Construction of a Smooth Lyapunov Function for the Robust and Exact Second-Order Differentiator

Directory of Open Access Journals (Sweden)

Tonametl Sanchez

2016-01-01

Full Text Available Differentiators play an important role in (continuous feedback control systems. In particular, the robust and exact second-order differentiator has shown some very interesting properties and it has been used successfully in sliding mode control, in spite of the lack of a Lyapunov based procedure to design its gains. As contribution of this paper, we provide a constructive method to determine a differentiable Lyapunov function for such a differentiator. Moreover, the Lyapunov function is used to provide a procedure to design the differentiator’s parameters. Also, some sets of such parameters are provided. The determination of the positive definiteness of the Lyapunov function and negative definiteness of its derivative is converted to the problem of solving a system of inequalities linear in the parameters of the Lyapunov function candidate and also linear in the gains of the differentiator, but bilinear in both.

Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

Science.gov (United States)

Nasiri, Alireza; Nguang, Sing Kiong; Swain, Akshya; Almakhles, Dhafer

2018-02-01

This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.

Interpolation of polytopic control Lyapunov functions for discrete–time linear systems

NARCIS (Netherlands)

Nguyen, T.T.; Lazar, M.; Spinu, V.; Boje, E.; Xia, X.

2014-01-01

This paper proposes a method for interpolating two (or more) polytopic control Lyapunov functions (CLFs) for discrete--time linear systems subject to polytopic constraints, thereby combining different control objectives. The corresponding interpolated CLF is used for synthesis of a stabilizing

Design of a stable fuzzy controller for an articulated vehicle.

Science.gov (United States)

Tanaka, K; Kosaki, T

1997-01-01

This paper presents a backward movement control of an articulated vehicle via a model-based fuzzy control technique. A nonlinear dynamic model of the articulated vehicle is represented by a Takagi-Sugeno fuzzy model. The concept of parallel distributed compensation is employed to design a fuzzy controller from the Takagi-Sugeno fuzzy model of the articulated vehicle. Stability of the designed fuzzy control system is guaranteed via Lyapunov approach. The stability conditions are characterized in terms of linear matrix inequalities since the stability analysis is reduced to a problem of finding a common Lyapunov function for a set of Lyapunov inequalities. Simulation results and experimental results show that the designed fuzzy controller effectively achieves the backward movement control of the articulated vehicle.

Lyapunov stability robust analysis and robustness design for linear continuous-time systems

NARCIS (Netherlands)

Luo, J.S.; Johnson, A.; Bosch, van den P.P.J.

1995-01-01

The linear continuous-time systems to be discussed are described by state space models with structured time-varying uncertainties. First, the explicit maximal perturbation bound for maintaining quadratic Lyapunov stability of the closed-loop systems is presented. Then, a robust design method is

Analysis and control of chaotic behavior in boost converter by ramp compensation based on Lyapunov exponents assignment: theoretical and experimental investigation

International Nuclear Information System (INIS)

Zamani, Najmeh; Ataei, Mohammad; Niroomand, Mehdi

2015-01-01

Highlights: • Applying nonlinear analysis of complex dynamics displayed by current-mode controlled boost converter. • The ramp compensation method is used to control bifurcation and chaos in these converters based on bifurcation diagram and Lyapunov exponents assignment. • A discrete-time iterative nonlinear mapping model has been derived by inserting the ramp compensation parameter in the dynamical equations of the system. • A design methodology for chaos control is provided in this converter based on Lyapunov exponents assignment in desired values theoretically by proper selection of compensator slope. • Practical results are provided to confirm the theoretical analysis and simulations. - Abstract: Nonlinear analysis of complex dynamics displayed by current mode dc–dc converter and idea of Lyapunov exponents assignment by ramp compensator in order to control chaotic behavior is proposed in this article. A discrete-time iterative nonlinear mapping model is derived. The occurrence of the complex behaviors of bifurcation and chaos generated by varying the circuit parameters are investigated through numerical analysis and software implementation of the circuit. Next, in order to control bifurcation and chaos in these converters, the ramp compensation method is used. By inserting the ramp compensation parameter in the dynamical equations of the system, these complex behaviors are examined theoretically and numerically as well. It is proved that through this method, the stable period-one operation of the converter can be extended. By evaluating the Lyapunov exponents (LEs) of the system, the impact of the slope on the location of LEs are determined analytically. This leads to a design methodology for control of chaos in this converter based on LEs assignment in desired values by proper selection of compensator slope. By developing an experimental set up, practical results are obtained to confirm the theoretical analysis and simulations.

