission line and nonlinear Schroedinger equations with incomplete sub-equation

Science.gov (United States)

Fendzi-Donfack, Emmanuel; Nguenang, Jean Pierre; Nana, Laurent

2018-02-01

We use the fractional complex transform with the modified Riemann-Liouville derivative operator to establish the exact and generalized solutions of two fractional partial differential equations. We determine the solutions of fractional nonlinear electrical transmission lines (NETL) and the perturbed nonlinear Schroedinger (NLS) equation with the Kerr law nonlinearity term. The solutions are obtained for the parameters in the range (0<α≤1) of the derivative operator and we found the traditional solutions for the limiting case of α =1. We show that according to the modified Riemann-Liouville derivative, the solutions found can describe physical systems with memory effect, transient effects in electrical systems and nonlinear transmission lines, and other systems such as optical fiber.

Semiglobal H-infinity State Feedback Control

DEFF Research Database (Denmark)

Cromme, Marc; Stoustrup, Jakob

1996-01-01

Semi-global set-stabilizing H-infinity controlis a local within some given compact set such that all statetrajectories are bounded inside the set, and are approaching an openloop invariant subset as time approaches infinity. Sufficientconditions for the existence of a continuous state feedback law...

Renormalization, averaging, conservation laws and AdS (in)stability

International Nuclear Information System (INIS)

Craps, Ben; Evnin, Oleg; Vanhoof, Joris

2015-01-01

We continue our analytic investigations of non-linear spherically symmetric perturbations around the anti-de Sitter background in gravity-scalar field systems, and focus on conservation laws restricting the (perturbatively) slow drift of energy between the different normal modes due to non-linearities. We discover two conservation laws in addition to the energy conservation previously discussed in relation to AdS instability. A similar set of three conservation laws was previously noted for a self-interacting scalar field in a non-dynamical AdS background, and we highlight the similarities of this system to the fully dynamical case of gravitational instability. The nature of these conservation laws is best understood through an appeal to averaging methods which allow one to derive an effective Lagrangian or Hamiltonian description of the slow energy transfer between the normal modes. The conservation laws in question then follow from explicit symmetries of this averaged effective theory.

Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations

International Nuclear Information System (INIS)

Hong Jialin; Li Chun

2006-01-01

In this paper, we consider the multi-symplectic Runge-Kutta (MSRK) methods applied to the nonlinear Dirac equation in relativistic quantum physics, based on a discovery of the multi-symplecticity of the equation. In particular, the conservation of energy, momentum and charge under MSRK discretizations is investigated by means of numerical experiments and numerical comparisons with non-MSRK methods. Numerical experiments presented reveal that MSRK methods applied to the nonlinear Dirac equation preserve exactly conservation laws of charge and momentum, and conserve the energy conservation in the corresponding numerical accuracy to the method utilized. It is verified numerically that MSRK methods are stable and convergent with respect to the conservation laws of energy, momentum and charge, and MSRK methods preserve not only the inner geometric structure of the equation, but also some crucial conservative properties in quantum physics. A remarkable advantage of MSRK methods applied to the nonlinear Dirac equation is the precise preservation of charge conservation law

Reinforcement learning controller design for affine nonlinear discrete-time systems using online approximators.

Science.gov (United States)

Yang, Qinmin; Jagannathan, Sarangapani

2012-04-01

In this paper, reinforcement learning state- and output-feedback-based adaptive critic controller designs are proposed by using the online approximators (OLAs) for a general multi-input and multioutput affine unknown nonlinear discretetime systems in the presence of bounded disturbances. The proposed controller design has two entities, an action network that is designed to produce optimal signal and a critic network that evaluates the performance of the action network. The critic estimates the cost-to-go function which is tuned online using recursive equations derived from heuristic dynamic programming. Here, neural networks (NNs) are used both for the action and critic whereas any OLAs, such as radial basis functions, splines, fuzzy logic, etc., can be utilized. For the output-feedback counterpart, an additional NN is designated as the observer to estimate the unavailable system states, and thus, separation principle is not required. The NN weight tuning laws for the controller schemes are also derived while ensuring uniform ultimate boundedness of the closed-loop system using Lyapunov theory. Finally, the effectiveness of the two controllers is tested in simulation on a pendulum balancing system and a two-link robotic arm system.

Social-ecological resilience and law

Science.gov (United States)

Garmestani, Ahjond S.; Allen, Craig R.

2014-01-01

Environmental law envisions ecological systems as existing in an equilibrium state, reinforcing a rigid legal framework unable to absorb rapid environmental changes and innovations in sustainability. For the past four decades, “resilience theory,” which embraces uncertainty and nonlinear dynamics in complex adaptive systems, has provided a robust, invaluable foundation for sound environmental management. Reforming American law to incorporate this knowledge is the key to sustainability. This volume features top legal and resilience scholars speaking on resilience theory and its legal applications to climate change, biodiversity, national parks, and water law.

An Artificial Neural Network Compensated Output Feedback Power-Level Control for Modular High Temperature Gas-Cooled Reactors

Directory of Open Access Journals (Sweden)

Zhe Dong

2014-02-01

Full Text Available Small modular reactors (SMRs could be beneficial in providing electricity power safely and also be viable for applications such as seawater desalination and heat production. Due to its inherent safety features, the modular high temperature gas-cooled reactor (MHTGR has been seen as one of the best candidates for building SMR-based nuclear power plants. Since the MHTGR dynamics display high nonlinearity and parameter uncertainty, it is necessary to develop a nonlinear adaptive power-level control law which is not only beneficial to the safe, stable, efficient and autonomous operation of the MHTGR, but also easy to implement practically. In this paper, based on the concept of shifted-ectropy and the physically-based control design approach, it is proved theoretically that the simple proportional-differential (PD output-feedback power-level control can provide asymptotic closed-loop stability. Then, based on the strong approximation capability of the multi-layer perceptron (MLP artificial neural network (ANN, a compensator is established to suppress the negative influence caused by system parameter uncertainty. It is also proved that the MLP-compensated PD power-level control law constituted by an experientially-tuned PD regulator and this MLP-based compensator can guarantee bounded closed-loop stability. Numerical simulation results not only verify the theoretical results, but also illustrate the high performance of this MLP-compensated PD power-level controller in suppressing the oscillation of process variables caused by system parameter uncertainty.

Adaptive feedback linearization applied to steering of ships

Directory of Open Access Journals (Sweden)

Thor I. Fossen

1993-10-01

Full Text Available This paper describes the application of feedback linearization to automatic steering of ships. The flexibility of the design procedure allows the autopilot to be optimized for both course-keeping and course-changing manoeuvres. Direct adaptive versions of both the course-keeping and turning controller are derived. The advantages of the adaptive controllers are improved performance and reduced fuel consumption. The application of nonlinear control theory also allows the designer in a systematic manner to compensate for nonlinearities in the control design.

Front tracking for hyperbolic conservation laws

CERN Document Server

Holden, Helge

2002-01-01

Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included. "It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." D. Serre, MathSciNet "I have read the book with great pleasure, and I can recommend it to experts as well as students. It can also be used for reliable and very exciting basis for a one-semester graduate course." S. Noelle, Book review, German Math. Soc. "Making it an ideal first book for the theory of nonlinear partial differential equations...an excellent reference for a graduate course on nonlinear conservation laws." M. Laforest, Comp. Phys. Comm.

Reinforcement-learning-based output-feedback control of nonstrict nonlinear discrete-time systems with application to engine emission control.

Science.gov (United States)

Shih, Peter; Kaul, Brian C; Jagannathan, Sarangapani; Drallmeier, James A

2009-10-01

A novel reinforcement-learning-based output adaptive neural network (NN) controller, which is also referred to as the adaptive-critic NN controller, is developed to deliver the desired tracking performance for a class of nonlinear discrete-time systems expressed in nonstrict feedback form in the presence of bounded and unknown disturbances. The adaptive-critic NN controller consists of an observer, a critic, and two action NNs. The observer estimates the states and output, and the two action NNs provide virtual and actual control inputs to the nonlinear discrete-time system. The critic approximates a certain strategic utility function, and the action NNs minimize the strategic utility function and control inputs. All NN weights adapt online toward minimization of a performance index, utilizing the gradient-descent-based rule, in contrast with iteration-based adaptive-critic schemes. Lyapunov functions are used to show the stability of the closed-loop tracking error, weights, and observer estimates. Separation and certainty equivalence principles, persistency of excitation condition, and linearity in the unknown parameter assumption are not needed. Experimental results on a spark ignition (SI) engine operating lean at an equivalence ratio of 0.75 show a significant (25%) reduction in cyclic dispersion in heat release with control, while the average fuel input changes by less than 1% compared with the uncontrolled case. Consequently, oxides of nitrogen (NO(x)) drop by 30%, and unburned hydrocarbons drop by 16% with control. Overall, NO(x)'s are reduced by over 80% compared with stoichiometric levels.

High-Speed Chaos in an Optical Feedback System with Flexible Timescales

National Research Council Canada - National Science Library

Blakely, Jonathan

2003-01-01

We describe a new optoelectronic device with timedelayed feedback that uses a Mach-Zehnder interferometer as passive nonlinearity and a semiconductor laser as a current-to-optical frequency converter...

Feedback coupling in dynamical systems

Science.gov (United States)

Trimper, Steffen; Zabrocki, Knud

2003-05-01

Different evolution models are considered with feedback-couplings. In particular, we study the Lotka-Volterra system under the influence of a cumulative term, the Ginzburg-Landau model with a convolution memory term and chemical rate equations with time delay. The memory leads to a modified dynamical behavior. In case of a positive coupling the generalized Lotka-Volterra system exhibits a maximum gain achieved after a finite time, but the population will die out in the long time limit. In the opposite case, the time evolution is terminated in a crash. Due to the nonlinear feedback coupling the two branches of a bistable model are controlled by the the strength and the sign of the memory. For a negative coupling the system is able to switch over between both branches of the stationary solution. The dynamics of the system is further controlled by the initial condition. The diffusion-limited reaction is likewise studied in case the reacting entities are not available simultaneously. Whereas for an external feedback the dynamics is altered, but the stationary solution remain unchanged, a self-organized internal feedback leads to a time persistent solution.

Hadron–Quark Combustion as a Nonlinear, Dynamical System

Directory of Open Access Journals (Sweden)

Amir Ouyed

2018-03-01

Full Text Available The hadron–quark combustion front is a system that couples various processes, such as chemical reactions, hydrodynamics, diffusion, and neutrino transport. Previous numerical work has shown that this system is very nonlinear, and can be very sensitive to some of these processes. In these proceedings, we contextualize the hadron–quark combustion as a nonlinear system, subject to dramatic feedback triggered by leptonic weak decays and neutrino transport.

Synchronization of coupled nonidentical multidelay feedback systems

International Nuclear Information System (INIS)

Hoang, Thang Manh; Nakagawa, Masahiro

2007-01-01

We present the lag synchronization of coupled nonidentical multidelay feedback systems, in which the synchronization signal is the sum of nonlinearly transformed components of delayed state variable. The sufficient condition for synchronization is considered by the Krasovskii-Lyapunov theory. The specific examples will demonstrate and verify the effectiveness of the proposed model

Automatic Thermal Control System with Temperature Difference or Derivation Feedback

Directory of Open Access Journals (Sweden)

Darina Matiskova

2016-02-01

Full Text Available Automatic thermal control systems seem to be non-linear systems with thermal inertias and time delay. A controller is also non-linear because its information and power signals are limited. The application of methods that are available to on-linear systems together with computer simulation and mathematical modelling creates a possibility to acquire important information about the researched system. This paper provides a new look at the heated system model and also designs the structure of the thermal system with temperature derivation feedback. The designed system was simulated by using a special software in Turbo Pascal. Time responses of this system are compared to responses of a conventional thermal system. The thermal system with temperature derivation feedback provides better transients, better quality of regulation and better dynamical properties.

Delay-controlled primary and stochastic resonances of the SD oscillator with stiffness nonlinearities

Science.gov (United States)

Yang, Tao; Cao, Qingjie

2018-03-01

This work presents analytical studies of the stiffness nonlinearities SD (smooth and discontinuous) oscillator under displacement and velocity feedback control with a time delay. The SD oscillator can capture the qualitative characteristics of quasi-zero-stiffness and negative-stiffness. We focus mainly on the primary resonance of the quasi-zero-stiffness SD oscillator and the stochastic resonance (SR) of the negative-stiffness SD oscillator. Using the averaging method, we have been analyzed the amplitude response of the quasi-zero-stiffness SD oscillator. In this regard, the optimum time delay for changing the control intensity according to the optimization standard proposed can be obtained. For the optimum time delay, increasing the displacement feedback intensity is advantageous to suppress the vibrations in resonant regime where vibration isolation is needed, however, increasing the velocity feedback intensity is advantageous to strengthen the vibrations. Moreover, the effects of time-delayed feedback on the SR of the negative-stiffness SD oscillator are investigated under harmonic forcing and Gaussian white noise, based on the Langevin and Fokker-Planck approaches. The time-delayed feedback can enhance the SR phenomenon where vibrational energy harvesting is needed. This paper established the relationship between the parameters and vibration properties of a stiffness nonlinearities SD which provides the guidance for optimizing time-delayed control for vibration isolation and vibrational energy harvesting of the nonlinear systems.

Drag reduction in channel flow using nonlinear control

Science.gov (United States)

Keefe, Laurence R.

1993-01-01

Two nonlinear control schemes have been applied to the problem of drag reduction in channel flow. Both schemes have been tested using numerical simulations at a mass flux Reynolds numbers of 4408, utilizing 2D nonlinear neutral modes for goal dynamics. The OGY-method, which requires feedback, reduces drag to 60-80 percent of the turbulent value at the same Reynolds number, and employs forcing only within a thin region near the wall. The H-method, or model-based control, fails to achieve any drag reduction when starting from a fully turbulent initial condition, but shows potential for suppressing or retarding laminar-to-turbulent transition by imposing instead a transition to a low drag, nonlinear traveling wave solution to the Navier-Stokes equation. The drag in this state corresponds to that achieved by the OGY-method. Model-based control requires no feedback, but in experiments to date has required the forcing be imposed within a thicker layer than the OGY-method. Control energy expenditures in both methods are small, representing less than 0.1 percent of the uncontrolled flow's energy.

Nonlinear heat conduction equations with memory: Physical meaning and analytical results

Science.gov (United States)

Artale Harris, Pietro; Garra, Roberto

2017-06-01

We study nonlinear heat conduction equations with memory effects within the framework of the fractional calculus approach to the generalized Maxwell-Cattaneo law. Our main aim is to derive the governing equations of heat propagation, considering both the empirical temperature-dependence of the thermal conductivity coefficient (which introduces nonlinearity) and memory effects, according to the general theory of Gurtin and Pipkin of finite velocity thermal propagation with memory. In this framework, we consider in detail two different approaches to the generalized Maxwell-Cattaneo law, based on the application of long-tail Mittag-Leffler memory function and power law relaxation functions, leading to nonlinear time-fractional telegraph and wave-type equations. We also discuss some explicit analytical results to the model equations based on the generalized separating variable method and discuss their meaning in relation to some well-known results of the ordinary case.

Transient eddy feedback and low-frequency variability

International Nuclear Information System (INIS)

Robinson, W.A.

1994-01-01

Superposed on any externally driven secular climatic change are fluctuations that arise from the internal nonlinear dynamics of the climate system. These internally generated variations may involve interactions between the atmosphere and the ocean, as in the case of El Nino, or they may arise from the dynamics of the atmosphere alone. Here we discuss the dynamics of interactions between transient eddies and lower-frequency motions in the atmosphere. The interactions between more transient and more persistent motions can be divided into two types. Nonlinear interactions among the transient motions can act as an essentially random source of low-frequency motion. The idea that the low-frequencies respond in a linear way to stochastic forcing from higher frequencies has been applied to the generation of planetary waves and to the forcing of changes in global angular momentum. In addition to stochastic coupling, there are systematic interactions, denoted feedbacks, through which the persistent motions modulate their own forcing by the transient eddies. This paper discusses the dynamics of these feedbacks

Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations

International Nuclear Information System (INIS)

Udaltsov, Vladimir S.; Goedgebuer, Jean-Pierre; Larger, Laurent; Cuenot, Jean-Baptiste; Levy, Pascal; Rhodes, William T.

2003-01-01

We report that signal encoding with high-dimensional chaos produced by delayed feedback systems with a strong nonlinearity can be broken. We describe the procedure and illustrate the method with chaotic waveforms obtained from a strongly nonlinear optical system that we used previously to demonstrate signal encryption/decryption with chaos in wavelength. The method can be extended to any systems ruled by nonlinear time-delayed differential equations

Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback

Directory of Open Access Journals (Sweden)

Lei Li

2016-10-01

Full Text Available The parametric excitation system consisting of a flexible beam and shuttle mass widely exists in microelectromechanical systems (MEMS, which can exhibit rich nonlinear dynamic behaviors. This article aims to theoretically investigate the nonlinear jumping phenomena and bifurcation conditions of a class of electrostatically-driven MEMS actuators with a time-delay feedback controller. Considering the comb structure consisting of a flexible beam and shuttle mass, the partial differential governing equation is obtained with both the linear and cubic nonlinear parametric excitation. Then, the method of multiple scales is introduced to obtain a slow flow that is analyzed for stability and bifurcation. Results show that time-delay feedback can improve resonance frequency and stability of the system. What is more, through a detailed mathematical analysis, the discriminant of Hopf bifurcation is theoretically derived, and appropriate time-delay feedback force can make the branch from the Hopf bifurcation point stable under any driving voltage value. Meanwhile, through global bifurcation analysis and saddle node bifurcation analysis, theoretical expressions about the system parameter space and maximum amplitude of monostable vibration are deduced. It is found that the disappearance of the global bifurcation point means the emergence of monostable vibration. Finally, detailed numerical results confirm the analytical prediction.

Regular network model for the sea ice-albedo feedback in the Arctic.

Science.gov (United States)

Müller-Stoffels, Marc; Wackerbauer, Renate

2011-03-01

The Arctic Ocean and sea ice form a feedback system that plays an important role in the global climate. The complexity of highly parameterized global circulation (climate) models makes it very difficult to assess feedback processes in climate without the concurrent use of simple models where the physics is understood. We introduce a two-dimensional energy-based regular network model to investigate feedback processes in an Arctic ice-ocean layer. The model includes the nonlinear aspect of the ice-water phase transition, a nonlinear diffusive energy transport within a heterogeneous ice-ocean lattice, and spatiotemporal atmospheric and oceanic forcing at the surfaces. First results for a horizontally homogeneous ice-ocean layer show bistability and related hysteresis between perennial ice and perennial open water for varying atmospheric heat influx. Seasonal ice cover exists as a transient phenomenon. We also find that ocean heat fluxes are more efficient than atmospheric heat fluxes to melt Arctic sea ice.