A Lyapunov Stability Theory-Based Control Strategy for Three-Level Shunt Active Power Filter

Directory of Open Access Journals (Sweden)

Yijia Cao

2017-01-01

Full Text Available The three-phase three-wire neutral-point-clamped shunt active power filter (NPC-SAPF, which most adopts classical closed-loop feedback control methods such as proportional-integral (PI, proportional-resonant (PR and repetitive control, can only output 1st–25th harmonic currents with 10–20 kHz switching frequency. The reason for this is that the controller design must make a compromise between system stability and harmonic current compensation ability under the condition of less than 20 kHz switching frequency. To broaden the bandwidth of the compensation current, a Lyapunov stability theory-based control strategy is presented in this paper for NPC-SAPF. The proposed control law is obtained by constructing the switching function on the basis of the mathematical model and the Lyapunov candidate function, which can avoid introducing closed-loop feedback control and keep the system globally asymptotically stable. By means of the proposed method, the NPC-SAPF has compensation ability for the 1st–50th harmonic currents, the total harmonic distortion (THD and each harmonic content of grid currents satisfy the requirements of IEEE Standard 519-2014. In order to verify the superiority of the proposed control strategy, stability conditions of the proposed strategy and the representative PR controllers are compared. The simulation results in MATLAB/Simulink (MathWorks, Natick, MA, USA and the experimental results obtained on a 6.6 kVA NPC-SAPF laboratory prototype validate the proposed control strategy.

Collective Lyapunov modes

International Nuclear Information System (INIS)

Takeuchi, Kazumasa A; Chaté, Hugues

2013-01-01

We show, using covariant Lyapunov vectors in addition to standard Lyapunov analysis, that there exists a set of collective Lyapunov modes in large chaotic systems exhibiting collective dynamics. Associated with delocalized Lyapunov vectors, they act collectively on the trajectory and hence characterize the instability of its collective dynamics. We further develop, for globally coupled systems, a connection between these collective modes and the Lyapunov modes in the corresponding Perron–Frobenius equation. We thereby address the fundamental question of the effective dimension of collective dynamics and discuss the extensivity of chaos in the presence of collective dynamics. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)

Synchronising chaotic Chua's circuit using switching feedback control based on piecewise quadratic Lyapunov functions

International Nuclear Information System (INIS)

Hong-Bin, Zhang; Jian-Wei, Xia; Yong-Bin, Yu; Chuang-Yin, Dang

2010-01-01

This paper investigates the chaos synchronisation between two coupled chaotic Chua's circuits. The sufficient condition presented by linear matrix inequalities (LMIs) of global asymptotic synchronisation is attained based on piecewise quadratic Lyapunov functions. First, we obtain the piecewise linear differential inclusions (pwLDIs) model of synchronisation error dynamics, then we design a switching (piecewise-linear) feedback control law to stabilise it based on the piecewise quadratic Laypunov functions. Then we give some numerical simulations to demonstrate the effectiveness of our theoretical results

State feedback integral control for a rotary direct drive servo valve using a Lyapunov function approach.

Science.gov (United States)

Yu, Jue; Zhuang, Jian; Yu, Dehong

2015-01-01

This paper concerns a state feedback integral control using a Lyapunov function approach for a rotary direct drive servo valve (RDDV) while considering parameter uncertainties. Modeling of this RDDV servovalve reveals that its mechanical performance is deeply influenced by friction torques and flow torques; however, these torques are uncertain and mutable due to the nature of fluid flow. To eliminate load resistance and to achieve satisfactory position responses, this paper develops a state feedback control that integrates an integral action and a Lyapunov function. The integral action is introduced to address the nonzero steady-state error; in particular, the Lyapunov function is employed to improve control robustness by adjusting the varying parameters within their value ranges. This new controller also has the advantages of simple structure and ease of implementation. Simulation and experimental results demonstrate that the proposed controller can achieve higher control accuracy and stronger robustness. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Hopf bifurcations, Lyapunov exponents and control of chaos for a class of centrifugal flywheel governor system