Numerical Methods for Nonlinear PDEs in Finance

DEFF Research Database (Denmark)

Mashayekhi, Sima

Nonlinear Black-Scholes equations arise from considering parameters such as feedback and illiquid markets eects or large investor preferences, volatile portfolio and nontrivial transaction costs into option pricing models to have more accurate option price. Here some nite dierence schemes have be...

Improving Vehicle Ride and Handling Using LQG CNF Fusion Control Strategy for an Active Antiroll Bar System

Directory of Open Access Journals (Sweden)

N. Zulkarnain

2014-01-01

Full Text Available This paper analyses a comparison of performance for an active antiroll bar (ARB system using two types of control strategy. First of all, the LQG control strategy is investigated and then a novel LQG CNF fusion control method is developed to improve the performances on vehicle ride and handling for an active antiroll bar system. However, the ARB system has to balance the trade-off between ride and handling performance, where the CNF consists of a linear feedback law and a nonlinear feedback law. Typically, the linear feedback is designed to yield a quick response at the initial stage, while the nonlinear feedback law is used to smooth out overshoots in the system output when it approaches the target reference. The half car model is combined with a linear single track model with roll dynamics which are used for the analysis and simulation of ride and handling. The performances of the control strategies are compared and the simulation results show the LQG CNF fusion improves the performances in vehicle ride and handling.

Target Tracking in 3-D Using Estimation Based Nonlinear Control Laws for UAVs

Directory of Open Access Journals (Sweden)

Mousumi Ahmed

2016-02-01

Full Text Available This paper presents an estimation based backstepping like control law design for an Unmanned Aerial Vehicle (UAV to track a moving target in 3-D space. A ground-based sensor or an onboard seeker antenna provides range, azimuth angle, and elevation angle measurements to a chaser UAV that implements an extended Kalman filter (EKF to estimate the full state of the target. A nonlinear controller then utilizes this estimated target state and the chaser’s state to provide speed, flight path, and course/heading angle commands to the chaser UAV. Tracking performance with respect to measurement uncertainty is evaluated for three cases: (1 stationary white noise; (2 stationary colored noise and (3 non-stationary (range correlated white noise. Furthermore, in an effort to improve tracking performance, the measurement model is made more realistic by taking into consideration range-dependent uncertainties in the measurements, i.e., as the chaser closes in on the target, measurement uncertainties are reduced in the EKF, thus providing the UAV with more accurate control commands. Simulation results for these cases are shown to illustrate target state estimation and trajectory tracking performance.

Time-domain simulation of constitutive relations for nonlinear acoustics including relaxation for frequency power law attenuation media modeling

Science.gov (United States)

Jiménez, Noé; Camarena, Francisco; Redondo, Javier; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.

2015-10-01

We report a numerical method for solving the constitutive relations of nonlinear acoustics, where multiple relaxation processes are included in a generalized formulation that allows the time-domain numerical solution by an explicit finite differences scheme. Thus, the proposed physical model overcomes the limitations of the one-way Khokhlov-Zabolotskaya-Kuznetsov (KZK) type models and, due to the Lagrangian density is implicitly included in the calculation, the proposed method also overcomes the limitations of Westervelt equation in complex configurations for medical ultrasound. In order to model frequency power law attenuation and dispersion, such as observed in biological media, the relaxation parameters are fitted to both exact frequency power law attenuation/dispersion media and also empirically measured attenuation of a variety of tissues that does not fit an exact power law. Finally, a computational technique based on artificial relaxation is included to correct the non-negligible numerical dispersion of the finite difference scheme, and, on the other hand, improve stability trough artificial attenuation when shock waves are present. This technique avoids the use of high-order finite-differences schemes leading to fast calculations. The present algorithm is especially suited for practical configuration where spatial discontinuities are present in the domain (e.g. axisymmetric domains or zero normal velocity boundary conditions in general). The accuracy of the method is discussed by comparing the proposed simulation solutions to one dimensional analytical and k-space numerical solutions.

Introduction to nonlinear science

CERN Document Server

Nicolis, G

1995-01-01

One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...

Dichotomy of nonlinear systems: Application to chaos control of nonlinear electronic circuit

International Nuclear Information System (INIS)

Wang Jinzhi; Duan Zhisheng; Huang Lin

2006-01-01

In this Letter a new method of chaos control for Chua's circuit and the modified canonical Chua's electrical circuit is proposed by using the results of dichotomy in nonlinear systems. A linear feedback control based on linear matrix inequality (LMI) is given such that chaos oscillation or hyperchaos phenomenon of circuit systems injected control signal disappear. Numerical simulations are presented to illustrate the efficiency of the proposed method

Nonlinear damping for vibration isolation of microsystems using shear thickening fluid

Science.gov (United States)

Iyer, S. S.; Vedad-Ghavami, R.; Lee, H.; Liger, M.; Kavehpour, H. P.; Candler, R. N.

2013-06-01

This work reports the measurement and analysis of nonlinear damping of micro-scale actuators immersed in shear thickening fluids (STFs). A power-law damping term is added to the linear second-order model to account for the shear-dependent viscosity of the fluid. This nonlinear model is substantiated by measurements of oscillatory motion of a torsional microactuator. At high actuation forces, the vibration velocity amplitude saturates. The model accurately predicts the nonlinear damping characteristics of the STF using a power-law index extracted from independent rheology experiments. This result reveals the potential to use STFs as adaptive, passive dampers for vibration isolation of microelectromechanical systems.

Overexpression of human kynurenine-3-monooxygenase protects against 3-hydroxykynurenine-mediated apoptosis through bidirectional nonlinear feedback.

Science.gov (United States)

Wilson, K; Auer, M; Binnie, M; Zheng, X; Pham, N T; Iredale, J P; Webster, S P; Mole, D J

2016-04-14

Kynurenine 3-monooxygenase (KMO) is a critical regulator of inflammation. The preferred KMO substrate, kynurenine, is converted to 3-hydroxykynurenine (3HK), and this product exhibits cytotoxicity through mechanisms that culminate in apoptosis. Here, we report that overexpression of human KMO with orthotopic localisation to mitochondria creates a metabolic environment during which the cell exhibits increased tolerance for exogenous 3HK-mediated cellular injury. Using the selective KMO inhibitor Ro61-8048, we show that KMO enzyme function is essential for cellular protection. Pan-caspase inhibition with Z-VAD-FMK confirmed apoptosis as the mode of cell death. By defining expression of pathway components upstream and downstream of KMO, we observed alterations in other key kynurenine pathway components, particularly tryptophan-2,3-dioxygenase upregulation, through bidirectional nonlinear feedback. KMO overexpression also increased expression of inducible nitric oxide synthase (iNOS). These changes in gene expression are functionally relevant, because siRNA knockdown of the pathway components kynureninase and quinolinate phosphoribosyl transferase caused cells to revert to a state of susceptibility to 3HK-mediated apoptosis. In summary, KMO overexpression, and importantly KMO activity, have metabolic repercussions that fundamentally affect resistance to cell stress.

Nonlinear Waves in the Terrestrial Quasiparallel Foreshock.

Science.gov (United States)

Hnat, B; Kolotkov, D Y; O'Connell, D; Nakariakov, V M; Rowlands, G

2016-12-02

We provide strongly conclusive evidence that the cubic nonlinearity plays an important part in the evolution of the large amplitude magnetic structures in the terrestrial foreshock. Large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency are identified after nonharmonic slow variations are filtered out by applying the empirical mode decomposition. Numerical solutions of the derivative nonlinear Schrödinger equation, predicted analytically by the use of a pseudopotential approach, are found to be consistent with the observed wave forms. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfvén speed. We suggest that the feedback of the large amplitude fluctuations on background plasma is reflected in the evolution of the pseudopotential.

Application of H∞ control theory to power control of a nonlinear reactor model

International Nuclear Information System (INIS)

Suzuki, Katsuo; Shimazaki, Junya; Shinohara, Yoshikuni

1993-01-01

The H∞ control theory is applied to the compensator design of a nonlinear nuclear reactor model, and the results are compared with standard linear quadratic Gaussian (LQG) control. The reactor model is assumed to be provided with a control rod drive system having the compensation of rod position feedback. The nonlinearity of the reactor model exerts a great influence on the stability of the control system, and hence, it is desirable for a power control system of a nuclear reactor to achieve robust stability and to improve the sensitivity of the feedback control system. A computer simulation based on a power control system synthesized by LQG control was performed revealing that the control system has some stationary offset and less stability. Therefore, here, attention is given to the development of a methodology for robust control that can withstand exogenous disturbances and nonlinearity in view of system parameter changes. The developed methodology adopts H∞ control theory in the feedback system and shows interesting features of robustness. The results of the computer simulation indicate that the feedback control system constructed by the developed H∞ compensator possesses sufficient robustness of control on the stability and disturbance attenuation, which are essential for the safe operation of a nuclear reactor

Passivity Based Stabilization of Non-minimum Phase Nonlinear Systems

Czech Academy of Sciences Publication Activity Database

Travieso-Torres, J.C.; Duarte-Mermoud, M.A.; Zagalak, Petr

2009-01-01

Roč. 45, č. 3 (2009), s. 417-426 ISSN 0023-5954 R&D Projects: GA ČR(CZ) GA102/07/1596 Institutional research plan: CEZ:AV0Z10750506 Keywords : nonlinear systems * stabilisation * passivity * state feedback Subject RIV: BC - Control Systems Theory Impact factor: 0.445, year: 2009 http://library.utia.cas.cz/separaty/2009/AS/zagalak-passivity based stabilization of non-minimum phase nonlinear systems.pdf

Solutions and conservation laws of Benjamin–Bona–Mahony

Indian Academy of Sciences (India)

In this paper, exact solutions of Benjamin–Bona–Mahony–Peregrine equation are obtained with power-law and dual power-law nonlinearities. The Lie group analysis as well as the simplest equation method are used to carry out the integration of these equations. The solutions obtained are cnoidal waves, periodic solutions ...

Truncated predictor feedback for time-delay systems

CERN Document Server

Zhou, Bin

2014-01-01

This book provides a systematic approach to the design of predictor based controllers for (time-varying) linear systems with either (time-varying) input or state delays. Differently from those traditional predictor based controllers, which are infinite-dimensional static feedback laws and may cause difficulties in their practical implementation, this book develops a truncated predictor feedback (TPF) which involves only finite dimensional static state feedback. Features and topics: A novel approach referred to as truncated predictor feedback for the stabilization of (time-varying) time-delay systems in both the continuous-time setting and the discrete-time setting is built systematically Semi-global and global stabilization problems of linear time-delay systems subject to either magnitude saturation or energy constraints are solved in a systematic manner Both stabilization of a single system and consensus of a group of systems (multi-agent systems) are treated in a unified manner by applying the truncated pre...

ON POTENTIAL REPRESENTATIONS OF THE DISTRIBUTION LAW OF RARE STRONGEST EARTHQUAKES

Directory of Open Access Journals (Sweden)

M. V. Rodkin

2014-01-01

'bend-down' is described by the finite distribution law, i.e. the bend-down occurs more efficiently than it is envisaged in the commonly used model developed by Y. Kagan (which treats the bend-dawn as an exponential decay law. However, despite the finiteness of the distribution law, density of magnitudes decline quite slowly in the area close to the maximum possible Мmах event as (Мmах – Mn, where n varies in the range between 4 and 6 in the majority of cases. As a result Мmах value can be estimated only with a large error. In rare cases, if the space-and-time area under study contains higher number of strongest earthquakes, the empirical distribution law becomes close to the exponential law; in this case n value is quite high, and Мmах values becomes unstable and tend to infinite growth.In our study, the distribution law of strongest earthquakes was investigated by the methods based on the extreme values theory (world data and several regional catalogues were examined, and the results of calculation do not reveal cases of  occurrence of characteristic events. However, such a seismic regime was revealed in a number of cases from paleoseismicity data and from some instrumental regional catalogues. Conditions providing for the occurrence of characteristic earthquakes are studied here using the multiplicative cascade model. According to [Rodkin, 2011], this model provides the simulation of all known regularities of seismic regime, such as a decrease in b-value in the vicinity of strong earthquakes, development of aftershock power cascade, and existence of seismic cycle and foreshock activity. This article considers an extension of the cascade model by adding of non-linear members in the kinetic cascade equation in order to describe effects of the 'bend-down' of the earthquake recurrence curve and the characteristic earthquakes occurrence. It is shown that in terms of the multiplicative cascade model, the occurrence of characteristic earthquakes is connected

Defocusing regimes of nonlinear waves in media with negative dispersion

DEFF Research Database (Denmark)

Bergé, L.; Kuznetsov, E.A.; Juul Rasmussen, J.

1996-01-01

Defocusing regimes of quasimonochromatic waves governed by a nonlinear Schrodinger equation with mixed-sign dispersion are investigated. For a power-law nonlinearity, we show that localized solutions to this equation defined at the so-called critical dimension cannot collapse in finite time...

Non-fragile robust stabilization and H{sub {infinity}} control for uncertain stochastic nonlinear time-delay systems

Energy Technology Data Exchange (ETDEWEB)

Zhang Jinhui [Department of Automatic Control, Beijing Institute of Technology, Beijing 100081 (China)], E-mail: jinhuizhang82@gmail.com; Shi Peng [Faculty of Advanced Technology, University of Glamorgan, Pontypridd CF37 1DL (United Kingdom); ILSCM, School of Science and Engineering, Victoria University, Melbourne, Vic. 8001 (Australia); School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA 5095 (Australia)], E-mail: pshi@glam.ac.uk; Yang Hongjiu [Department of Automatic Control, Beijing Institute of Technology, Beijing 100081 (China)], E-mail: yanghongjiu@gmail.com

2009-12-15

This paper deals with the problem of non-fragile robust stabilization and H{sub {infinity}} control for a class of uncertain stochastic nonlinear time-delay systems. The parametric uncertainties are real time-varying as well as norm bounded. The time-delay factors are unknown and time-varying with known bounds. The aim is to design a memoryless non-fragile state feedback control law such that the closed-loop system is stochastically asymptotically stable in the mean square and the effect of the disturbance input on the controlled output is less than a prescribed level for all admissible parameter uncertainties. New sufficient conditions for the existence of such controllers are presented based on the linear matrix inequalities (LMIs) approach. Numerical example is given to illustrate the effectiveness of the developed techniques.

Nonlinear optics an analytical approach

CERN Document Server

Mandel, Paul

2010-01-01

Based on the author's extensive teaching experience and lecture notes, this textbook provides a substantially analytical rather than descriptive presentation of nonlinear optics. Divided into five parts, with most chapters corresponding to a two-hour lecture, the book begins with a unique account of the historical development from Kirchhoff's law for the black-body radiation to Planck's quantum hypothesis and Einstein's discovery of spontaneous emission - providing all the explicit proofs. The subsequent sections deal with matter quantization, ultrashort pulse propagation in 2-level media, cavity nonlinear optics, chi(2) and chi(3) media. For graduate and PhD students in nonlinear optics or photonics, while also representing a valuable reference for researchers in these fields.

Fractal scattering of Gaussian solitons in directional couplers with logarithmic nonlinearities

Energy Technology Data Exchange (ETDEWEB)

Teixeira, Rafael M.P.; Cardoso, Wesley B., E-mail: wesleybcardoso@gmail.com

2016-08-12

In this paper we study the interaction of Gaussian solitons in a dispersive and nonlinear media with log-law nonlinearity. The model is described by the coupled logarithmic nonlinear Schrödinger equations, which is a nonintegrable system that allows the observation of a very rich scenario in the collision patterns. By employing a variational approach and direct numerical simulations, we observe a fractal-scattering phenomenon from the exit velocities of each soliton as a function of the input velocities. Furthermore, we introduce a linearization model to identify the position of the reflection/transmission window that emerges within the chaotic region. This enables us the possibility of controlling the scattering of solitons as well as the lifetime of bound states. - Highlights: • We study the interaction of Gaussian solitons in a system with log-law nonlinearity. • The model is described by the coupled logarithmic nonlinear Schrödinger equations. • We observe a fractal-scattering phenomenon of the solitons.

Discretely Conservative Finite-Difference Formulations for Nonlinear Conservation Laws in Split Form: Theory and Boundary Conditions

Science.gov (United States)

Fisher, Travis C.; Carpenter, Mark H.; Nordstroem, Jan; Yamaleev, Nail K.; Swanson, R. Charles

2011-01-01

Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived; these guarantee the conservative form of the combined operator.

Third Conference on nonlinear science and complexity (NSC)

CERN Document Server

Machado, José; Baleanu, Dumitru; Dynamical Systems and Methods

2012-01-01

Nonlinear Systems and Methods For Mechanical, Electrical and Biosystems presents topics observed at the 3rd Conference on Nonlinear Science and Complexity(NSC), focusing on energy transfer and synchronization in hybrid nonlinear systems. The studies focus on fundamental theories and principles,analytical and symbolic approaches, computational techniques in nonlinear physical science and mathematics. Broken into three parts, the text covers:\\ Parametrical excited pendulum, nonlinear dynamics in hybrid systems, dynamical system synchronization and (N+1) body dynamics as well as new views different from the existing results in nonlinear dynamics. Mathematical methods for dynamical systems including conservation laws, dynamical symmetry in nonlinear differential equations and invex energies. Nonlinear phenomena in physical problems such as solutions, complex flows, chemical kinetics, Toda lattices and parallel manipulator. This book is useful to scholars, researchers and advanced technical members of industrial l...

Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings.

Science.gov (United States)

Tang, Yang; Gao, Huijun; Zou, Wei; Kurths, Jürgen

2013-02-01

In this paper, the distributed synchronization problem of networks of agent systems with controllers and nonlinearities subject to Bernoulli switchings is investigated. Controllers and adaptive updating laws injected in each vertex of networks depend on the state information of its neighborhood. Three sets of Bernoulli stochastic variables are introduced to describe the occurrence probabilities of distributed adaptive controllers, updating laws and nonlinearities, respectively. By the Lyapunov functions method, we show that the distributed synchronization of networks composed of agent systems with multiple randomly occurring nonlinearities, multiple randomly occurring controllers, and multiple randomly occurring updating laws can be achieved in mean square under certain criteria. The conditions derived in this paper can be solved by semi-definite programming. Moreover, by mathematical analysis, we find that the coupling strength, the probabilities of the Bernoulli stochastic variables, and the form of nonlinearities have great impacts on the convergence speed and the terminal control strength. The synchronization criteria and the observed phenomena are demonstrated by several numerical simulation examples. In addition, the advantage of distributed adaptive controllers over conventional adaptive controllers is illustrated.

Implications of a wavepacket formulation for the nonlinear parabolized stability equations to hypersonic boundary layers

Science.gov (United States)

Kuehl, Joseph

2016-11-01

The parabolized stability equations (PSE) have been developed as an efficient and powerful tool for studying the stability of advection-dominated laminar flows. In this work, a new "wavepacket" formulation of the PSE is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a "nonlinear coupling coefficient." It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening and results in disturbance saturation amplitudes consistent with experiment. A Mach 6 flared-cone example is presented. Support from the AFOSR Young Investigator Program via Grant FA9550-15-1-0129 is gratefully acknowledges.