International Nuclear Information System (INIS)

Zhang Jiangang; Li Xianfeng; Chu Yandong; Yu Jianning; Chang Yingxiang

2009-01-01

In this paper, complex dynamical behavior of a class of centrifugal flywheel governor system is studied. These systems have a rich variety of nonlinear behavior, which are investigated here by numerically integrating the Lagrangian equations of motion. A tiny change in parameters can lead to an enormous difference in the long-term behavior of the system. Bubbles of periodic orbits may also occur within the bifurcation sequence. Hyperchaotic behavior is also observed in cases where two of the Lyapunov exponents are positive, one is zero, and one is negative. The routes to chaos are analyzed using Poincare maps, which are found to be more complicated than those of nonlinear rotational machines. Periodic and chaotic motions can be clearly distinguished by all of the analytical tools applied here, namely Poincare sections, bifurcation diagrams, Lyapunov exponents, and Lyapunov dimensions. This paper proposes a parametric open-plus-closed-loop approach to controlling chaos, which is capable of switching from chaotic motion to any desired periodic orbit. The theoretical work and numerical simulations of this paper can be extended to other systems. Finally, the results of this paper are of practical utility to designers of rotational machines.

Nonlinear Lyapunov-based boundary control of distributed heat transfer mechanisms in membrane distillation plant

KAUST Repository

Eleiwi, Fadi

2015-07-01

This paper presents a nonlinear Lyapunov-based boundary control for the temperature difference of a membrane distillation boundary layers. The heat transfer mechanisms inside the process are modeled with a 2D advection-diffusion equation. The model is semi-descretized in space, and a nonlinear state-space representation is provided. The control is designed to force the temperature difference along the membrane sides to track a desired reference asymptotically, and hence a desired flux would be generated. Certain constraints are put on the control law inputs to be within an economic range of energy supplies. The effect of the controller gain is discussed. Simulations with real process parameters for the model, and the controller are provided. © 2015 American Automatic Control Council.

Sliding Mode Controller and Lyapunov Redesign Controller to Improve Microgrid Stability

DEFF Research Database (Denmark)

Hossain, Eklas; Perez, Ron; Padmanaban, Sanjeevikumar

2017-01-01

technique is used to enhance stability of microgrids. Besides adopting this technique here, Sliding Mode Controller (SMC) and Lyapunov Redesign Controller (LRC), two of the most prominent nonlinear control techniques, are individually implemented to control microgrid system stability with desired robustness....... CPL power is then varied to compare robustness of these two control techniques. This investigation revealed the better performance of the LRC system compared to SMC to retain stability in microgrid with dense CPL load. All the necessary results are simulated in Matlab/Simulink platform for authentic......To mitigate the microgrid instability despite the presence of dense Constant Power Load (CPL) loads in the system, a number of compensation techniques have already been gone through extensive research, proposed, and implemented around the world. In this paper, a storage based load side compensation...

Lyapunov based control of hybrid energy storage system in electric vehicles

DEFF Research Database (Denmark)

El Fadil, H.; Giri, F.; Guerrero, Josep M.

2012-01-01

This paper deals with a Lyapunov based control principle in a hybrid energy storage system for electric vehicle. The storage system consists on fuel cell (FC) as a main power source and a supercapacitor (SC) as an auxiliary power source. The power stage of energy conversion consists on a boost...

Lyapunov Exponents

CERN Document Server

Crauel, Hans; Eckmann, Jean-Pierre

1991-01-01

Since the predecessor to this volume (LNM 1186, Eds. L. Arnold, V. Wihstutz)appeared in 1986, significant progress has been made in the theory and applications of Lyapunov exponents - one of the key concepts of dynamical systems - and in particular, pronounced shifts towards nonlinear and infinite-dimensional systems and engineering applications are observable. This volume opens with an introductory survey article (Arnold/Crauel) followed by 26 original (fully refereed) research papers, some of which have in part survey character. From the Contents: L. Arnold, H. Crauel: Random Dynamical Systems.- I.Ya. Goldscheid: Lyapunov exponents and asymptotic behaviour of the product of random matrices.- Y. Peres: Analytic dependence of Lyapunov exponents on transition probabilities.- O. Knill: The upper Lyapunov exponent of Sl (2, R) cocycles:Discontinuity and the problem of positivity.- Yu.D. Latushkin, A.M. Stepin: Linear skew-product flows and semigroups of weighted composition operators.- P. Baxendale: Invariant me...