An efficient technique for the point reactor kinetics equations with Newtonian temperature feedback effects

International Nuclear Information System (INIS)

Nahla, Abdallah A.

2011-01-01

Highlights: → An efficient technique for the nonlinear reactor kinetics equations is presented. → This method is based on Backward Euler or Crank Nicholson and fundamental matrix. → Stability of efficient technique is defined and discussed. → This method is applied to point kinetics equations of six-groups of delayed neutrons. → Step, ramp, sinusoidal and temperature feedback reactivities are discussed. - Abstract: The point reactor kinetics equations of multi-group of delayed neutrons in the presence Newtonian temperature feedback effects are a system of stiff nonlinear ordinary differential equations which have not any exact analytical solution. The efficient technique for this nonlinear system is based on changing this nonlinear system to a linear system by the predicted value of reactivity and solving this linear system using the fundamental matrix of the homogenous linear differential equations. The nonlinear point reactor kinetics equations are rewritten in the matrix form. The solution of this matrix form is introduced. This solution contains the exponential function of a variable coefficient matrix. This coefficient matrix contains the unknown variable, reactivity. The predicted values of reactivity in the explicit form are determined replacing the exponential function of the coefficient matrix by two kinds, Backward Euler and Crank Nicholson, of the rational approximations. The nonlinear point kinetics equations changed to a linear system of the homogenous differential equations. The fundamental matrix of this linear system is calculated using the eigenvalues and the corresponding eigenvectors of the coefficient matrix. Stability of the efficient technique is defined and discussed. The efficient technique is applied to the point kinetics equations of six-groups of delayed neutrons with step, ramp, sinusoidal and the temperature feedback reactivities. The results of these efficient techniques are compared with the traditional methods.

Research on nonlinearity effect of secondary electron multiplier

International Nuclear Information System (INIS)

Wei Xingjian; Liao Junsheng; Deng Dachao; Yu Chunrong; Yuan Li

2007-01-01

The nonlinearity of secondary electron multiplier (SEM) of a thermal ionization mass spectrometer has been researched by using UTB-500 uranium isotope reference material and multi-collecting technique. The results show that the nonlinearity effect of SEM exists in the whole ion counting range, and there is an extreme point of the nonlinearity when the ion counting rate is about 20000 cps. The deviation between measured value of the extreme point and the reference value of the reference sample can be up to 3%, and the nonlinearity obeys logarithm linearity law on both sides of extreme point. A kind of mathematics model of nonlinearity calibration has been put forward. Using this model, the nonlinearity of SEM of TIMS can be calibrated. (authors)

Random distributed feedback fibre lasers

Energy Technology Data Exchange (ETDEWEB)

Turitsyn, Sergei K., E-mail: s.k.turitsyn@aston.ac.uk [Aston Institute of Photonic Technologies, Aston University, Birmingham B4 7ET (United Kingdom); Novosibirsk State University, 2 Pirogova str., 630090, Novosibirsk (Russian Federation); Babin, Sergey A. [Novosibirsk State University, 2 Pirogova str., 630090, Novosibirsk (Russian Federation); Institute of Automation and Electrometry SB RAS, 1 Ac. Koptug. ave., 630090, Novosibirsk (Russian Federation); Churkin, Dmitry V. [Aston Institute of Photonic Technologies, Aston University, Birmingham B4 7ET (United Kingdom); Novosibirsk State University, 2 Pirogova str., 630090, Novosibirsk (Russian Federation); Institute of Automation and Electrometry SB RAS, 1 Ac. Koptug. ave., 630090, Novosibirsk (Russian Federation); Vatnik, Ilya D.; Nikulin, Maxim [Institute of Automation and Electrometry SB RAS, 1 Ac. Koptug. ave., 630090, Novosibirsk (Russian Federation); Podivilov, Evgenii V. [Novosibirsk State University, 2 Pirogova str., 630090, Novosibirsk (Russian Federation); Institute of Automation and Electrometry SB RAS, 1 Ac. Koptug. ave., 630090, Novosibirsk (Russian Federation)

2014-09-10

generation of a stationary near-Gaussian beam with a narrow spectrum. A random distributed feedback fibre laser has efficiency and performance that are comparable to and even exceed those of similar conventional fibre lasers. The key features of the generated radiation of random distributed feedback fibre lasers include: a stationary narrow-band continuous modeless spectrum that is free of mode competition, nonlinear power broadening, and an output beam with a Gaussian profile in the fundamental transverse mode (generated both in single mode and multi-mode fibres). This review presents the current status of research in the field of random fibre lasers and shows their potential and perspectives. We start with an introductory overview of conventional distributed feedback lasers and traditional random lasers to set the stage for discussion of random fibre lasers. We then present a theoretical analysis and experimental studies of various random fibre laser configurations, including widely tunable, multi-wavelength, narrow-band generation, and random fibre lasers operating in different spectral bands in the 1–1.6 μm range. Then we discuss existing and future applications of random fibre lasers, including telecommunication and distributed long reach sensor systems. A theoretical description of random lasers is very challenging and is strongly linked with the theory of disordered systems and kinetic theory. We outline two key models governing the generation of random fibre lasers: the average power balance model and the nonlinear Schrödinger equation based model. Recently invented random distributed feedback fibre lasers represent a new and exciting field of research that brings together such diverse areas of science as laser physics, the theory of disordered systems, fibre optics and nonlinear science. Stable random generation in optical fibre opens up new possibilities for research on wave transport and localization in disordered media. We hope that this review will provide

Random distributed feedback fibre lasers

International Nuclear Information System (INIS)

Turitsyn, Sergei K.; Babin, Sergey A.; Churkin, Dmitry V.; Vatnik, Ilya D.; Nikulin, Maxim; Podivilov, Evgenii V.

2014-01-01

generation of a stationary near-Gaussian beam with a narrow spectrum. A random distributed feedback fibre laser has efficiency and performance that are comparable to and even exceed those of similar conventional fibre lasers. The key features of the generated radiation of random distributed feedback fibre lasers include: a stationary narrow-band continuous modeless spectrum that is free of mode competition, nonlinear power broadening, and an output beam with a Gaussian profile in the fundamental transverse mode (generated both in single mode and multi-mode fibres). This review presents the current status of research in the field of random fibre lasers and shows their potential and perspectives. We start with an introductory overview of conventional distributed feedback lasers and traditional random lasers to set the stage for discussion of random fibre lasers. We then present a theoretical analysis and experimental studies of various random fibre laser configurations, including widely tunable, multi-wavelength, narrow-band generation, and random fibre lasers operating in different spectral bands in the 1–1.6 μm range. Then we discuss existing and future applications of random fibre lasers, including telecommunication and distributed long reach sensor systems. A theoretical description of random lasers is very challenging and is strongly linked with the theory of disordered systems and kinetic theory. We outline two key models governing the generation of random fibre lasers: the average power balance model and the nonlinear Schrödinger equation based model. Recently invented random distributed feedback fibre lasers represent a new and exciting field of research that brings together such diverse areas of science as laser physics, the theory of disordered systems, fibre optics and nonlinear science. Stable random generation in optical fibre opens up new possibilities for research on wave transport and localization in disordered media. We hope that this review will provide

H∞ control of Lur'e systems with sector and slope restricted nonlinearities

International Nuclear Information System (INIS)

Park, Ju H.; Ji, D.H.; Won, S.C.; Lee, S.M.; Choi, S.J.

2009-01-01

This Letter considers H ∞ controller design scheme for Lur'e systems with sector/slope restrictions and external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, a state feedback controller is designed to not only guarantee stability of systems but also reduce the effect of external disturbance to an H ∞ norm constraint. The nonlinearities are expressed as convex combinations of sector and slope bounds so that equality constraints are converted into inequality constraints using convex properties of the nonlinear function. Then, the stabilizing feedback gain matrix is derived through LMI formulation. Finally, a numerical example shows the effectiveness of the proposed method.

Nonlinear Dynamic Models in Advanced Life Support

Science.gov (United States)

Jones, Harry

2002-01-01

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

The Use of Nonlinear Constitutive Equations to Evaluate Draw Resistance and Filter Ventilation

Directory of Open Access Journals (Sweden)

Eitzinger B

2014-12-01

Full Text Available This study investigates by nonlinear constitutive equations the influence of tipping paper, cigarette paper, filter, and tobacco rod on the degree of filter ventilation and draw resistance. Starting from the laws of conservation, the path to the theory of fluid dynamics in porous media and Darcy's law is reviewed and, as an extension to Darcy's law, two different nonlinear pressure drop-flow relations are proposed. It is proven that these relations are valid constitutive equations and the partial differential equations for the stationary flow in an unlit cigarette covering anisotropic, inhomogeneous and nonlinear behaviour are derived. From these equations a system of ordinary differential equations for the one-dimensional flow in the cigarette is derived by averaging pressure and velocity over the cross section of the cigarette. By further integration, the concept of an electrical analog is reached and discussed in the light of nonlinear pressure drop-flow relations. By numerical calculations based on the system of ordinary differential equations, it is shown that the influence of nonlinearities cannot be neglected because variations in the degree of filter ventilation can reach up to 20% of its nominal value.

Corticocortical feedback increases the spatial extent of normalization.

Science.gov (United States)

Nassi, Jonathan J; Gómez-Laberge, Camille; Kreiman, Gabriel; Born, Richard T

2014-01-01

Normalization has been proposed as a canonical computation operating across different brain regions, sensory modalities, and species. It provides a good phenomenological description of non-linear response properties in primary visual cortex (V1), including the contrast response function and surround suppression. Despite its widespread application throughout the visual system, the underlying neural mechanisms remain largely unknown. We recently observed that corticocortical feedback contributes to surround suppression in V1, raising the possibility that feedback acts through normalization. To test this idea, we characterized area summation and contrast response properties in V1 with and without feedback from V2 and V3 in alert macaques and applied a standard normalization model to the data. Area summation properties were well explained by a form of divisive normalization, which computes the ratio between a neuron's driving input and the spatially integrated activity of a "normalization pool." Feedback inactivation reduced surround suppression by shrinking the spatial extent of the normalization pool. This effect was independent of the gain modulation thought to mediate the influence of contrast on area summation, which remained intact during feedback inactivation. Contrast sensitivity within the receptive field center was also unaffected by feedback inactivation, providing further evidence that feedback participates in normalization independent of the circuit mechanisms involved in modulating contrast gain and saturation. These results suggest that corticocortical feedback contributes to surround suppression by increasing the visuotopic extent of normalization and, via this mechanism, feedback can play a critical role in contextual information processing.

A remark on "Nonlinear output feedback control of underwater vehicle propellers using feedback form estimated axial flow velocity"

DEFF Research Database (Denmark)

Jouffroy, Jerome; Lottin, Jacques

2002-01-01

For original paper see T.I.Fossen and M.Blanke, ibid., vol.25, pp.241-55 (2000). In the work presented by Fossen and Blanke, a nonlinear observer for estimation of propeller axial flow velocity for UUVs was introduced. The proof of the convergence behavior of the observer was carried out with a L......For original paper see T.I.Fossen and M.Blanke, ibid., vol.25, pp.241-55 (2000). In the work presented by Fossen and Blanke, a nonlinear observer for estimation of propeller axial flow velocity for UUVs was introduced. The proof of the convergence behavior of the observer was carried out...

Analysis and design of robust decentralized controllers for nonlinear systems

Energy Technology Data Exchange (ETDEWEB)

Schoenwald, D.A.

1993-07-01

Decentralized control strategies for nonlinear systems are achieved via feedback linearization techniques. New results on optimization and parameter robustness of non-linear systems are also developed. In addition, parametric uncertainty in large-scale systems is handled by sensitivity analysis and optimal control methods in a completely decentralized framework. This idea is applied to alleviate uncertainty in friction parameters for the gimbal joints on Space Station Freedom. As an example of decentralized nonlinear control, singular perturbation methods and distributed vibration damping are merged into a control strategy for a two-link flexible manipulator.

On Stabilization of Nonautonomous Nonlinear Systems

International Nuclear Information System (INIS)

Bogdanov, A. Yu.

2008-01-01

The procedures to obtain the sufficient conditions of asymptotic stability for nonlinear nonstationary continuous-time systems are discussed. We consider different types of the following general controlled system: x = X(t,x,u) = F(t,x)+B(t,x)u, x(t 0 ) = x 0 . (*) The basis of investigation is limiting equations, limiting Lyapunov functions, etc. The improved concept of observability of the pair of functional matrices is presented. By these results the problem of synthesis of asymptotically stable control nonlinear nonautonomous systems (with linear parts) involving the quadratic time-dependent Lyapunov functions is solved as well as stabilizing a given unstable system with nonlinear control law.

Robust nonlinear PID-like fuzzy logic control of a planar parallel (2PRP-PPR) manipulator.

Science.gov (United States)

Londhe, P S; Singh, Yogesh; Santhakumar, M; Patre, B M; Waghmare, L M

2016-07-01

In this paper, a robust nonlinear proportional-integral-derivative (PID)-like fuzzy control scheme is presented and applied to complex trajectory tracking control of a 2PRP-PPR (P-prismatic, R-revolute) planar parallel manipulator (motion platform) with three degrees-of-freedom (DOF) in the presence of parameter uncertainties and external disturbances. The proposed control law consists of mainly two parts: first part uses a feed forward term to enhance the control activity and estimated perturbed term to compensate for the unknown effects namely external disturbances and unmodeled dynamics, and the second part uses a PID-like fuzzy logic control as a feedback portion to enhance the overall closed-loop stability of the system. Experimental results are presented to show the effectiveness of the proposed control scheme. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Exact optical solitons in (n + 1)-dimensions with anti-cubic nonlinearity

Science.gov (United States)

Younis, Muhammad; Shahid, Iram; Anbreen, Sumaira; Rizvi, Syed Tahir Raza

2018-02-01

The paper studies the propagation of optical solitons in (n + 1)-dimensions under anti-cubic law of nonlinearity. The bright, dark and singular optical solitons are extracted using the extended trial equation method. The constraint conditions, for the existence of these solitons, are also listed. Additionally, a couple of other solutions known as singular periodic and Jacobi elliptic solutions, fall out as a by-product of this scheme. The obtained results are new and reported first time in (n + 1)-dimensions with anti-cubic law of nonlinearity.

Consequences of nonlinear heat transport laws on expected plasma profiles

International Nuclear Information System (INIS)

Lackner, K.

1987-03-01

The expected variation of plasma pressure profiles against changes in power deposition is investigated by using a simple linear heat transport law as well as a quadratic one. Applying the quadratic transport law it can be shown that the stiffening of the resulting profiles is sufficient to understand the experimentally measured phenomenon of 'profile consistence' without further assumptions of nonlocal effects. (orig.) [de

Machine learning control taming nonlinear dynamics and turbulence

CERN Document Server

Duriez, Thomas; Noack, Bernd R

2017-01-01

This is the first book on a generally applicable control strategy for turbulence and other complex nonlinear systems. The approach of the book employs powerful methods of machine learning for optimal nonlinear control laws. This machine learning control (MLC) is motivated and detailed in Chapters 1 and 2. In Chapter 3, methods of linear control theory are reviewed. In Chapter 4, MLC is shown to reproduce known optimal control laws for linear dynamics (LQR, LQG). In Chapter 5, MLC detects and exploits a strongly nonlinear actuation mechanism of a low-dimensional dynamical system when linear control methods are shown to fail. Experimental control demonstrations from a laminar shear-layer to turbulent boundary-layers are reviewed in Chapter 6, followed by general good practices for experiments in Chapter 7. The book concludes with an outlook on the vast future applications of MLC in Chapter 8. Matlab codes are provided for easy reproducibility of the presented results. The book includes interviews with leading r...

High-Alpha Research Vehicle Lateral-Directional Control Law Description, Analyses, and Simulation Results

Science.gov (United States)

Davidson, John B.; Murphy, Patrick C.; Lallman, Frederick J.; Hoffler, Keith D.; Bacon, Barton J.

1998-01-01

This report contains a description of a lateral-directional control law designed for the NASA High-Alpha Research Vehicle (HARV). The HARV is a F/A-18 aircraft modified to include a research flight computer, spin chute, and thrust-vectoring in the pitch and yaw axes. Two separate design tools, CRAFT and Pseudo Controls, were integrated to synthesize the lateral-directional control law. This report contains a description of the lateral-directional control law, analyses, and nonlinear simulation (batch and piloted) results. Linear analysis results include closed-loop eigenvalues, stability margins, robustness to changes in various plant parameters, and servo-elastic frequency responses. Step time responses from nonlinear batch simulation are presented and compared to design guidelines. Piloted simulation task scenarios, task guidelines, and pilot subjective ratings for the various maneuvers are discussed. Linear analysis shows that the control law meets the stability margin guidelines and is robust to stability and control parameter changes. Nonlinear batch simulation analysis shows the control law exhibits good performance and meets most of the design guidelines over the entire range of angle-of-attack. This control law (designated NASA-1A) was flight tested during the Summer of 1994 at NASA Dryden Flight Research Center.

MTPA control of mechanical sensorless IPMSM based on adaptive nonlinear control.

Science.gov (United States)

Najjar-Khodabakhsh, Abbas; Soltani, Jafar

2016-03-01

In this paper, an adaptive nonlinear control scheme has been proposed for implementing maximum torque per ampere (MTPA) control strategy corresponding to interior permanent magnet synchronous motor (IPMSM) drive. This control scheme is developed in the rotor d-q axis reference frame using adaptive input-output state feedback linearization (AIOFL) method. The drive system control stability is supported by Lyapunov theory. The motor inductances are online estimated by an estimation law obtained by AIOFL. The estimation errors of these parameters are proved to be asymptotically converged to zero. Based on minimizing the motor current amplitude, the MTPA control strategy is performed by using the nonlinear optimization technique while considering the online reference torque. The motor reference torque is generated by a conventional rotor speed PI controller. By performing MTPA control strategy, the generated online motor d-q reference currents were used in AIOFL controller to obtain the SV-PWM reference voltages and the online estimation of the motor d-q inductances. In addition, the stator resistance is online estimated using a conventional PI controller. Moreover, the rotor position is detected using the online estimation of the stator flux and online estimation of the motor q-axis inductance. Simulation and experimental results obtained prove the effectiveness and the capability of the proposed control method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Three religious rules of nonlinear physics

International Nuclear Information System (INIS)

Yankov, V.V.

1993-01-01

The theory of strong turbulence is a part of nonlinear physics. The three open-quotes religious rulesclose quotes of nonlinear physics present a heuristic viewpoint that can be used to qualitatively predict the evolution of nonlinear systems. These rules are as follows. (1) The basic results can be obtained from the conservation laws. If some kind of process is not forbidden by these laws, it generally occurs. If it doesn't this means that another conserved quantity imposing the constraint is being missed. (2) The universal law of open-quotes 20/80close quotes takes place: 20% of people drink 80% of beer. In other words, interesting processes usually take place in localized structures occupying a small share of volume. The localized structures interact weakly and therefore maintain their identity. For this reason they are universal and can be investigated. (3) The open-quotes general situationclose quotes is nonintegrable. The special case of exact solutions in integrable models represent a degenerate (nontypical) behavior. Particular exact solutions cannot be taken as representative solutions unless they are attractors. The presence of attractors simplifies the analysis and clarifies the situation. In plasma physics one deals with infinite-dimensional (PDE) systems distributed in space. The application of the religious rules 1 and 2 then leads to the following. If the conservation laws do not prohibit the development of singularities they do occur. If the singularities are prohibited, then stable localized structures take place. Solitons (or solitary waves) and vortices are examples of such stable structures. Wave collapse, wave-breaking, shock waves, magnetic reconnection and singularities in ideal Euler liquid are the examples of singularities. According to rule 3, exact solutions are very essential if they are attractors in some sense. Analysis of this problem is presented for solitons in nonintegrable wave systems and 2D vortices

Features and states of microscopic particles in nonlinear quantum-mechanics systems

Institute of Scientific and Technical Information of China (English)

2008-01-01

In this paper,we present the elementary principles of nonlinear quantum mechanics(NLQM),which is based on some problems in quantum mechanics.We investigate in detail the motion laws and some main properties of microscopic particles in nonlinear quantum systems using these elementary principles.Concretely speaking,we study in this paper the wave-particle duality of the solution of the nonlinear Schr6dinger equation,the stability of microscopic particles described by NLQM,invariances and conservation laws of motion of particles,the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamilton equations,the classical rule of microscopic particle motion,the mechanism and rules of particle collision,the features of reflection and the transmission of particles at interfaces,and the uncertainty relation of particle motion as well as the eigenvalue and eigenequations of particles,and so on.We obtained the invariance and conservation laws of mass,energy and momentum and angular momenturn for the microscopic particles,which are also some elementary and universal laws of matter in the NLQM and give further the methods and ways of solving the above questions.We also find that the laws of motion of microscopic particles in such a case are completely different from that in the linear quantum mechanics(LQM).They have a lot of new properties;for example,the particles possess the real wave-corpuscle duality,obey the classical rule of motion and conservation laws of energy,momentum and mass,satisfy minimum uncertainty relation,can be localized due to the nonlinear interaction,and its position and momentum can also be determined,etc.From these studies,we see clearly that rules and features of microscopic particle motion in NLQM is different from that in LQM.Therefore,the NLQM is a new physical theory,and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic particles in nonlinear systems,which can

Density gradient effects in weakly nonlinear ablative Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Wang, L. F.; Ye, W. H.; He, X. T.

2012-01-01

In this research, density gradient effects (i.e., finite thickness of ablation front effects) in ablative Rayleigh-Taylor instability (ARTI), in the presence of preheating within the weakly nonlinear regime, are investigated numerically. We analyze the weak, medium, and strong ablation surfaces which have different isodensity contours, respectively, to study the influences of finite thickness of ablation front on the weakly nonlinear behaviors of ARTI. Linear growth rates, generation coefficients of the second and the third harmonics, and coefficients of the third-order feedback to the fundamental mode are obtained. It is found that the linear growth rate which has a remarkable maximum, is reduced, especially when the perturbation wavelength λ is short and a cut-off perturbation wavelength λ c appears when the perturbation wavelength λ is sufficiently short, where no higher harmonics exists when λ c . The phenomenon of third-order positive feedback to the fundamental mode near the λ c [J. Sanz et al., Phys. Rev. Lett. 89, 195002 (2002); J. Garnier et al., Phys. Rev. Lett. 90, 185003 (2003); J. Garnier and L. Masse, Phys. Plasmas 12, 062707 (2005)] is confirmed in numerical simulations, and the physical mechanism of the third-order positive feedback is qualitatively discussed. Moreover, it is found that generations and growths of the second and the third harmonics are stabilized (suppressed and reduced) by the ablation effect. Meanwhile, the third-order negative feedback to the fundamental mode is also reduced by the ablation effect, and hence, the linear saturation amplitude (typically ∼0.2λ in our simulations) is increased significantly and therefore exceeds the classical prediction 0.1λ, especially for the strong ablation surface with a small perturbation wavelength. Overall, the ablation effect stabilizes the ARTI in the weakly nonlinear regime. Numerical results obtained are in general agreement with the recent weakly nonlinear theories and simulations

Chaotic and steady state behaviour of a nonlinear controlled gyro subjected to harmonic disturbances

International Nuclear Information System (INIS)

Perez Polo, Manuel F.; Perez Molina, Manuel

2007-01-01

Chaotic and steady state motions of a nonlinear controlled gimbals suspension gyro used to stabilize an external body are studied in this paper. The equations of the gyro without nonlinear control are deduced from the Euler-Lagrange equations by using the nutation theory. The equations of the system show that a cyclic variable appears. Its elimination allows us to find an auxiliary nonlinear system from which it is possible to deduce a nonlinear control law in order to obtain a desired equilibrium point. From the analysis of the nonlinear control law it is possible to show that due to both harmonic disturbances in the platform of the gyro and in the body to stabilize, regular and chaotic motions can appear. The chaotic motion is researched by means of chaos maps, bifurcation diagrams, sensitivity to initial conditions, Lyapunov exponents and Fourier spectrum density. The transition from chaotic to steady state motion by eliminating the harmonic disturbances from the modification of the initial nonlinear control law is also researched. Next, the paper shows how to use the chaotic motion in order to obtain small input signals so that the desired equilibrium state of the gyro can be reached. The developed methodology and its compared performance are evaluated through analytical methods and numerical simulations

Chaotic and steady state behaviour of a nonlinear controlled gyro subjected to harmonic disturbances

Energy Technology Data Exchange (ETDEWEB)

Perez Polo, Manuel F. [Department of Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Escuela Politecnica Superior, Campus de San Vicente, 03071 Alicante (Spain)]. E-mail: manolo@dfists.ua.es; Perez Molina, Manuel [Facultad de Ciencias Matematicas, Universidad Nacional de Educacion a Distancia, UNED, C/Boyero 12-1A, Alicante 03007 (Spain)]. E-mail: ma_perez_m@hotmail.com

2007-07-15

Chaotic and steady state motions of a nonlinear controlled gimbals suspension gyro used to stabilize an external body are studied in this paper. The equations of the gyro without nonlinear control are deduced from the Euler-Lagrange equations by using the nutation theory. The equations of the system show that a cyclic variable appears. Its elimination allows us to find an auxiliary nonlinear system from which it is possible to deduce a nonlinear control law in order to obtain a desired equilibrium point. From the analysis of the nonlinear control law it is possible to show that due to both harmonic disturbances in the platform of the gyro and in the body to stabilize, regular and chaotic motions can appear. The chaotic motion is researched by means of chaos maps, bifurcation diagrams, sensitivity to initial conditions, Lyapunov exponents and Fourier spectrum density. The transition from chaotic to steady state motion by eliminating the harmonic disturbances from the modification of the initial nonlinear control law is also researched. Next, the paper shows how to use the chaotic motion in order to obtain small input signals so that the desired equilibrium state of the gyro can be reached. The developed methodology and its compared performance are evaluated through analytical methods and numerical simulations.

Identification and robust water level control of horizontal steam generators using quantitative feedback theory

International Nuclear Information System (INIS)

Safarzadeh, O.; Khaki-Sedigh, A.; Shirani, A.S.

2011-01-01

Highlights: → A robust water level controller for steam generators (SGs) is designed based on the Quantitative Feedback Theory. → To design the controller, fairly accurate linear models are identified for the SG. → The designed controller is verified using a developed novel global locally linear neuro-fuzzy model of the SG. → Both of the linear and nonlinear models are based on the SG mathematical thermal-hydraulic model developed using the simulation computer code. → The proposed method is easy to apply and guarantees desired closed loop performance. - Abstract: In this paper, a robust water level control system for the horizontal steam generator (SG) using the quantitative feedback theory (QFT) method is presented. To design a robust QFT controller for the nonlinear uncertain SG, control oriented linear models are identified. Then, the nonlinear system is modeled as an uncertain linear time invariant (LTI) system. The robust designed controller is applied to the nonlinear plant model. This nonlinear model is based on a locally linear neuro-fuzzy (LLNF) model. This model is trained using the locally linear model tree (LOLIMOT) algorithm. Finally, simulation results are employed to show the effectiveness of the designed QFT level controller. It is shown that it will ensure the entire designer's water level closed loop specifications.

Identification and robust water level control of horizontal steam generators using quantitative feedback theory

Energy Technology Data Exchange (ETDEWEB)

Safarzadeh, O., E-mail: O_Safarzadeh@sbu.ac.ir [Shahid Beheshti University, P.O. Box: 19839-63113, Tehran (Iran, Islamic Republic of); Khaki-Sedigh, A. [K. N. Toosi University of Technology, Tehran (Iran, Islamic Republic of); Shirani, A.S. [Shahid Beheshti University, P.O. Box: 19839-63113, Tehran (Iran, Islamic Republic of)

2011-09-15

Highlights: {yields} A robust water level controller for steam generators (SGs) is designed based on the Quantitative Feedback Theory. {yields} To design the controller, fairly accurate linear models are identified for the SG. {yields} The designed controller is verified using a developed novel global locally linear neuro-fuzzy model of the SG. {yields} Both of the linear and nonlinear models are based on the SG mathematical thermal-hydraulic model developed using the simulation computer code. {yields} The proposed method is easy to apply and guarantees desired closed loop performance. - Abstract: In this paper, a robust water level control system for the horizontal steam generator (SG) using the quantitative feedback theory (QFT) method is presented. To design a robust QFT controller for the nonlinear uncertain SG, control oriented linear models are identified. Then, the nonlinear system is modeled as an uncertain linear time invariant (LTI) system. The robust designed controller is applied to the nonlinear plant model. This nonlinear model is based on a locally linear neuro-fuzzy (LLNF) model. This model is trained using the locally linear model tree (LOLIMOT) algorithm. Finally, simulation results are employed to show the effectiveness of the designed QFT level controller. It is shown that it will ensure the entire designer's water level closed loop specifications.

Internal Decoupling in Nonlinear Process Control

Directory of Open Access Journals (Sweden)

Jens G. Balchen

1988-07-01

Full Text Available A simple method has been investigated for the total or partial removal of the effect of non-linear process phenomena in multi-variable feedback control systems. The method is based upon computing the control variables which will drive the process at desired rates. It is shown that the effect of model errors in the linearization of the process can be partly removed through the use of large feedback gains. In practice there will be limits on how large gains can he used. The sensitivity to parameter errors is less pronounced and the transient behaviour is superior to that of ordinary PI controllers.

Characteristics of a reactor with power reactivity feedback

International Nuclear Information System (INIS)

Li Fengyu; Zhang Yusheng; Zhang Guangfu; Liu Ying

2008-01-01

The point-reactor model with power reactivity feedback becomes a nonlinear system. Its dynamic characteristic shows great complexity. According to the mathematic definition of stability in differential equation qualitative theory, the model of a reactor with power reactivity feedback is judged unstable. The equilibrium point is a saddle-node point. A portion of the trajectory in the neighborhood of the equilibrium point is parabolic fan curve, and the other is hyperbolic fan curve. Based on phase locus near the equilibrium point, it is pointed out that the model is still stable within physical limits. The difference between stabilities in the mathematical sense and in the physical sense is indicated. (authors)

Decentralized Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Robotic Walking*

Science.gov (United States)

Hamed, Kaveh Akbari; Gregg, Robert D.

2016-01-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg. PMID:27990059

Assessment of Effects of a Delay Block and a Nonlinear Block in Systems with Chaotic Behavior Using Lyapunov Exponents

Directory of Open Access Journals (Sweden)

Pablo César Rodríguez Gómez

2017-05-01

Full Text Available Context: Because feedback systems are very common and widely used, studies of the structural characteristics under which chaotic behavior is generated have been developed. These can be separated into a nonlinear system and a linear system at least of the third order. Methods such as the descriptive function have been used for analysis. Method: A feedback system is proposed comprising a linear system, a nonlinear system and a delay block, in order to assess his behavior using Lyapunov exponents. It is evaluated with three different linear systems, different delay values and different values for parameters of nonlinear characteristic, aiming to reach chaotic behavior. Results: One hundred experiments were carried out for each of the three linear systems, by changing the value of some parameters, assessing their influence on the dynamics of the system. Contour plots that relate these parameters to the Largest Lyapunov exponent were obtained and analyzed. Conclusions: In spite non-linearity is a condition for the existence of chaos, this does not imply that any nonlinear characteristic generates a chaotic system, it is reflected by the contour plots showing the transitions between chaotic and no chaotic behavior of the feedback system. Language: English

Feedback linearization based control of a variable air volume air conditioning system for cooling applications.

Science.gov (United States)

Thosar, Archana; Patra, Amit; Bhattacharyya, Souvik

2008-07-01

Design of a nonlinear control system for a Variable Air Volume Air Conditioning (VAVAC) plant through feedback linearization is presented in this article. VAVAC systems attempt to reduce building energy consumption while maintaining the primary role of air conditioning. The temperature of the space is maintained at a constant level by establishing a balance between the cooling load generated in the space and the air supply delivered to meet the load. The dynamic model of a VAVAC plant is derived and formulated as a MIMO bilinear system. Feedback linearization is applied for decoupling and linearization of the nonlinear model. Simulation results for a laboratory scale plant are presented to demonstrate the potential of keeping comfort and maintaining energy optimal performance by this methodology. Results obtained with a conventional PI controller and a feedback linearizing controller are compared and the superiority of the proposed approach is clearly established.

An accurate technique for the solution of the nonlinear point kinetics equations

International Nuclear Information System (INIS)

Picca, Paolo; Ganapol, Barry D.; Furfaro, Roberto

2011-01-01

A novel methodology for the solution of non-linear point kinetic (PK) equations is proposed. The technique is based on a piecewise constant approximation of PK system of ODEs and explicitly accounts for reactivity feedback effects, through an iterative cycle. High accuracy is reached by introducing a sub-mesh for the numerical evaluation of integrals involved and by correcting the source term to include the non-linear effect on a finer time scale. The use of extrapolation techniques for convergence acceleration is also explored. Results for adiabatic feedback model are reported and compared with other benchmarks in literature. The convergence trend makes the algorithm particularly attractive for applications, including in multi-point kinetics and quasi-static frameworks. (author)

Corticocortical feedback increases the spatial extent of normalization

Science.gov (United States)

Nassi, Jonathan J.; Gómez-Laberge, Camille; Kreiman, Gabriel; Born, Richard T.

2014-01-01

Normalization has been proposed as a canonical computation operating across different brain regions, sensory modalities, and species. It provides a good phenomenological description of non-linear response properties in primary visual cortex (V1), including the contrast response function and surround suppression. Despite its widespread application throughout the visual system, the underlying neural mechanisms remain largely unknown. We recently observed that corticocortical feedback contributes to surround suppression in V1, raising the possibility that feedback acts through normalization. To test this idea, we characterized area summation and contrast response properties in V1 with and without feedback from V2 and V3 in alert macaques and applied a standard normalization model to the data. Area summation properties were well explained by a form of divisive normalization, which computes the ratio between a neuron's driving input and the spatially integrated activity of a “normalization pool.” Feedback inactivation reduced surround suppression by shrinking the spatial extent of the normalization pool. This effect was independent of the gain modulation thought to mediate the influence of contrast on area summation, which remained intact during feedback inactivation. Contrast sensitivity within the receptive field center was also unaffected by feedback inactivation, providing further evidence that feedback participates in normalization independent of the circuit mechanisms involved in modulating contrast gain and saturation. These results suggest that corticocortical feedback contributes to surround suppression by increasing the visuotopic extent of normalization and, via this mechanism, feedback can play a critical role in contextual information processing. PMID:24910596

A Kinematic Conservation Law in Free Surface Flow

OpenAIRE

Gavrilyuk , Sergey; Kalisch , Henrik; Khorsand , Zahra

2015-01-01

The Green-Naghdi system is used to model highly nonlinear weakly dispersive waves propagating at the surface of a shallow layer of a perfect fluid. The system has three associated conservation laws which describe the conservation of mass, momentum, and energy due to the surface wave motion. In addition, the system features a fourth conservation law which is the main focus of this note. It will be shown how this fourth conservation law can be interpreted in terms of a concrete kinematic quanti...

Preface: Multiscale feedbacks in ecogeomorphology

Science.gov (United States)

Wheaton, Joseph M.; Gibbins, Chris; Wainwright, John; Larsen, Laurel G.; McElroy, Brandon

2011-01-01

Geomorphic systems are known to exhibit nonlinear responses to physical–biological feedbacks (Thornes, 1985; Baas, 2002; Reinhardt et al., 2010). These responses make understanding and/or predicting system response to change highly challenging. With growing concerns over ecosystem health, a pressing need exists for research that tries to elucidate these feedbacks (Jerolmack, 2008; Darby, 2010; National Research Council, 2010). A session was convened at the Fall 2008 meeting of the American Geophysical Union (AGU) to provide an outlet for some of this truly interdisciplinary and original research, which is central to understanding geomorphic and ecological dynamics. The session attracted over 39 contributions, which were divided into two well-attended oral sessions and a very busy poster session. This special issue presents new research from the AGU session, which highlights clear physical–biological feedbacks. The aim is to bring together contrasting perspectives on biological and geomorphic feedbacks in a diversity of physiographic settings, ranging from wetlands and estuaries, through rivers, to uplands. These papers highlight biological and physical feedbacks which involve the modulation or amplification of geomorphic processes. These papers will be of interest to a core geomorphology audience, and should also draw attention from the fields of ecohydraulics, hydroecology, ecohydrology, ecomorphology, biogeochemistry and biogeography, and biogeomorphology as well as the more traditional fields of hydrology, ecology and biology. In this preface to the special issue, we a) review past contributions to the emerging field of ecogeomorphology and related disciplines, b) provide some context for how this topical special issue came to fruition, and c) summarize the contributions to this special issue.

Singularity-Free Neural Control for the Exponential Trajectory Tracking in Multiple-Input Uncertain Systems with Unknown Deadzone Nonlinearities

Directory of Open Access Journals (Sweden)

J. Humberto Pérez-Cruz

2014-01-01

Full Text Available The trajectory tracking for a class of uncertain nonlinear systems in which the number of possible states is equal to the number of inputs and each input is preceded by an unknown symmetric deadzone is considered. The unknown dynamics is identified by means of a continuous time recurrent neural network in which the control singularity is conveniently avoided by guaranteeing the invertibility of the coupling matrix. Given this neural network-based mathematical model of the uncertain system, a singularity-free feedback linearization control law is developed in order to compel the system state to follow a reference trajectory. By means of Lyapunov-like analysis, the exponential convergence of the tracking error to a bounded zone can be proven. Likewise, the boundedness of all closed-loop signals can be guaranteed.