Controlled test for predictive power of Lyapunov exponents: their inability to predict epileptic seizures.

Science.gov (United States)

Lai, Ying-Cheng; Harrison, Mary Ann F; Frei, Mark G; Osorio, Ivan

2004-09-01

Lyapunov exponents are a set of fundamental dynamical invariants characterizing a system's sensitive dependence on initial conditions. For more than a decade, it has been claimed that the exponents computed from electroencephalogram (EEG) or electrocorticogram (ECoG) signals can be used for prediction of epileptic seizures minutes or even tens of minutes in advance. The purpose of this paper is to examine the predictive power of Lyapunov exponents. Three approaches are employed. (1) We present qualitative arguments suggesting that the Lyapunov exponents generally are not useful for seizure prediction. (2) We construct a two-dimensional, nonstationary chaotic map with a parameter slowly varying in a range containing a crisis, and test whether this critical event can be predicted by monitoring the evolution of finite-time Lyapunov exponents. This can thus be regarded as a "control test" for the claimed predictive power of the exponents for seizure. We find that two major obstacles arise in this application: statistical fluctuations of the Lyapunov exponents due to finite time computation and noise from the time series. We show that increasing the amount of data in a moving window will not improve the exponents' detective power for characteristic system changes, and that the presence of small noise can ruin completely the predictive power of the exponents. (3) We report negative results obtained from ECoG signals recorded from patients with epilepsy. All these indicate firmly that, the use of Lyapunov exponents for seizure prediction is practically impossible as the brain dynamical system generating the ECoG signals is more complicated than low-dimensional chaotic systems, and is noisy. Copyright 2004 American Institute of Physics

Stability of time-delay systems via Lyapunov functions

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Carlos F. Alastruey

2002-01-01

Full Text Available In this paper, a Lyapunov function candidate is introduced for multivariable systems with inner delays, without assuming a priori stability for the nondelayed subsystem. By using this Lyapunov function, a controller is deduced. Such a controller utilizes an input–output description of the original system, a circumstance that facilitates practical applications of the proposed approach.

? and ? nonquadratic stabilisation of discrete-time Takagi-Sugeno systems based on multi-instant fuzzy Lyapunov functions

Science.gov (United States)

Tognetti, Eduardo S.; Oliveira, Ricardo C. L. F.; Peres, Pedro L. D.

2015-01-01

The problem of state feedback control design for discrete-time Takagi-Sugeno (TS) (T-S) fuzzy systems is investigated in this paper. A Lyapunov function, which is quadratic in the state and presents a multi-polynomial dependence on the fuzzy weighting functions at the current and past instants of time, is proposed.This function contains, as particular cases, other previous Lyapunov functions already used in the literature, being able to provide less conservative conditions of control design for TS fuzzy systems. The structure of the proposed Lyapunov function also motivates the design of a new stabilising compensator for Takagi-Sugeno fuzzy systems. The main novelty of the proposed state feedback control law is that the gain is composed of matrices with multi-polynomial dependence on the fuzzy weighting functions at a set of past instants of time, including the current one. The conditions for the existence of a stabilising state feedback control law that minimises an upper bound to the ? or ? norms are given in terms of linear matrix inequalities. Numerical examples show that the approach can be less conservative and more efficient than other methods available in the literature.

MPC for LPV Systems Based on Parameter-Dependent Lyapunov Function with Perturbation on Control Input Strategy

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Pornchai Bumroongsri

2012-04-01

Full Text Available In this paper, the model predictive control (MPC algorithm for linear parameter varying (LPV systems is proposed. The proposed algorithm consists of two steps. The first step is derived by using parameter-dependent Lyapunov function and the second step is derived by using the perturbation on control input strategy. In order to achieve good control performance, the bounds on the rate of variation of the parameters are taken into account in the controller synthesis. An overall algorithm is proved to guarantee robust stability. The controller design is illustrated with two case studies of continuous stirred-tank reactors. Comparisons with other MPC algorithms for LPV systems have been undertaken. The results show that the proposed algorithm can achieve better control performance.