Comparative study of flare control laws. [optimal control of b-737 aircraft approach and landing

Science.gov (United States)

Nadkarni, A. A.; Breedlove, W. J., Jr.

1979-01-01

A digital 3-D automatic control law was developed to achieve an optimal transition of a B-737 aircraft between various initial glid slope conditions and the desired final touchdown condition. A discrete, time-invariant, optimal, closed-loop control law presented for a linear regulator problem, was extended to include a system being acted upon by a constant disturbance. Two forms of control laws were derived to solve this problem. One method utilized the feedback of integral states defined appropriately and augmented with the original system equations. The second method formulated the problem as a control variable constraint, and the control variables were augmented with the original system. The control variable constraint control law yielded a better performance compared to feedback control law for the integral states chosen.

Linearizing feedforward/feedback attitude control

Science.gov (United States)

Paielli, Russell A.; Bach, Ralph E.

1991-01-01

An approach to attitude control theory is introduced in which a linear form is postulated for the closed-loop rotation error dynamics, then the exact control law required to realize it is derived. The nonminimal (four-component) quaternion form is used to attitude because it is globally nonsingular, but the minimal (three-component) quaternion form is used for attitude error because it has no nonlinear constraints to prevent the rotational error dynamics from being linearized, and the definition of the attitude error is based on quaternion algebra. This approach produces an attitude control law that linearizes the closed-loop rotational error dynamics exactly, without any attitude singularities, even if the control errors become large.

Stability and Bifurcation in Magnetic Flux Feedback Maglev Control System

Directory of Open Access Journals (Sweden)

Wen-Qing Zhang

2013-01-01

Full Text Available Nonlinear properties of magnetic flux feedback control system have been investigated mainly in this paper. We analyzed the influence of magnetic flux feedback control system on control property by time delay and interfering signal of acceleration. First of all, we have established maglev nonlinear model based on magnetic flux feedback and then discussed hopf bifurcation’s condition caused by the acceleration’s time delay. The critical value of delayed time is obtained. It is proved that the period solution exists in maglev control system and the stable condition has been got. We obtained the characteristic values by employing center manifold reduction theory and normal form method, which represent separately the direction of hopf bifurcation, the stability of the period solution, and the period of the period motion. Subsequently, we discussed the influence maglev system on stability of by acceleration’s interfering signal and obtained the stable domain of interfering signal. Some experiments have been done on CMS04 maglev vehicle of National University of Defense Technology (NUDT in Tangshan city. The results of experiments demonstrate that viewpoints of this paper are correct and scientific. When time lag reaches the critical value, maglev system will produce a supercritical hopf bifurcation which may cause unstable period motion.

Nonlinear dynamics and control of a vibrating rectangular plate

Science.gov (United States)

Shebalin, J. V.

1983-01-01

The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.

Non-linear laws of echoic memory and auditory change detection in humans.

Science.gov (United States)

Inui, Koji; Urakawa, Tomokazu; Yamashiro, Koya; Otsuru, Naofumi; Nishihara, Makoto; Takeshima, Yasuyuki; Keceli, Sumru; Kakigi, Ryusuke

2010-07-03

The detection of any abrupt change in the environment is important to survival. Since memory of preceding sensory conditions is necessary for detecting changes, such a change-detection system relates closely to the memory system. Here we used an auditory change-related N1 subcomponent (change-N1) of event-related brain potentials to investigate cortical mechanisms underlying change detection and echoic memory. Change-N1 was elicited by a simple paradigm with two tones, a standard followed by a deviant, while subjects watched a silent movie. The amplitude of change-N1 elicited by a fixed sound pressure deviance (70 dB vs. 75 dB) was negatively correlated with the logarithm of the interval between the standard sound and deviant sound (1, 10, 100, or 1000 ms), while positively correlated with the logarithm of the duration of the standard sound (25, 100, 500, or 1000 ms). The amplitude of change-N1 elicited by a deviance in sound pressure, sound frequency, and sound location was correlated with the logarithm of the magnitude of physical differences between the standard and deviant sounds. The present findings suggest that temporal representation of echoic memory is non-linear and Weber-Fechner law holds for the automatic cortical response to sound changes within a suprathreshold range. Since the present results show that the behavior of echoic memory can be understood through change-N1, change-N1 would be a useful tool to investigate memory systems.

Synthetic Jet Actuator-Based Aircraft Tracking Using a Continuous Robust Nonlinear Control Strategy

Directory of Open Access Journals (Sweden)

N. Ramos-Pedroza

2017-01-01

Full Text Available A robust nonlinear control law that achieves trajectory tracking control for unmanned aerial vehicles (UAVs equipped with synthetic jet actuators (SJAs is presented in this paper. A key challenge in the control design is that the dynamic characteristics of SJAs are nonlinear and contain parametric uncertainty. The challenge resulting from the uncertain SJA actuator parameters is mitigated via innovative algebraic manipulation in the tracking error system derivation along with a robust nonlinear control law employing constant SJA parameter estimates. A key contribution of the paper is a rigorous analysis of the range of SJA actuator parameter uncertainty within which asymptotic UAV trajectory tracking can be achieved. A rigorous stability analysis is carried out to prove semiglobal asymptotic trajectory tracking. Detailed simulation results are included to illustrate the effectiveness of the proposed control law in the presence of wind gusts and varying levels of SJA actuator parameter uncertainty.

International Conference on Structural Nonlinear Dynamics and Diagnosis

CERN Document Server

CSNDD 2012; CSNDD 2014

2015-01-01

This book, which presents the peer-reviewed post-proceedings of CSNDD 2012 and CSNDD 2014, addresses the important role that relevant concepts and tools from nonlinear and complex dynamics could play in present and future engineering applications. It includes 22 chapters contributed by outstanding researchers and covering various aspects of applications, including: structural health monitoring, diagnosis and damage detection, experimental methodologies, active vibration control and smart structures, passive control of structures using nonlinear energy sinks, vibro-impact dynamic MEMS/NEMS/AFM, energy-harvesting materials and structures, and time-delayed feedback control, as well as aspects of deterministic versus stochastic dynamics and control of nonlinear phenomena in physics.  Researchers and engineers interested in the challenges posed and opportunities offered by nonlinearities in the development of passive and active control strategies, energy harvesting, novel design criteria, modeling and characteriz...

Merger negotiations with stock market feedback

OpenAIRE

Betton, Sandra; Eckbo, B. Espen; Thompson, Rex; Thorburn, Karin S.

2011-01-01

Merger negotiations routinely occur amidst economically significant a target stock price runups. Since the source of the runup is unobservable (is it a target stand-alone value change and/or deal anticipation?), feeding the runup back into the offer price risks "paying twice" for the target shares. We present a novel structural empirical analysis of this runup feedback hypothesis. We show that rational deal anticipation implies a nonlinear relationship between the runup and the offer price ma...

Differential quadrature method of nonlinear bending of functionally graded beam

Science.gov (United States)

Gangnian, Xu; Liansheng, Ma; Wang, Youzhi; Quan, Yuan; Weijie, You

2018-02-01

Using the third-order shear deflection beam theory (TBT), nonlinear bending of functionally graded (FG) beams composed with various amounts of ceramic and metal is analyzed utilizing the differential quadrature method (DQM). The properties of beam material are supposed to accord with the power law index along to thickness. First, according to the principle of stationary potential energy, the partial differential control formulae of the FG beams subjected to a distributed lateral force are derived. To obtain numerical results of the nonlinear bending, non-dimensional boundary conditions and control formulae are dispersed by applying the DQM. To verify the present solution, several examples are analyzed for nonlinear bending of homogeneous beams with various edges. A minute parametric research is in progress about the effect of the law index, transverse shear deformation, distributed lateral force and boundary conditions.

Time series with tailored nonlinearities

Science.gov (United States)

Räth, C.; Laut, I.

2015-10-01

It is demonstrated how to generate time series with tailored nonlinearities by inducing well-defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of nonlinearities are established and their origin is explained. By applying a set of simple constraints on the phases of an originally linear and uncorrelated Gaussian time series, the observed scaling behavior of the intensity distribution of empirical time series can be reproduced. The power law character of the intensity distributions being typical for, e.g., turbulence and financial data can thus be explained in terms of phase correlations.

Adaptive Output Tracking Control for Nonlinear Systems with Failed Actuators and Aircraft Flight System Applications

OpenAIRE

Hou, Chuanjing; Hu, Lisheng; Zhang, Yingwei

2015-01-01

An adaptive failure compensation scheme using output feedback is proposed for a class of nonlinear systems with nonlinearities depending on the unmeasured states of systems. Adaptive high-gain K-filters are presented to suppress the nonlinearities while the proposed backstepping adaptive high-gain controller guarantees the stability of the closed-loop system and small tracking errors. Simulation results verify that the adaptive failure compensation scheme is effective.

Estimation of dynamic reactivity using an H∞ optimal filter with a nonlinear term

International Nuclear Information System (INIS)

Suzuki, Katsuo; Watanabe, Koiti

1996-01-01

A method of nonlinear filtering is applied to the problem of estimating the dynamic reactivity of a nonlinear reactor system. The nonlinear filtering algorithm developed is a simple modification of a linear H ∞ optimal filter with a nonlinear feedback loop added. The linear filter is designed on the basis of a linearized dynamical system model that consists of linearized point reactor kinetic equations and a reactivity state equation driven by a fictitious signal. The latter is artificially introduced to deal with the reactivity as a state variable. The results of the computer simulation show that the nonlinear filtering algorithm can be applied to estimate the dynamic reactivity of the nonlinear reactor system, even under relatively large reactivity disturbances

Nonlinear Dynamic Modeling of a Fixed-Wing Unmanned Aerial Vehicle: a Case Study of Wulung

Directory of Open Access Journals (Sweden)

Fadjar Rahino Triputra

2015-07-01

Full Text Available Developing a nonlinear adaptive control system for a fixed-wing unmanned aerial vehicle (UAV requires a mathematical representation of the system dynamics analytically as a set of differential equations in the form of a strict-feedback systems. This paper presents a method for modeling a nonlinear flight dynamics of the fixed-wing UAV of BPPT Wulung in any conditions of the flight altitude and airspeed for the first step into designing a nonlinear adaptive controller. The model was formed into 10-DOF differential equations in the form of strict-feedback systems which separates the terms of elevator, aileron, rudder and throttle from the model. The model simulation results show the behavior of the flight dynamics of the Wulung UAV and also prove the compliance with the actual flight test results.

Comparative study of flare control laws

Science.gov (United States)

Nadkarni, A. A.

1981-01-01

The development of a digital, three dimensional, automatic control law designed to achieve an optimal transition of a B-737 aircraft between glide slope conditions and the desired final touchdown condition is presented. The digital control law is a time invariant, state estimate feedback law, and the design is capable of using the microwave landing system. Major emphasis is placed on the reduction of aircraft noise in communities surroundings airports, the reduction of fuel consumption, the reduction of the effects of adverse weather conditions on aircraft operations, and the efficient use of airspace in congested terminal areas. Attention is also given to the development of the capability to perform automatic flares from steep glide slopes to precise touchdown locations.

Nonlinear Viscoelastic Rheology and the Occurrence of Aftershocks

Science.gov (United States)

Shcherbakov, R.; Zhang, X.

2017-12-01

Aftershocks are ubiquitous in nature. They are the manifestation of relaxation phenomena observed in various physical systems. In one prominent example, they typically occur after large earthquakes. The observed aftershock sequences usually obey several well defined non-trivial empirical laws in magnitude, temporal, and spatial domains. In many cases their characteristics follow scale-invariant distributions. The occurrence of aftershocks displays a prominent temporal behavior due to time-dependent mechanisms of stress and/or energy transfer. There are compelling evidences that the lower continental crust and upper mantle are governed by various solid state creep mechanisms. Among those mechanisms a power-law viscous flow was suggested to explain the postseismic surface deformation after large earthquakes. In this work, we consider a slider-block model to mimic the behavior of a seismogenic fault. In the model, we introduce a nonlinear viscoelastic coupling mechanism to capture the essential characteristics of crustal rheology and stress interaction between the blocks and the medium. For this purpose we employ nonlinear Kelvin-Voigt elements consisting of an elastic spring and a dashpot assembled in parallel to introduce viscoelastic coupling between the blocks and the driving plate. By mapping the model into a cellular automaton we derive the functional form of the stress transfer mechanism in the model. We show that the nonlinear viscoelasticity plays a critical role in triggering of aftershocks. It explains the functional form of the Omori-Utsu law and gives physical interpretation of its parameters. The proposed model also suggests that the power-law rheology of the fault gauge and underlying lower crust and upper mantle controls the decay rate of aftershocks. To verify this, we analyze several prominent aftershock sequences to estimate their decay rates and correlate with the rheological properties of the underlying lower crust and mantle, which were estimated

Observer-based output-feedback control to eliminate torsional drill-string vibrations

NARCIS (Netherlands)

Vromen, T.G.M.; Wouw, van de N.; Doris, A.; Astrid, P.; Nijmeijer, H.

2014-01-01

Torsional stick-slip vibrations decrease the performance and reliability of drilling systems used for the exploration of energy and mineral resources. In this work, we present the design of a nonlinear observer-based output-feedback control strategy to eliminate these vibrations. We apply the

Uplink SDMA with Limited Feedback: Throughput Scaling

Directory of Open Access Journals (Sweden)

Jeffrey G. Andrews

2008-01-01

Full Text Available Combined space division multiple access (SDMA and scheduling exploit both spatial multiplexing and multiuser diversity, increasing throughput significantly. Both SDMA and scheduling require feedback of multiuser channel sate information (CSI. This paper focuses on uplink SDMA with limited feedback, which refers to efficient techniques for CSI quantization and feedback. To quantify the throughput of uplink SDMA and derive design guidelines, the throughput scaling with system parameters is analyzed. The specific parameters considered include the numbers of users, antennas, and feedback bits. Furthermore, different SNR regimes and beamforming methods are considered. The derived throughput scaling laws are observed to change for different SNR regimes. For instance, the throughput scales logarithmically with the number of users in the high SNR regime but double logarithmically in the low SNR regime. The analysis of throughput scaling suggests guidelines for scheduling in uplink SDMA. For example, to maximize throughput scaling, scheduling should use the criterion of minimum quantization errors for the high SNR regime and maximum channel power for the low SNR regime.

L2-gain and passivity techniques in nonlinear control

CERN Document Server

van der Schaft, Arjan

2017-01-01

This standard text gives a unified treatment of passivity and L2-gain theory for nonlinear state space systems, preceded by a compact treatment of classical passivity and small-gain theorems for nonlinear input-output maps. The synthesis between passivity and L2-gain theory is provided by the theory of dissipative systems. Specifically, the small-gain and passivity theorems and their implications for nonlinear stability and stabilization are discussed from this standpoint. The connection between L2-gain and passivity via scattering is detailed. Feedback equivalence to a passive system and resulting stabilization strategies are discussed. The passivity concepts are enriched by a generalised Hamiltonian formalism, emphasising the close relations with physical modeling and control by interconnection, and leading to novel control methodologies going beyond passivity. The potential of L2-gain techniques in nonlinear control, including a theory of all-pass factorizations of nonlinear systems, and of parametrization...

Irregular persistent activity induced by synaptic excitatory feedback

Directory of Open Access Journals (Sweden)

Francesca Barbieri

2007-11-01

Full Text Available Neurophysiological experiments on monkeys have reported highly irregular persistent activity during the performance of an oculomotor delayed-response task. These experiments show that during the delay period the coefficient of variation (CV of interspike intervals (ISI of prefrontal neurons is above 1, on average, and larger than during the fixation period. In the present paper, we show that this feature can be reproduced in a network in which persistent activity is induced by excitatory feedback, provided that (i the post-spike reset is close enough to threshold , (ii synaptic efficacies are a non-linear function of the pre-synaptic firing rate. Non-linearity between presynaptic rate and effective synaptic strength is implemented by a standard short-term depression mechanism (STD. First, we consider the simplest possible network with excitatory feedback: a fully connected homogeneous network of excitatory leaky integrate-and-fire neurons, using both numerical simulations and analytical techniques. The results are then confirmed in a network with selective excitatory neurons and inhibition. In both the cases there is a large range of values of the synaptic efficacies for which the statistics of firing of single cells is similar to experimental data.

Propagation of flexural waves in inhomogeneous plates exhibiting hysteretic nonlinearity: Nonlinear acoustic black holes.

Science.gov (United States)

Gusev, Vitalyi E; Ni, Chenyin; Lomonosov, Alexey; Shen, Zhonghua

2015-08-01

Theory accounting for the influence of hysteretic nonlinearity of micro-inhomogeneous material on flexural wave in the plates of continuously varying thickness is developed. For the wedges with thickness increasing as a power law of distance from its edge strong modifications of the wave dynamics with propagation distance are predicted. It is found that nonlinear absorption progressively disappearing with diminishing wave amplitude leads to complete attenuation of acoustic waves in most of the wedges exhibiting black hole phenomenon. It is also demonstrated that black holes exist beyond the geometrical acoustic approximation. Applications include nondestructive evaluation of micro-inhomogeneous materials and vibrations damping. Copyright © 2015 Elsevier B.V. All rights reserved.

Modelling nonlinear viscoelastic behaviours of loudspeaker suspensions-like structures

Science.gov (United States)

Maillou, Balbine; Lotton, Pierrick; Novak, Antonin; Simon, Laurent

2018-03-01

Mechanical properties of an electrodynamic loudspeaker are mainly determined by its suspensions (surround and spider) that behave nonlinearly and typically exhibit frequency dependent viscoelastic properties such as creep effect. The paper aims at characterizing the mechanical behaviour of electrodynamic loudspeaker suspensions at low frequencies using nonlinear identification techniques developed in recent years. A Generalized Hammerstein based model can take into account both frequency dependency and nonlinear properties. As shown in the paper, the model generalizes existing nonlinear or viscoelastic models commonly used for loudspeaker modelling. It is further experimentally shown that a possible input-dependent law may play a key role in suspension characterization.

Relaxation rates of gene expression kinetics reveal the feedback signs of autoregulatory gene networks

Science.gov (United States)

Jia, Chen; Qian, Hong; Chen, Min; Zhang, Michael Q.

2018-03-01

The transient response to a stimulus and subsequent recovery to a steady state are the fundamental characteristics of a living organism. Here we study the relaxation kinetics of autoregulatory gene networks based on the chemical master equation model of single-cell stochastic gene expression with nonlinear feedback regulation. We report a novel relation between the rate of relaxation, characterized by the spectral gap of the Markov model, and the feedback sign of the underlying gene circuit. When a network has no feedback, the relaxation rate is exactly the decaying rate of the protein. We further show that positive feedback always slows down the relaxation kinetics while negative feedback always speeds it up. Numerical simulations demonstrate that this relation provides a possible method to infer the feedback topology of autoregulatory gene networks by using time-series data of gene expression.

Adaptive Output Tracking Control for Nonlinear Systems with Failed Actuators and Aircraft Flight System Applications

Directory of Open Access Journals (Sweden)

Chuanjing Hou

2015-01-01

Full Text Available An adaptive failure compensation scheme using output feedback is proposed for a class of nonlinear systems with nonlinearities depending on the unmeasured states of systems. Adaptive high-gain K-filters are presented to suppress the nonlinearities while the proposed backstepping adaptive high-gain controller guarantees the stability of the closed-loop system and small tracking errors. Simulation results verify that the adaptive failure compensation scheme is effective.

Synchronization of FitzHugh-Nagumo neurons in external electrical stimulation via nonlinear control

International Nuclear Information System (INIS)

Wang Jiang; Zhang Ting; Deng Bin

2007-01-01

Synchronization of FitzHugh-Nagumo neural system under external electrical stimulation via the nonlinear control is investigated in this paper. Firstly, the different dynamical behavior of the nonlinear cable model based on the FitzHugh-Nagumo model responding to various external electrical stimulations is studied. Next, using the result of the analysis, a nonlinear feedback linearization control scheme and an adaptive control strategy are designed to synchronization two neurons. Computer simulations are provided to verify the efficiency of the designed synchronization schemes

Rotating black string with nonlinear source

International Nuclear Information System (INIS)

Hendi, S. H.

2010-01-01

In this paper, we derive rotating black string solutions in the presence of two kinds of nonlinear electromagnetic fields, so-called Born-Infeld and power Maxwell invariant. Investigation of the solutions show that for the Born-Infeld black string the singularity is timelike and the asymptotic behavior of the solutions is anti-de Sitter, but for power Maxwell invariant solutions, depending on the values of nonlinearity parameter, the singularity may be timelike as well as spacelike and the solutions are not asymptotically anti-de Sitter for all values of the nonlinearity parameter. Next, we calculate the conserved quantities of the solutions by using the counterterm method, and find that these quantities do not depend on the nonlinearity parameter. We also compute the entropy, temperature, the angular velocity, the electric charge, and the electric potential of the solutions, in which the conserved and thermodynamics quantities satisfy the first law of thermodynamics.

Suboptimal RED Feedback Control for Buffered TCP Flow Dynamics in Computer Network

Directory of Open Access Journals (Sweden)

N. U. Ahmed

2007-01-01

Full Text Available We present an improved dynamic system that simulates the behavior of TCP flows and active queue management (AQM system. This system can be modeled by a set of stochastic differential equations driven by a doubly stochastic point process with intensities being the controls. The feedback laws proposed monitor the status of buffers and multiplexor of the router, detect incipient congestion by sending warning signals to the sources. The simulation results show that the optimal feedback control law from the class of linear as well as quadratic polynomials can improve the system performance significantly in terms of maximizing the link utilization, minimizing congestion, packet losses, as well as global synchronization. The optimization process used is based on random recursive search technique known as RRS.

Chaotic dynamics and chaos control in nonlinear laser systems

International Nuclear Information System (INIS)

Fang Jinqing; Yao Weiguang

2001-01-01

Chaotic dynamics and chaos control have become a great challenge in nonlinear laser systems and its advances are reviewed mainly based on the ring cavity laser systems. The principle and stability conditions for time-delay feedback control are analyzed and applied to chaos control in the laser systems. Other advanced methods of chaos control, such as weak spatial perturbation and occasional proportional feedback technique, are discussed. Prospects of chaos control for application (such as improvement of laser power and performance, synchronized chaos secure communication and information processing) are pointed out finally

Design and Validation of Optimized Feedforward with Robust Feedback Control of a Nuclear Reactor

International Nuclear Information System (INIS)

Shaffer, Roman; He Weidong; Edwards, Robert M.

2004-01-01

Design applications for robust feedback and optimized feedforward control, with confirming results from experiments conducted on the Pennsylvania State University TRIGA reactor, are presented. The combination of feedforward and feedback control techniques complement each other in that robust control offers guaranteed closed-loop stability in the presence of uncertainties, and optimized feedforward offers an approach to achieving performance that is sometimes limited by overly conservative robust feedback control. The design approach taken in this work combines these techniques by first designing robust feedback control. Alternative methods for specifying a low-order linear model and uncertainty specifications, while seeking as much performance as possible, are discussed and evaluated. To achieve desired performance characteristics, the optimized feedforward control is then computed by using the nominal nonlinear plant model that incorporates the robust feedback control

Non-linear laws of echoic memory and auditory change detection in humans

Directory of Open Access Journals (Sweden)

Takeshima Yasuyuki

2010-07-01

Full Text Available Abstract Background The detection of any abrupt change in the environment is important to survival. Since memory of preceding sensory conditions is necessary for detecting changes, such a change-detection system relates closely to the memory system. Here we used an auditory change-related N1 subcomponent (change-N1 of event-related brain potentials to investigate cortical mechanisms underlying change detection and echoic memory. Results Change-N1 was elicited by a simple paradigm with two tones, a standard followed by a deviant, while subjects watched a silent movie. The amplitude of change-N1 elicited by a fixed sound pressure deviance (70 dB vs. 75 dB was negatively correlated with the logarithm of the interval between the standard sound and deviant sound (1, 10, 100, or 1000 ms, while positively correlated with the logarithm of the duration of the standard sound (25, 100, 500, or 1000 ms. The amplitude of change-N1 elicited by a deviance in sound pressure, sound frequency, and sound location was correlated with the logarithm of the magnitude of physical differences between the standard and deviant sounds. Conclusions The present findings suggest that temporal representation of echoic memory is non-linear and Weber-Fechner law holds for the automatic cortical response to sound changes within a suprathreshold range. Since the present results show that the behavior of echoic memory can be understood through change-N1, change-N1 would be a useful tool to investigate memory systems.

Nonlinear Analysis of Renal Autoregulation Under Broadband Forcing Conditions

DEFF Research Database (Denmark)

Marmarelis, V Z; Chon, K H; Chen, Y M

1994-01-01

Linear analysis of renal blood flow fluctuations, induced experimentally in rats by broad-band (pseudorandom) arterial blood pressure forcing at various power levels, has been unable to explain fully the dynamics of renal autoregulation at low frequencies. This observation has suggested...... the possibility of nonlinear mechanisms subserving renal autoregulation at frequencies below 0.2 Hz. This paper presents results of 3rd-order Volterra-Wiener analysis that appear to explain adequately the nonlinearities in the pressure-flow relation below 0.2 Hz in rats. The contribution of the 3rd-order kernel...... in describing the dynamic pressure-flow relation is found to be important. Furthermore, the dependence of 1st-order kernel waveforms on the power level of broadband pressure forcing indicates the presence of nonlinear feedback (of sigmoid type) based on previously reported analysis of a class of nonlinear...

Robust Control and Motion Planning for Nonlinear Underactuated Systems Using H infinity Techniques

National Research Council Canada - National Science Library

Toussaint, Gregory

2000-01-01

This thesis presents new techniques for planning and robustly controlling the motion of nonlinear underactuated vehicles when disturbances are present and only imperfect state measurements are available for feedback...

Nonlinear H∞ Optimal Control Scheme for an Underwater Vehicle with Regional Function Formulation

Directory of Open Access Journals (Sweden)

Zool H. Ismail

2013-01-01

Full Text Available A conventional region control technique cannot meet the demands for an accurate tracking performance in view of its inability to accommodate highly nonlinear system dynamics, imprecise hydrodynamic coefficients, and external disturbances. In this paper, a robust technique is presented for an Autonomous Underwater Vehicle (AUV with region tracking function. Within this control scheme, nonlinear H∞ and region based control schemes are used. A Lyapunov-like function is presented for stability analysis of the proposed control law. Numerical simulations are presented to demonstrate the performance of the proposed tracking control of the AUV. It is shown that the proposed control law is robust against parameter uncertainties, external disturbances, and nonlinearities and it leads to uniform ultimate boundedness of the region tracking error.

Output Feedback-Based Boundary Control of Uncertain Coupled Semilinear Parabolic PDE Using Neurodynamic Programming.

Science.gov (United States)

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

In this paper, neurodynamic programming-based output feedback boundary control of distributed parameter systems governed by uncertain coupled semilinear parabolic partial differential equations (PDEs) under Neumann or Dirichlet boundary control conditions is introduced. First, Hamilton-Jacobi-Bellman (HJB) equation is formulated in the original PDE domain and the optimal control policy is derived using the value functional as the solution of the HJB equation. Subsequently, a novel observer is developed to estimate the system states given the uncertain nonlinearity in PDE dynamics and measured outputs. Consequently, the suboptimal boundary control policy is obtained by forward-in-time estimation of the value functional using a neural network (NN)-based online approximator and estimated state vector obtained from the NN observer. Novel adaptive tuning laws in continuous time are proposed for learning the value functional online to satisfy the HJB equation along system trajectories while ensuring the closed-loop stability. Local uniformly ultimate boundedness of the closed-loop system is verified by using Lyapunov theory. The performance of the proposed controller is verified via simulation on an unstable coupled diffusion reaction process.

Nonlinear Feedback Control and Stability Analysis of a Proof-of-Work Blockchain

Directory of Open Access Journals (Sweden)

Geir Hovland

2017-10-01

Full Text Available In this paper a novel feedback controller and stability analysis of a blockchain implementation is developed by using a control engineering perspective. The controller output equals the difficulty adjustment in the mining process while the feedback variable is the average block time over a certain time period. The computational power (hash rate of the miners is considered a disturbance in the model. The developed controller is tested against a simulation model with constant disturbance, step and ramp responses as well as with a high-frequency sinusoidal disturbance. Stability and a fast response is demonstrated in all these cases with a controller which adjusts it's output at every new block. Finally the performance of the controller is implemented and demonstrated on a testnet with a constant hash rate as well as on the mainnet of a public open source blockchain project.

Feedforward-feedback hybrid control for magnetic shape memory alloy actuators based on the Krasnosel'skii-Pokrovskii model.

Directory of Open Access Journals (Sweden)

Miaolei Zhou

Full Text Available As a new type of smart material, magnetic shape memory alloy has the advantages of a fast response frequency and outstanding strain capability in the field of microdrive and microposition actuators. The hysteresis nonlinearity in magnetic shape memory alloy actuators, however, limits system performance and further application. Here we propose a feedforward-feedback hybrid control method to improve control precision and mitigate the effects of the hysteresis nonlinearity of magnetic shape memory alloy actuators. First, hysteresis nonlinearity compensation for the magnetic shape memory alloy actuator is implemented by establishing a feedforward controller which is an inverse hysteresis model based on Krasnosel'skii-Pokrovskii operator. Secondly, the paper employs the classical Proportion Integration Differentiation feedback control with feedforward control to comprise the hybrid control system, and for further enhancing the adaptive performance of the system and improving the control accuracy, the Radial Basis Function neural network self-tuning Proportion Integration Differentiation feedback control replaces the classical Proportion Integration Differentiation feedback control. Utilizing self-learning ability of the Radial Basis Function neural network obtains Jacobian information of magnetic shape memory alloy actuator for the on-line adjustment of parameters in Proportion Integration Differentiation controller. Finally, simulation results show that the hybrid control method proposed in this paper can greatly improve the control precision of magnetic shape memory alloy actuator and the maximum tracking error is reduced from 1.1% in the open-loop system to 0.43% in the hybrid control system.

Feedforward-feedback hybrid control for magnetic shape memory alloy actuators based on the Krasnosel'skii-Pokrovskii model.

Science.gov (United States)

Zhou, Miaolei; Zhang, Qi; Wang, Jingyuan

2014-01-01

As a new type of smart material, magnetic shape memory alloy has the advantages of a fast response frequency and outstanding strain capability in the field of microdrive and microposition actuators. The hysteresis nonlinearity in magnetic shape memory alloy actuators, however, limits system performance and further application. Here we propose a feedforward-feedback hybrid control method to improve control precision and mitigate the effects of the hysteresis nonlinearity of magnetic shape memory alloy actuators. First, hysteresis nonlinearity compensation for the magnetic shape memory alloy actuator is implemented by establishing a feedforward controller which is an inverse hysteresis model based on Krasnosel'skii-Pokrovskii operator. Secondly, the paper employs the classical Proportion Integration Differentiation feedback control with feedforward control to comprise the hybrid control system, and for further enhancing the adaptive performance of the system and improving the control accuracy, the Radial Basis Function neural network self-tuning Proportion Integration Differentiation feedback control replaces the classical Proportion Integration Differentiation feedback control. Utilizing self-learning ability of the Radial Basis Function neural network obtains Jacobian information of magnetic shape memory alloy actuator for the on-line adjustment of parameters in Proportion Integration Differentiation controller. Finally, simulation results show that the hybrid control method proposed in this paper can greatly improve the control precision of magnetic shape memory alloy actuator and the maximum tracking error is reduced from 1.1% in the open-loop system to 0.43% in the hybrid control system.

Nonlinear Vibration and Mode Shapes of FG Cylindrical Shells

Directory of Open Access Journals (Sweden)

Saeed Mahmoudkhani

Full Text Available Abstract The nonlinear vibration and normal mode shapes of FG cylindrical shells are investigated using an efficient analytical method. The equations of motion of the shell are based on the Donnell’s non-linear shallow-shell, and the material is assumed to be gradually changed across the thickness according to the simple power law. The solution is provided by first discretizing the equations of motion using the multi-mode Galerkin’s method. The nonlinear normal mode of the system is then extracted using the invariant manifold approach and employed to decouple the discretized equations. The homotopy analysis method is finally used to determine the nonlinear frequency. Numerical results are presented for the backbone curves of FG cylindrical shells, nonlinear mode shapes and also the nonlinear invariant modal surfaces. The volume fraction index and the geometric properties of the shell are found to be effective on the type of nonlinear behavior and also the nonlinear mode shapes of the shell. The circumferential half-wave numbers of the nonlinear mode shapes are found to change with time especially in a thinner cylinder.

Nonlinear identification of process dynamics using neural networks

International Nuclear Information System (INIS)

Parlos, A.G.; Atiya, A.F.; Chong, K.T.

1992-01-01

In this paper the nonlinear identification of process dynamics encountered in nuclear power plant components is addressed, in an input-output sense, using artificial neural systems. A hybrid feedforward/feedback neural network, namely, a recurrent multilayer perceptron, is used as the model structure to be identified. The feedforward portion of the network architecture provides its well-known interpolation property, while through recurrency and cross-talk, the local information feedback enables representation of temporal variations in the system nonlinearities. The standard backpropagation learning algorithm is modified, and it is used for the supervised training of the proposed hybrid network. The performance of recurrent multilayer perceptron networks in identifying process dynamics is investigated via the case study of a U-tube steam generator. The response of representative steam generator is predicted using a neural network, and it is compared to the response obtained from a sophisticated computer model based on first principles. The transient responses compare well, although further research is warranted to determine the predictive capabilities of these networks during more severe operational transients and accident scenarios

When Economics Meets Law

DEFF Research Database (Denmark)

Elsmore, Matthew James

This is not an ordinary textbook, which reflects the author and intended audience, and mostly the subject of study. The subject of ‘law-and-economics’ can be intimidating to begin with, bringing together arguably two very old and very different disciplines into one learning challenge. In my...... experience, many readers and students of law-and-economics feel they have to work twice as hard for half the reward. It is not a traditional subject. This first impression may be with some good reason, but let me assure you the subject’s bark is far worse than its bite, at least with the help of this book......’s approach reflects around two decades of teaching and research in the subject of law-and-economics. A main piece of feedback I receive regularly is the difficulty of the subject and the inability to find out what it’s all about, neither of which are helped by the perceived unsuitable US-biased textbooks...

Tutorial on beam-based feedback systems for linacs

International Nuclear Information System (INIS)

Hendrickson, L.; Allison, S.; Gromme, T.; Grossberg, P.; Himel, T.; Krauter, K.; MacKenzie, R.; Ross, M.; Sass, R.; Shoaee, H.

1994-08-01

A generalized fast feedback system stabilizes beams in the SLC. It performs measurements and modifies actuator settings to control beam states such as position, angle, energy and intensity on a pulse to pulse basis. An adaptive cascade feature allows communication between a series of linac loops, avoiding overcorrection problems. The system is based on the state space formalism of digital control theory. Due to the database-driven design, new loops are added without requiring software modifications. Recent enhancements support the monitoring and control of nonlinear states such as beam phase using excitation techniques. In over three years of operation, the feedback system has grown from its original eight loops to more than fifty loops, and it has been invaluable in stabilizing the machine

Asymptotic expansion of unsteady gravity flow of a power-law fluid ...

African Journals Online (AJOL)

We present a paper on the asymptotic expansion of unsteady non-linear rheological effects of a power-law fluid under gravity. The fluid flows through a porous medium. The asymptotic expansion is employed to obtain solution of the nonlinear problem. The results show the existence of traveling waves. It is assumed that the ...

Nonlinear control for a class of hydraulic servo system.

Science.gov (United States)

Yu, Hong; Feng, Zheng-jin; Wang, Xu-yong

2004-11-01

The dynamics of hydraulic systems are highly nonlinear and the system may be subjected to non-smooth and discontinuous nonlinearities due to directional change of valve opening, friction, etc. Aside from the nonlinear nature of hydraulic dynamics, hydraulic servo systems also have large extent of model uncertainties. To address these challenging issues, a robust state-feedback controller is designed by employing backstepping design technique such that the system output tracks a given signal arbitrarily well, and all signals in the closed-loop system remain bounded. Moreover, a relevant disturbance attenuation inequality is satisfied by the closed-loop signals. Compared with previously proposed robust controllers, this paper's robust controller based on backstepping recursive design method is easier to design, and is more suitable for implementation.

Quantized Passive Dynamic Output Feedback Control with Actuator Failure

Directory of Open Access Journals (Sweden)

Zu-Xin Li

2016-01-01

Full Text Available This paper investigates the problem of passive dynamic output feedback control for fuzzy discrete nonlinear systems with quantization and actuator failures, where the measurement output of the system is quantized by a logarithmic quantizer before being transferred to the fuzzy controller. By employing the fuzzy-basis-dependent Lyapunov function, sufficient condition is established to guarantee the closed-loop system to be mean-square stable and the prescribed passive performance. Based on the sufficient condition, the fuzzy dynamic output feedback controller is proposed for maintaining acceptable performance levels in the case of actuator failures and quantization effects. Finally, a numerical example is given to show the usefulness of the proposed method.