Lyapunov matrices approach to the parametric optimization of time-delay systems

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Duda Józef

2015-09-01

Full Text Available In the paper a Lyapunov matrices approach to the parametric optimization problem of time-delay systems with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix

Relative Lyapunov Center Bifurcations

DEFF Research Database (Denmark)

Wulff, Claudia; Schilder, Frank

2014-01-01

Relative equilibria (REs) and relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur, for example, in celestial mechanics, molecular dynamics, and rigid body motion. REs are equilibria, and RPOs are periodic orbits of the symmetry reduced system. Relative Lyapunov...... center bifurcations are bifurcations of RPOs from REs corresponding to Lyapunov center bifurcations of the symmetry reduced dynamics. In this paper we first prove a relative Lyapunov center theorem by combining recent results on the persistence of RPOs in Hamiltonian systems with a symmetric Lyapunov...... center theorem of Montaldi, Roberts, and Stewart. We then develop numerical methods for the detection of relative Lyapunov center bifurcations along branches of RPOs and for their computation. We apply our methods to Lagrangian REs of the N-body problem....

Observer-based design of set-point tracking adaptive controllers for nonlinear chaotic systems

International Nuclear Information System (INIS)

Khaki-Sedigh, A.; Yazdanpanah-Goharrizi, A.

2006-01-01

A gradient based approach for the design of set-point tracking adaptive controllers for nonlinear chaotic systems is presented. In this approach, Lyapunov exponents are used to select the controller gain. In the case of unknown or time varying chaotic plants, the Lyapunov exponents may vary during the plant operation. In this paper, an effective adaptive strategy is used for online identification of Lyapunov exponents and adaptive control of nonlinear chaotic plants. Also, a nonlinear observer for estimation of the states is proposed. Simulation results are provided to show the effectiveness of the proposed methodology

Observer-based design of set-point tracking adaptive controllers for nonlinear chaotic systems

Energy Technology Data Exchange (ETDEWEB)

Khaki-Sedigh, A. [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran 16314 (Iran, Islamic Republic of)]. E-mail: sedigh@kntu.ac.ir; Yazdanpanah-Goharrizi, A. [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran 16314 (Iran, Islamic Republic of)]. E-mail: yazdanpanah@ee.kntu.ac.ir

2006-09-15

A gradient based approach for the design of set-point tracking adaptive controllers for nonlinear chaotic systems is presented. In this approach, Lyapunov exponents are used to select the controller gain. In the case of unknown or time varying chaotic plants, the Lyapunov exponents may vary during the plant operation. In this paper, an effective adaptive strategy is used for online identification of Lyapunov exponents and adaptive control of nonlinear chaotic plants. Also, a nonlinear observer for estimation of the states is proposed. Simulation results are provided to show the effectiveness of the proposed methodology.

Nonlinear Lyapunov-based boundary control of distributed heat transfer mechanisms in membrane distillation plant

KAUST Repository

Eleiwi, Fadi; Laleg-Kirati, Taous-Meriem

2015-01-01

This paper presents a nonlinear Lyapunov-based boundary control for the temperature difference of a membrane distillation boundary layers. The heat transfer mechanisms inside the process are modeled with a 2D advection-diffusion equation. The model

Lyapunov-based decentralized control of a rougher flotation phenomenological simulator

International Nuclear Information System (INIS)

Benaskeur, A.R.; Desbiens, A.

1999-01-01

In this paper a new approach to decentralized control of linear two-by-two plants is presented. The novelty lies in the use of a modified control function of Lyapunov and the introduction of an integral action in each manipulated variable, to ensure zero tracking errors. An appropriate choice of the regulated errors, allows the elimination of the cross terms in the obtained backstepping-based multivariable controller. It will be proven that if the H ∞ -norm of the plant interaction quotient is less than one, the centralized controller can be split up into two independent scalar output feedback regulators. Under these conditions, the global stability and zero tracking errors will still be guaranteed. The developed scheme is successfully applied to the control of a rougher flotation phenomenological simulator. (author)

Nonlinear observer-based Lyapunov boundary control of distributed heat transfer mechanisms for membrane distillation plant