Nonlinear elasticity in resonance experiments

Science.gov (United States)

Li, Xun; Sens-Schönfelder, Christoph; Snieder, Roel

2018-04-01

Resonant bar experiments have revealed that dynamic deformation induces nonlinearity in rocks. These experiments produce resonance curves that represent the response amplitude as a function of the driving frequency. We propose a model to reproduce the resonance curves with observed features that include (a) the log-time recovery of the resonant frequency after the deformation ends (slow dynamics), (b) the asymmetry in the direction of the driving frequency, (c) the difference between resonance curves with the driving frequency that is swept upward and downward, and (d) the presence of a "cliff" segment to the left of the resonant peak under the condition of strong nonlinearity. The model is based on a feedback cycle where the effect of softening (nonlinearity) feeds back to the deformation. This model provides a unified interpretation of both the nonlinearity and slow dynamics in resonance experiments. We further show that the asymmetry of the resonance curve is caused by the softening, which is documented by the decrease of the resonant frequency during the deformation; the cliff segment of the resonance curve is linked to a bifurcation that involves a steep change of the response amplitude when the driving frequency is changed. With weak nonlinearity, the difference between the upward- and downward-sweeping curves depends on slow dynamics; a sufficiently slow frequency sweep eliminates this up-down difference. With strong nonlinearity, the up-down difference results from both the slow dynamics and bifurcation; however, the presence of the bifurcation maintains the respective part of the up-down difference, regardless of the sweep rate.

Non-linear feedback neural networks VLSI implementations and applications

CERN Document Server

Ansari, Mohd Samar

2014-01-01

This book aims to present a viable alternative to the Hopfield Neural Network (HNN) model for analog computation. It is well known that the standard HNN suffers from problems of convergence to local minima, and requirement of a large number of neurons and synaptic weights. Therefore, improved solutions are needed. The non-linear synapse neural network (NoSyNN) is one such possibility and is discussed in detail in this book. This book also discusses the applications in computationally intensive tasks like graph coloring, ranking, and linear as well as quadratic programming. The material in the book is useful to students, researchers and academician working in the area of analog computation.

Feedforward Nonlinear Control Using Neural Gas Network

Directory of Open Access Journals (Sweden)

Iván Machón-González

2017-01-01

Full Text Available Nonlinear systems control is a main issue in control theory. Many developed applications suffer from a mathematical foundation not as general as the theory of linear systems. This paper proposes a control strategy of nonlinear systems with unknown dynamics by means of a set of local linear models obtained by a supervised neural gas network. The proposed approach takes advantage of the neural gas feature by which the algorithm yields a very robust clustering procedure. The direct model of the plant constitutes a piece-wise linear approximation of the nonlinear system and each neuron represents a local linear model for which a linear controller is designed. The neural gas model works as an observer and a controller at the same time. A state feedback control is implemented by estimation of the state variables based on the local transfer function that was provided by the local linear model. The gradient vectors obtained by the supervised neural gas algorithm provide a robust procedure for feedforward nonlinear control, that is, supposing the inexistence of disturbances.

A random-parametric reactor model with direct feedback and non-white noise

International Nuclear Information System (INIS)

Sako, O.; Taniguchi, A.; Kuroda, Y.

1982-01-01

The effects of multiplicative direct power feedback and non-white reactivity noise on the fluctuations of the neutron density are studied, based on the master equation using the cumulant expansion and the system-size expansion. The results obtained are the following: non-whiteness of reactivity noise reduces the variance of neutron density, as well as the level of the power spectral density. The nonlinear effect of power feedback gives rise to at least a pair of corner frequencies, in contrast to the single corner frequency in linearized case. (author)

Feedback Robust Cubature Kalman Filter for Target Tracking Using an Angle Sensor.

Science.gov (United States)

Wu, Hao; Chen, Shuxin; Yang, Binfeng; Chen, Kun

2016-05-09

The direction of arrival (DOA) tracking problem based on an angle sensor is an important topic in many fields. In this paper, a nonlinear filter named the feedback M-estimation based robust cubature Kalman filter (FMR-CKF) is proposed to deal with measurement outliers from the angle sensor. The filter designs a new equivalent weight function with the Mahalanobis distance to combine the cubature Kalman filter (CKF) with the M-estimation method. Moreover, by embedding a feedback strategy which consists of a splitting and merging procedure, the proper sub-filter (the standard CKF or the robust CKF) can be chosen in each time index. Hence, the probability of the outliers' misjudgment can be reduced. Numerical experiments show that the FMR-CKF performs better than the CKF and conventional robust filters in terms of accuracy and robustness with good computational efficiency. Additionally, the filter can be extended to the nonlinear applications using other types of sensors.

Linear and nonlinear stability analysis, associated to experimental fast reactors. Part 2

International Nuclear Information System (INIS)

Amorim, E.S. do; Moura Neto, C. de; Rosa, M.A.P.

1980-07-01

The nonlinear effects in fast reactors kinetics and their stability are studied. The Lyapunov criteria and the Lurie-Letov functions for nonlinear systems were established and simulated. Small oscillations were studied by a Fourier analysis to clarify particular aspects of feedback and load functions in fast reactor at zero power, or/and in normal power level. The results were in agreement with the experimental data existing in the literature. (E.G.) [pt

Optimisation-based worst-case analysis and anti-windup synthesis for uncertain nonlinear systems

Science.gov (United States)

Menon, Prathyush Purushothama

This thesis describes the development and application of optimisation-based methods for worst-case analysis and anti-windup synthesis for uncertain nonlinear systems. The worst-case analysis methods developed in the thesis are applied to the problem of nonlinear flight control law clearance for highly augmented aircraft. Local, global and hybrid optimisation algorithms are employed to evaluate worst-case violations of a nonlinear response clearance criterion, for a highly realistic aircraft simulation model and flight control law. The reliability and computational overheads associated with different opti misation algorithms are compared, and the capability of optimisation-based approaches to clear flight control laws over continuous regions of the flight envelope is demonstrated. An optimisation-based method for computing worst-case pilot inputs is also developed, and compared with current industrial approaches for this problem. The importance of explicitly considering uncertainty in aircraft parameters when computing worst-case pilot demands is clearly demonstrated. Preliminary results on extending the proposed framework to the problems of limit-cycle analysis and robustness analysis in the pres ence of time-varying uncertainties are also included. A new method for the design of anti-windup compensators for nonlinear constrained systems controlled using nonlinear dynamics inversion control schemes is presented and successfully applied to some simple examples. An algorithm based on the use of global optimisation is proposed to design the anti-windup compensator. Some conclusions are drawn from the results of the research presented in the thesis, and directions for future work are identified.

New results on the mathematical problems in nonlinear physics

International Nuclear Information System (INIS)

1980-01-01

The main topics treated in this report are: I) Existence of generalized Lagrangians. II) Conserved densities for odd-order polynomial evolution equations and linear evolution systems. III ) Conservation laws for Klein-Gordon, Di rae and Maxwell equations. IV) Stability conditions for finite-energy solutions of a non-linear Klein-Gordon equation. V) Hamiltonian approach to non-linear evolution equations and Backlund transformations. VI) Anharmonic vibrations: Status of results and new possible approaches. (Author) 83 refs

The Nonlinear Distortions in the Oscillatory System of Generator on CFOA

Directory of Open Access Journals (Sweden)

Yuriy Konstantinovich Rybin

2012-01-01

Full Text Available In recent years, many articles came out where one could find the analysis of oscillatory systems of electric sinusoid signals generators with amplifiers called CFOA—current feedback operational amplifiers. As a rule, the analysis of such systems is made by applying mathematical modeling methods on the basis of the amplifier linear model, which does not allow estimating advantages and disadvantages of the systems realized with those amplifiers in comparison with classical systems. A nonlinear model of a current feedback operational amplifier (CFOA is introduced in the paper; nonlinearity of “current mirror” is reflected in the form of current double limiting. The analysis of two known oscillatory systems has been carried out with the use of this non-linear model. Dependence between current limiting level, output voltage amplitude, and maximum oscillation frequency has been obtained. The paper shows that output current limiting under current output connection of capacitive load reduces frequency range and output voltage amplitude considerably and increases harmonic distortions in comparison with classical oscillatory systems. The research done has found that the application of new amplifiers does not give considerable advantages to the oscillatory systems with CFOA.

H∞ control for path tracking of autonomous underwater vehicle motion

Directory of Open Access Journals (Sweden)

Lin-Lin Wang

2015-05-01

Full Text Available In order to simplify the design of path tracking controller and solve the problem relating to nonlinear dynamic model of autonomous underwater vehicle motion planning, feedback linearization method is first adopted to transform the nonlinear dynamic model into an equivalent pseudo-linear dynamic model in horizontal coordinates. Then considering wave disturbance effect, mixed-sensitivity method of H∞ robust control is applied to design state-feedback controller for this equivalent dynamic model. Finally, control law of pseudo-linear dynamic model is transformed into state (surge velocity and yaw angular rate tracking control law of nonlinear dynamic model through inverse coordinate transformation. Simulation indicates that autonomous underwater vehicle path tracking is successfully implemented with this proposed method, and the influence of parameter variation in autonomous underwater vehicle dynamic model on its tracking performance is reduced by H∞ controller. All the results show that the method proposed in this article is effective and feasible.

Synthesis for robust synchronization of chaotic systems under output feedback control with multiple random delays

International Nuclear Information System (INIS)

Wen Guilin; Wang Qingguo; Lin Chong; Han Xu; Li Guangyao

2006-01-01

Synchronization under output feedback control with multiple random time delays is studied, using the paradigm in nonlinear physics-Chua's circuit. Compared with other synchronization control methods, output feedback control with multiple random delay is superior for a realistic synchronization application to secure communications. Sufficient condition for global stability of delay-dependent synchronization is established based on the LMI technique. Numerical simulations fully support the analytical approach, in spite of the random delays

On Madelung systems in nonlinear optics: A reciprocal invariance

Science.gov (United States)

Rogers, Colin; Malomed, Boris

2018-05-01

The role of the de Broglie-Bohm potential, originally established as central to Bohmian quantum mechanics, is examined for two canonical Madelung systems in nonlinear optics. In a seminal case, a Madelung system derived by Wagner et al. via the paraxial approximation and in which the de Broglie-Bohm potential is present is shown to admit a multi-parameter class of what are here introduced as "q-gaussons." In the limit, as the Tsallis parameter q → 1, the q-gaussons are shown to lead to standard gausson solitons, as admitted by the logarithmic nonlinear Schrödinger equation encapsulating the Madelung system. The q-gaussons are obtained for optical media with dual power-law refractive index. In the second case, a Madelung system originally derived via an eikonal approximation in the context of laser beam propagation and in which the de Broglie Bohm term is neglected is shown to admit invariance under a novel class of two-parameter class of reciprocal transformations. Model optical laws analogous to the celebrated Kármán-Tsien law of classical gas dynamics are introduced.

Numerical solution for identification of feedback coefficients in nuclear reactors

International Nuclear Information System (INIS)

Ebizuka, Yoshie; Sakai, Hideo

1975-01-01

Quasilinearization technique was studied to determine the Kinetic parameters of nuclear reactors. The method of solution was generalized to the determination of the parameters contained in a nonlinear system with nonlinear boundary conditions. A computer program, SNR-3, was developed to solve the resulting nonlinear two-point boundary value equations with generalized boundary conditions. In this paper, the problem formulation and the method of solution are explained for a general type of time dependent problem. A flow chart shows the procedure of numerical solution. The method was then applied to the determination of the critical factor and the reactivity feedback coefficients of reactors to investigate the accuracy and the applicability of the present method. The results showed that the present method was considerably successful, but that the random observation error effected the results of the identification. (Aoki, K.)

Four-dimensional black holes with scalar hair in nonlinear electrodynamics

International Nuclear Information System (INIS)

Barrientos, Jose; Gonzalez, P.A.; Vasquez, Yerko

2016-01-01

We consider a gravitating system consisting of a scalar field minimally coupled to gravity with a self-interacting potential and a U(1) nonlinear electromagnetic field. Solving analytically and numerically the coupled system for both power-law and Born-Infeld type electrodynamics, we find charged hairy black hole solutions. Then we study the thermodynamics of these solutions and we find that at a low temperature the topological charged black hole with scalar hair is thermodynamically preferred, whereas the topological charged black hole without scalar hair is thermodynamically preferred at a high temperature for power-law electrodynamics. Interestingly enough, these phase transitions occur at a fixed critical temperature and do not depend on the exponent p of the nonlinear electrodynamics. (orig.)

Four-dimensional black holes with scalar hair in nonlinear electrodynamics

Energy Technology Data Exchange (ETDEWEB)

Barrientos, Jose [Universidad de Concepcion, Departamento de Fisica, Concepcion (Chile); Universidad Catolica del Norte, Departamento de Ensenanza de las Ciencias Basicas, Coquimbo (Chile); Gonzalez, P.A. [Universidad Diego Portales, Facultad de Ingenieria, Santiago (Chile); Vasquez, Yerko [Universidad de La Serena, Departamento de Fisica y Astronomia, Facultad de Ciencias, La Serena (Chile)

2016-12-15

We consider a gravitating system consisting of a scalar field minimally coupled to gravity with a self-interacting potential and a U(1) nonlinear electromagnetic field. Solving analytically and numerically the coupled system for both power-law and Born-Infeld type electrodynamics, we find charged hairy black hole solutions. Then we study the thermodynamics of these solutions and we find that at a low temperature the topological charged black hole with scalar hair is thermodynamically preferred, whereas the topological charged black hole without scalar hair is thermodynamically preferred at a high temperature for power-law electrodynamics. Interestingly enough, these phase transitions occur at a fixed critical temperature and do not depend on the exponent p of the nonlinear electrodynamics. (orig.)

Effects of feedback reliability on feedback-related brain activity: A feedback valuation account.

Science.gov (United States)

Ernst, Benjamin; Steinhauser, Marco

2018-04-06

Adaptive decision making relies on learning from feedback. Because feedback sometimes can be misleading, optimal learning requires that knowledge about the feedback's reliability be utilized to adjust feedback processing. Although previous research has shown that feedback reliability indeed influences feedback processing, the underlying mechanisms through which this is accomplished remain unclear. Here we propose that feedback processing is adjusted by the adaptive, top-down valuation of feedback. We assume that unreliable feedback is devalued relative to reliable feedback, thus reducing the reward prediction errors that underlie feedback-related brain activity and learning. A crucial prediction of this account is that the effects of feedback reliability are susceptible to contrast effects. That is, the effects of feedback reliability should be enhanced when both reliable and unreliable feedback are experienced within the same context, as compared to when only one level of feedback reliability is experienced. To evaluate this prediction, we measured the event-related potentials elicited by feedback in two experiments in which feedback reliability was varied either within or between blocks. We found that the fronto-central valence effect, a correlate of reward prediction errors during reinforcement learning, was reduced for unreliable feedback. But this result was obtained only when feedback reliability was varied within blocks, thus indicating a contrast effect. This suggests that the adaptive valuation of feedback is one mechanism underlying the effects of feedback reliability on feedback processing.

Construction of local and non-local conservation laws for non-linear field equations

International Nuclear Information System (INIS)

Vladimirov, V.S.; Volovich, I.V.

1984-08-01

A method of constructing conserved currents for non-linear field equations is presented. More explicitly for non-linear equations, which can be derived from compatibility conditions of some linear system with a parameter, a procedure of obtaining explicit expressions for local and non-local currents is developed. Some examples such as the classical Heisenberg spin chain and supersymmetric Yang-Mills theory are considered. (author)

Lie symmetry analysis and conservation laws for the time fractional fourth-order evolution equation

Directory of Open Access Journals (Sweden)

Wang Li

2017-06-01

Full Text Available In this paper, we study Lie symmetry analysis and conservation laws for the time fractional nonlinear fourth-order evolution equation. Using the method of Lie point symmetry, we provide the associated vector fields, and derive the similarity reductions of the equation, respectively. The method can be applied wisely and efficiently to get the reduced fractional ordinary differential equations based on the similarity reductions. Finally, by using the nonlinear self-adjointness method and Riemann-Liouville time-fractional derivative operator as well as Euler-Lagrange operator, the conservation laws of the equation are obtained.

The Integration of Social-Ecological Resilience and Law

Science.gov (United States)

Growing recognition of the inherent uncertainty associated with the dynamics of ecological systems and their often non-linear and surprising behavior, however, presents a set of problems outside the scope of classic environmental law, and has lead to a fundamental understanding a...

Infinite sets of conservation laws for linear and non-linear field equations

International Nuclear Information System (INIS)

Niederle, J.

1984-01-01

The work was motivated by a desire to understand group theoretically the existence of an infinite set of conservation laws for non-interacting fields and to carry over these conservation laws to the case of interacting fields. The relation between an infinite set of conservation laws of a linear field equation and the enveloping algebra of its space-time symmetry group was established. It is shown that in the case of the Korteweg-de Vries (KdV) equation to each symmetry of the corresponding linear equation delta sub(o)uxxx=u sub() determined by an element of the enveloping algebra of the space translation algebra, there corresponds a symmetry of the full KdV equation

Adaptive semi-active control of buildings under seismic solicitations

International Nuclear Information System (INIS)

Roberti, V.; Jezequel, L.

1993-01-01

This paper describes an adaptive semi-active control method whereby nonlinear distributed systems are identified by their dynamical response. Approximate procedures are proposed which take into account the nonlinear behavior of the dynamic system considered. It is shown that only slight knowledge of nonlinearities is needed to apply feedback and feedforward control laws. The method is implemented to a simple example of a building with three degrees of freedom and the numerical results are analyzed

Chaos control for the family of Roessler systems using feedback controllers

International Nuclear Information System (INIS)

Liao Xiaoxin; Yu Pei

2006-01-01

This paper presents a new method for controlling chaos in several classical chaotic Roessler systems using feedback control strategy. In particular, for an arbitrarily given equilibrium point of a Roessler system, we design explicit and simple feedback control laws by which the equilibrium point is globally and exponentially stabilized. Six typical Roessler systems are studied, and explicit formulas are derived for estimating the convergence rate of these systems. Numerical examples are presented to illustrate the theoretical results. A mistake has been found in the existing literature, and a correct result is given

Nonlinearity measure and internal model control based linearization in anti-windup design

Energy Technology Data Exchange (ETDEWEB)

Perev, Kamen [Systems and Control Department, Technical University of Sofia, 8 Cl. Ohridski Blvd., 1756 Sofia (Bulgaria)

2013-12-18

This paper considers the problem of internal model control based linearization in anti-windup design. The nonlinearity measure concept is used for quantifying the control system degree of nonlinearity. The linearizing effect of a modified internal model control structure is presented by comparing the nonlinearity measures of the open-loop and closed-loop systems. It is shown that the linearization properties are improved by increasing the control system local feedback gain. However, it is emphasized that at the same time the stability of the system deteriorates. The conflicting goals of stability and linearization are resolved by solving the design problem in different frequency ranges.

Nonlinear Fokker-Planck Equations Fundamentals and Applications

CERN Document Server

Frank, Till Daniel

2005-01-01

Providing an introduction to the theory of nonlinear Fokker-Planck equations, this book discusses fundamental properties of transient and stationary solutions, emphasizing the stability analysis of stationary solutions by means of self-consistency equations, linear stability analysis, and Lyapunov's direct method. Also treated are Langevin equations and correlation functions. Nonlinear Fokker-Planck Equations addresses various phenomena such as phase transitions, multistability of systems, synchronization, anomalous diffusion, cut-off solutions, travelling-wave solutions and the emergence of power law solutions. A nonlinear Fokker-Planck perspective to quantum statistics, generalized thermodynamics, and linear nonequilibrium thermodynamics is given. Theoretical concepts are illustrated where possible by simple examples. The book also reviews several applications in the fields of condensed matter physics, the physics of porous media and liquid crystals, accelerator physics, neurophysics, social sciences, popul...

Approaches to the Optimal Nonlinear Analysis of Microcalorimeter Pulses

Science.gov (United States)

Fowler, J. W.; Pappas, C. G.; Alpert, B. K.; Doriese, W. B.; O'Neil, G. C.; Ullom, J. N.; Swetz, D. S.

2018-03-01

We consider how to analyze microcalorimeter pulses for quantities that are nonlinear in the data, while preserving the signal-to-noise advantages of linear optimal filtering. We successfully apply our chosen approach to compute the electrothermal feedback energy deficit (the "Joule energy") of a pulse, which has been proposed as a linear estimator of the deposited photon energy.

Massively parallel computation of conservation laws

Energy Technology Data Exchange (ETDEWEB)

Garbey, M [Univ. Claude Bernard, Villeurbanne (France); Levine, D [Argonne National Lab., IL (United States)

1990-01-01

The authors present a new method for computing solutions of conservation laws based on the use of cellular automata with the method of characteristics. The method exploits the high degree of parallelism available with cellular automata and retains important features of the method of characteristics. It yields high numerical accuracy and extends naturally to adaptive meshes and domain decomposition methods for perturbed conservation laws. They describe the method and its implementation for a Dirichlet problem with a single conservation law for the one-dimensional case. Numerical results for the one-dimensional law with the classical Burgers nonlinearity or the Buckley-Leverett equation show good numerical accuracy outside the neighborhood of the shocks. The error in the area of the shocks is of the order of the mesh size. The algorithm is well suited for execution on both massively parallel computers and vector machines. They present timing results for an Alliant FX/8, Connection Machine Model 2, and CRAY X-MP.

Non-Darcy flow of water-based carbon nanotubes with nonlinear radiation and heat generation/absorption

Directory of Open Access Journals (Sweden)

T. Hayat

2018-03-01

Full Text Available Here modeling and computations are presented to introduce the novel concept of Darcy-Forchheimer three-dimensional flow of water-based carbon nanotubes with nonlinear thermal radiation and heat generation/absorption. Bidirectional stretching surface induces the flow. Darcy’s law is commonly replace by Forchheimer relation. Xue model is implemented for nonliquid transport mechanism. Nonlinear formulation based upon conservation laws of mass, momentum and energy is first modeled and then solved by optimal homotopy analysis technique. Optimal estimations of auxiliary variables are obtained. Importance of influential variables on the velocity and thermal fields is interpreted graphically. Moreover velocity and temperature gradients are discussed and analyzed. Physical interpretation of influential variables is examined. Keywords: Porous medium, Heat generation/absorption, SWCNTs and MWCNTs, Nonlinear radiation

Collisions of Two Spatial Solitons in Inhomogeneous Nonlinear Media

International Nuclear Information System (INIS)

Zhong Weiping; Yi Lin; Yang Zhengping; Xie Ruihua; Milivoj, Belic; Chen Goong

2008-01-01

Collisions of spatial solitons occurring in the nonlinear Schroeinger equation with harmonic potential are studied, using conservation laws and the split-step Fourier method. We find an analytical solution for the separation distance between the spatial solitons in an inhomogeneous nonlinear medium when the light beam is self-trapped in the transverse dimension. In the self-focusing nonlinear media the spatial solitons can be transmitted stably, and the interaction between spatial solitons is enhanced due to the linear focusing effect (and also diminished for the linear defocusing effect). In the self-defocusing nonlinear media, in the absence of self-trapping or in the presence of linear self-defocusing, no transmission of stable spatial solitons is possible. However, in such media the linear focusing effect can be exactly compensated, and the spatial solitons can propagate through

Addressing the high levels of psychological distress in law students through intentional assessment and feedback design in the first year law curriculum

OpenAIRE

Rachael Field; Sally Kift

2010-01-01

A study of the Brain and Mind Institute released in 2009 established that more than one third of Australian law students suffer from psychological distress (BMRI, 2009). The psychological health of law students is therefore a critical issue for Australian legal education, and strategic change is necessary to address the stressful nature of studying law. This paper argues that intentional first year curriculum design has a critical role to play in addressing and preventing psychological distre...

Waves, conservation laws and symmetries of a third-order nonlinear ...

African Journals Online (AJOL)

order is under consideration. Important properties concerning advanced character such like conservation laws and the equation of continuity are given. Characteristic wave properties such like dispersion relations and both the group and phase ...

Results on stabilization of nonlinear systems under finite data-rate constraints

NARCIS (Netherlands)

Persis, Claudio De

2004-01-01

We discuss in this paper a result concerning the stabilization problem of nonlinear systems under data-rate constraints using output feedback. To put the result in a broader context, we shall first review a number of recent contributions on the stabilization problem under data-rate constraints when

Foundations of the non-linear mechanics of continua

CERN Document Server

Sedov, L I

1966-01-01

International Series of Monographs on Interdisciplinary and Advanced Topics in Science and Engineering, Volume 1: Foundations of the Non-Linear Mechanics of Continua deals with the theoretical apparatus, principal concepts, and principles used in the construction of models of material bodies that fill space continuously. This book consists of three chapters. Chapters 1 and 2 are devoted to the theory of tensors and kinematic applications, focusing on the little-known theory of non-linear tensor functions. The laws of dynamics and thermodynamics are covered in Chapter 3.This volume is suitable

Synchronizing movements with the metronome: nonlinear error correction and unstable periodic orbits.

Science.gov (United States)

Engbert, Ralf; Krampe, Ralf Th; Kurths, Jürgen; Kliegl, Reinhold

2002-02-01

The control of human hand movements is investigated in a simple synchronization task. We propose and analyze a stochastic model based on nonlinear error correction; a mechanism which implies the existence of unstable periodic orbits. This prediction is tested in an experiment with human subjects. We find that our experimental data are in good agreement with numerical simulations of our theoretical model. These results suggest that feedback control of the human motor systems shows nonlinear behavior. Copyright 2001 Elsevier Science (USA).

Nonlinear analysis of pupillary dynamics.

Science.gov (United States)

Onorati, Francesco; Mainardi, Luca Tommaso; Sirca, Fabiola; Russo, Vincenzo; Barbieri, Riccardo

2016-02-01

Pupil size reflects autonomic response to different environmental and behavioral stimuli, and its dynamics have been linked to other autonomic correlates such as cardiac and respiratory rhythms. The aim of this study is to assess the nonlinear characteristics of pupil size of 25 normal subjects who participated in a psychophysiological experimental protocol with four experimental conditions, namely “baseline”, “anger”, “joy”, and “sadness”. Nonlinear measures, such as sample entropy, correlation dimension, and largest Lyapunov exponent, were computed on reconstructed signals of spontaneous fluctuations of pupil dilation. Nonparametric statistical tests were performed on surrogate data to verify that the nonlinear measures are an intrinsic characteristic of the signals. We then developed and applied a piecewise linear regression model to detrended fluctuation analysis (DFA). Two joinpoints and three scaling intervals were identified: slope α0, at slow time scales, represents a persistent nonstationary long-range correlation, whereas α1 and α2, at middle and fast time scales, respectively, represent long-range power-law correlations, similarly to DFA applied to heart rate variability signals. Of the computed complexity measures, α0 showed statistically significant differences among experimental conditions (pnonlinear dynamics, (b) three well-defined and distinct long-memory processes exist at different time scales, and (c) autonomic stimulation is partially reflected in nonlinear dynamics. (c) autonomic stimulation is partially reflected in nonlinear dynamics.

Generalized projective synchronization of chaotic nonlinear gyros coupled with dead-zone input

International Nuclear Information System (INIS)

Hung, M.-L.; Yan, J.-J.; Liao, T.-L.

2008-01-01

This paper addresses the synchronization problem of drive-response chaotic gyros coupled with dead-zone nonlinear input. Using the sliding mode control technique, a novel control law is established which guarantees generalized projective synchronization even when the dead-zone nonlinearity is present. Numerical simulations are presented to verify that the synchronization can be achieved by using the proposed synchronization scheme

Linear and nonlinear stability analysis, associated to experimental fast reactors

International Nuclear Information System (INIS)

Amorim, E.S. do; Moura Neto, C. de; Rosa, M.A.P.

1980-07-01

Phenomena associated to the physics of fast neutrons were analysed by linear and nonlinear Kinetics with arbitrary feedback. The theoretical foundations of linear kinetics and transfer functions aiming at the analysis of fast reactors stability, are established. These stability conditions were analitically proposed and investigated by digital and analogic programs. (E.G.) [pt

A novel nonlinear nano-scale wear law for metallic brake pads.

Science.gov (United States)

Patil, Sandeep P; Chilakamarri, Sri Harsha; Markert, Bernd

2018-05-03

In the present work, molecular dynamics simulations were carried out to investigate the temperature distribution as well as the fundamental friction characteristics such as the coefficient of friction and wear in a disc-pad braking system. A wide range of constant velocity loadings was applied on metallic brake pads made of aluminium, copper and iron with different rotating speeds of a diamond-like carbon brake disc. The average temperature of Newtonian atoms and the coefficient of friction of the brake pad were investigated. The resulting relationship of the average temperature with the speed of the disc as well as the applied loading velocity can be described by power laws. The quantitative description of the volume lost from the brake pads was investigated, and it was found that the volume lost increases linearly with the sliding distance. Our results show that Archard's linear wear law is not applicable to a wide range of normal loads, e.g., in cases of low normal load where the wear rate was increased considerably and in cases of high load where there was a possibility of severe wear. In this work, a new formula for the brake pad wear in a disc brake assembly is proposed, which displays a power law relationship between the lost volume of the metallic brake pads per unit sliding distance and the applied normal load with an exponent of 0.62 ± 0.02. This work provides new insights into the fundamental understanding of the wear mechanism at the nano-scale leading to a new bottom-up wear law for metallic brake pads.

Chaotic synchronization via adaptive sliding mode observers subject to input nonlinearity

International Nuclear Information System (INIS)

Lin Juisheng; Yan Junjuh; Liao Tehlu

2005-01-01

This paper is concerned with the state reconstruction of nonlinear chaotic systems with uncertainty having unknown bounds. An adaptive output feedback sliding mode observer (AOFSMO) is established from the available output measurement. Unlike most works we further consider the presence of input nonlinearity due to physical limitations and no restrictive assumption is imposed on the system. Thus, the range of applicability of the proposed method becomes broad. Finally, a hyperchaotic Roessler system is used as an illustrative example to demonstrate the effectiveness of the proposed AOFSMO design method

Effect of nonlinear void reactivity on bifurcation characteristics of a lumped-parameter model of a BWR: A study relevant to RBMK

Energy Technology Data Exchange (ETDEWEB)

Verma, Dinkar, E-mail: dinkar@iitk.ac.in [Nuclear Engineering and Technology Program, Indian Institute of Technology Kanpur, Kanpur 208 016 (India); Kalra, Manjeet Singh, E-mail: drmanjeet.singh@dituniversity.edu.in [DIT University, Dehradun 248 009 (India); Wahi, Pankaj, E-mail: wahi@iitk.ac.in [Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016 (India)

2017-04-15

Highlights: • A simplified model with nonlinear void reactivity feedback is studied. • Method of multiple scales for nonlinear analysis and oscillation characteristics. • Second order void reactivity dominates in determining system dynamics. • Opposing signs of linear and quadratic void reactivity enhances global safety. - Abstract: In the present work, the effect of nonlinear void reactivity on the dynamics of a simplified lumped-parameter model for a boiling water reactor (BWR) is investigated. A mathematical model of five differential equations comprising of neutronics and thermal-hydraulics encompassing the nonlinearities associated with both the reactivity feedbacks and the heat transfer process has been used. To this end, we have considered parameters relevant to RBMK for which the void reactivity is known to be nonlinear. A nonlinear analysis of the model exploiting the method of multiple time scales (MMTS) predicts the occurrence of the two types of Hopf bifurcation, namely subcritical and supercritical, leading to the evolution of limit cycles for a range of parameters. Numerical simulations have been performed to verify the analytical results obtained by MMTS. The study shows that the nonlinear reactivity has a significant influence on the system dynamics. A parametric study with varying nominal reactor power and operating conditions in coolant channel has also been performed which shows the effect of change in concerned parameter on the boundary between regions of sub- and super-critical Hopf bifurcations in the space constituted by the two coefficients of reactivities viz. the void and the Doppler coefficient of reactivities. In particular, we find that introduction of a negative quadratic term in the void reactivity feedback significantly increases the supercritical region and dominates in determining the system dynamics.

Microcircuit Modeling and Simulation beyond Ohm's Law

Science.gov (United States)

Saxena, T.; Chek, D. C. Y.; Tan, M. L. P.; Arora, V. K.

2011-01-01

Circuit theory textbooks rely heavily on the applicability of Ohm's law, which collapses as electronic components reach micro- and nanoscale dimensions. Circuit analysis is examined in the regime where the applied voltage V is greater than the critical voltage V[subscript c], which triggers the nonlinear behavior. The critical voltage is infinity…

Distributed cooperative H∞ optimal tracking control of MIMO nonlinear multi-agent systems in strict-feedback form via adaptive dynamic programming

Science.gov (United States)

Luy, N. T.

2018-04-01

The design of distributed cooperative H∞ optimal controllers for multi-agent systems is a major challenge when the agents' models are uncertain multi-input and multi-output nonlinear systems in strict-feedback form in the presence of external disturbances. In this paper, first, the distributed cooperative H∞ optimal tracking problem is transformed into controlling the cooperative tracking error dynamics in affine form. Second, control schemes and online algorithms are proposed via adaptive dynamic programming (ADP) and the theory of zero-sum differential graphical games. The schemes use only one neural network (NN) for each agent instead of three from ADP to reduce computational complexity as well as avoid choosing initial NN weights for stabilising controllers. It is shown that despite not using knowledge of cooperative internal dynamics, the proposed algorithms not only approximate values to Nash equilibrium but also guarantee all signals, such as the NN weight approximation errors and the cooperative tracking errors in the closed-loop system, to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is shown by simulation results of an application to wheeled mobile multi-robot systems.

Networked Predictive Control for Nonlinear Systems With Arbitrary Region Quantizers.

Science.gov (United States)

Yang, Hongjiu; Xu, Yang; Xia, Yuanqing; Zhang, Jinhui

2017-04-06

In this paper, networked predictive control is investigated for planar nonlinear systems with quantization by an extended state observer (ESO). The ESO is used not only to deal with nonlinear terms but also to generate predictive states for dealing with network-induced delays. Two arbitrary region quantizers are applied to take effective values of signals in forward channel and feedback channel, respectively. Based on a "zoom" strategy, sufficient conditions are given to guarantee stabilization of the closed-loop networked control system with quantization. A simulation example is proposed to exhibit advantages and availability of the results.

Toward a unified description of nonlinearity and frequency dispersion of piezoelectric and dielectric responses in Pb(Zr,Ti)O3

International Nuclear Information System (INIS)

Damjanovic, D.; Bharadwaja, S.S.N.; Setter, N.

2005-01-01

A phenomenological approach is proposed describing both nonlinearity and frequency dispersion in dielectric and piezoelectric properties of lead zirconate titanate, Pb(Zr,Ti)O 3 (PZT), thin films and ceramics. The approach couples the frequency dependent response in form of the power law, 1/ω β , with the rate-independent nonlinear response described by the Rayleigh law. The main experimental trends are well described by the model

On Optimal Feedback Control for Stationary Linear Systems

International Nuclear Information System (INIS)

Russell, David L.

2010-01-01

We study linear-quadratic optimal control problems for finite dimensional stationary linear systems AX+BU=Z with output Y=CX+DU from the viewpoint of linear feedback solution. We interpret solutions in relation to system robustness with respect to disturbances Z and relate them to nonlinear matrix equations of Riccati type and eigenvalue-eigenvector problems for the corresponding Hamiltonian system. Examples are included along with an indication of extensions to continuous, i.e., infinite dimensional, systems, primarily of elliptic type.

Robust output-feedback control to eliminate stick-slip oscillations in drill-string systems

NARCIS (Netherlands)

Vromen, T.G.M.; Dai, C.H.; van de Wouw, N.; Oomen, T.A.E.; Astrid, P.; Nijmeijer, H.

2015-01-01

The aim of this paper is to design a robust output-feedback controller to eliminate torsional stick-slip vibrations. A multi-modal model of the torsional dynamics with a nonlinear bit-rock interaction model is used. The controller design is based on skewed-μ DK-iteration and the stability of the

Pseudorandom numbers: evolutionary models in image processing, biology, and nonlinear dynamic systems

Science.gov (United States)

Yaroslavsky, Leonid P.

1996-11-01

We show that one can treat pseudo-random generators, evolutionary models of texture images, iterative local adaptive filters for image restoration and enhancement and growth models in biology and material sciences in a unified way as special cases of dynamic systems with a nonlinear feedback.

Hyperbolicity of the Nonlinear Models of Maxwell's Equations

Science.gov (United States)

Serre, Denis

. We consider the class of nonlinear models of electromagnetism that has been described by Coleman & Dill [7]. A model is completely determined by its energy density W(B,D). Viewing the electromagnetic field (B,D) as a 3×2 matrix, we show that polyconvexity of W implies the local well-posedness of the Cauchy problem within smooth functions of class Hs with s>1+d/2. The method follows that designed by Dafermos in his book [9] in the context of nonlinear elasticity. We use the fact that B×D is a (vectorial, non-convex) entropy, and we enlarge the system from 6 to 9 equations. The resulting system admits an entropy (actually the energy) that is convex. Since the energy conservation law does not derive from the system of conservation laws itself (Faraday's and Ampère's laws), but also needs the compatibility relations divB=divD=0 (the latter may be relaxed in order to take into account electric charges), the energy density is not an entropy in the classical sense. Thus the system cannot be symmetrized, strictly speaking. However, we show that the structure is close enough to symmetrizability, so that the standard estimates still hold true.

Bistability and low-frequency fluctuations in semiconductor lasers with optical feedback: a theoretical analysis

DEFF Research Database (Denmark)

Mørk, Jesper; Tromborg, Bjarne; Christiansen, Peter Leth

1988-01-01

Near-threshold operation of a semiconductor laser exposed to moderate optical feedback may lead to low-frequency fluctuations. In the same region, a kink is observed in the light-current characteristic. Here it is demonstrated that these nonlinear phenomena are predicted by a noise driven multimode...

SOLUTION OF HARMONIC OSCILLATOR OF NONLINEAR MASTER SCHRÖDINGER

Directory of Open Access Journals (Sweden)