KAUST Repository

Eleiwi, Fadi

2016-09-19

This paper presents a nonlinear observer-based Lyapunov control for a membrane distillation (MD) process. The control considers the inlet temperatures of the feed and the permeate solutions as inputs, transforming it to boundary control process, and seeks to maintain the temperature difference along the membrane boundaries around a sufficient level to promote water production. MD process is modeled with advection diffusion equation model in two dimensions, where the diffusion and convection heat transfer mechanisms are best described. Model analysis, effective order reduction and parameters physical interpretation, are provided. Moreover, a nonlinear observer has been designed to provide the control with estimates of the temperature evolution at each time instant. In addition, physical constraints are imposed on the control to have an acceptable range of feasible inputs, and consequently, better energy consumption. Numerical simulations for the complete process with real membrane parameter values are provided, in addition to detailed explanations for the role of the controller and the observer. (C) 2016 Elsevier Ltd. All rights reserved.

Robust chaotic control of Lorenz system by backstepping design

International Nuclear Information System (INIS)

Peng, C.-C.; Chen, C.-L.

2008-01-01

This work presents a robust chaotic control strategy for the Lorenz chaos via backstepping design. Backstepping technique is a systematic tool of control law design to provide Lyapunov stability. The concept of extended system is used such that a continuous sliding mode control (SMC) effort is generated using backstepping scheme. In the proposed control algorithm, an adaptation law is applied to estimate the system parameter and the SMC offers the robustness to model uncertainties and external disturbances so that the asymptotical convergence of tracking error can be achieved. Regarding the SMC, an equivalent control algorithm is chosen based on the selection of Lyapunov stability criterion during backstepping approach. The converging rate of error state is relative to the corresponding dynamics of sliding surface. Numerical simulations demonstrate its advantages to a regulation problem and an orbit tracking problem of the Lorenz chaos

Experimental validation of a Lyapunov-based controller for the plasma safety factor and plasma pressure in the TCV tokamak

Science.gov (United States)

Mavkov, B.; Witrant, E.; Prieur, C.; Maljaars, E.; Felici, F.; Sauter, O.; the TCV-Team

2018-05-01

In this paper, model-based closed-loop algorithms are derived for distributed control of the inverse of the safety factor profile and the plasma pressure parameter β of the TCV tokamak. The simultaneous control of the two plasma quantities is performed by combining two different control methods. The control design of the plasma safety factor is based on an infinite-dimensional setting using Lyapunov analysis for partial differential equations, while the control of the plasma pressure parameter is designed using control techniques for single-input and single-output systems. The performance and robustness of the proposed controller is analyzed in simulations using the fast plasma transport simulator RAPTOR. The control is then implemented and tested in experiments in TCV L-mode discharges using the RAPTOR model predicted estimates for the q-profile. The distributed control in TCV is performed using one co-current and one counter-current electron cyclotron heating actuation.

Lyapunov exponent for aging process in induction motor

Science.gov (United States)

Bayram, Duygu; Ünnü, Sezen Yıdırım; Şeker, Serhat

2012-09-01

focused on the controlling the mechanical parameters of the electrical machines. Brushless DC motor (BLDCM) and the other general purpose permanent magnet (PM) motors are the most widely examined motors [1, 8, 9]. But the researches, about Lyapunov Exponent, subjected to the induction motors are mostly focused on the control theory of the motors. Flux estimation of rotor, external load disturbances and speed tracking and vector control position system are the main research areas for induction motors [10, 11, 12-14]. For all the data sets which can be collected from an induction motor, vibration data have the key role for understanding the mechanical behaviours like aging, bearing damage and stator insulation damage [15-18]. In this paper aging of an induction motor is investigated by using the vibration signals. The signals consist of new and aged motor data. These data are examined by their 2 dimensional phase portraits and the geometric interpretation is applied for detecting the Lyapunov Exponents. These values are compared in order to define the character and state estimation of the aging processes.

Structured Lyapunov functions for synchronization of identical affine-in-control agents-Unified approach

Czech Academy of Sciences Publication Activity Database

Hengster-Movric, K.; Šebek, M.; Čelikovský, Sergej

2016-01-01

Roč. 353, č. 14 (2016), s. 3457-3486 ISSN 0016-0032 R&D Projects: GA ČR GA13-20433S Grant - others:GA ČR(CZ) GJ16-25493Y Institutional support: RVO:67985556 Keywords : Multi-agent nonlinear systems * structured Lyapunov functions Subject RIV: BC - Control Systems Theory Impact factor: 3.139, year: 2016 http://library.utia.cas.cz/separaty/2016/TR/celikovsky-0462691.pdf

Sliding Mode Controller and Lyapunov Redesign Controller to Improve Microgrid Stability:A Comparative Analysis with CPL Power Variation

OpenAIRE

Hossain, Eklas; Perez, Ron; Padmanaban, Sanjeevikumar; Mihet-Popa, Lucian; Blaabjerg, Frede; Ramachandaramurthy, Vigna K.

2017-01-01

To mitigate the microgrid instability despite the presence of dense Constant Power Load (CPL) loads in the system, a number of compensation techniques have already been gone through extensive research, proposed, and implemented around the world. In this paper, a storage based load side compensation technique is used to enhance stability of microgrids. Besides adopting this technique here, Sliding Mode Controller (SMC) and Lyapunov Redesign Controller (LRC), two of the most prominent nonlinear...

Robust Structured Control Design via LMI Optimization

DEFF Research Database (Denmark)

Adegas, Fabiano Daher; Stoustrup, Jakob

2011-01-01

This paper presents a new procedure for discrete-time robust structured control design. Parameter-dependent nonconvex conditions for stabilizable and induced L2-norm performance controllers are solved by an iterative linear matrix inequalities (LMI) optimization. A wide class of controller...... structures including decentralized of any order, fixed-order dynamic output feedback, static output feedback can be designed robust to polytopic uncertainties. Stability is proven by a parameter-dependent Lyapunov function. Numerical examples on robust stability margins shows that the proposed procedure can...

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

Lyapunov-based Stability of Feedback Interconnections of Negative Imaginary Systems

KAUST Repository

Ghallab, Ahmed G.

2017-10-19

Feedback control systems using sensors and actuators such as piezoelectric sensors and actuators, micro-electro-mechanical systems (MEMS) sensors and opto-mechanical sensors, are allowing new advances in designing such high precision technologies. The negative imaginary control systems framework allows for robust control design for such high precision systems in the face of uncertainties due to unmodelled dynamics. The stability of the feedback interconnection of negative imaginary systems has been well established in the literature. However, the proofs of stability feedback interconnection which are used in some previous papers have a shortcoming due to a matrix inevitability issue. In this paper, we provide a new and correct Lyapunov-based proof of one such result and show that the result is still true.

Lyapunov-based Stability of Feedback Interconnections of Negative Imaginary Systems

KAUST Repository

Ghallab, Ahmed G.; Mabrok, Mohamed; Petersen, Ian R.

2017-01-01

Feedback control systems using sensors and actuators such as piezoelectric sensors and actuators, micro-electro-mechanical systems (MEMS) sensors and opto-mechanical sensors, are allowing new advances in designing such high precision technologies. The negative imaginary control systems framework allows for robust control design for such high precision systems in the face of uncertainties due to unmodelled dynamics. The stability of the feedback interconnection of negative imaginary systems has been well established in the literature. However, the proofs of stability feedback interconnection which are used in some previous papers have a shortcoming due to a matrix inevitability issue. In this paper, we provide a new and correct Lyapunov-based proof of one such result and show that the result is still true.

Lyapunov-based control of limit cycle oscillations in uncertain aircraft systems

Science.gov (United States)

Bialy, Brendan

Store-induced limit cycle oscillations (LCO) affect several fighter aircraft and is expected to remain an issue for next generation fighters. LCO arises from the interaction of aerodynamic and structural forces, however the primary contributor to the phenomenon is still unclear. The practical concerns regarding this phenomenon include whether or not ordnance can be safely released and the ability of the aircrew to perform mission-related tasks while in an LCO condition. The focus of this dissertation is the development of control strategies to suppress LCO in aircraft systems. The first contribution of this work (Chapter 2) is the development of a controller consisting of a continuous Robust Integral of the Sign of the Error (RISE) feedback term with a neural network (NN) feedforward term to suppress LCO behavior in an uncertain airfoil system. The second contribution of this work (Chapter 3) is the extension of the development in Chapter 2 to include actuator saturation. Suppression of LCO behavior is achieved through the implementation of an auxiliary error system that features hyperbolic functions and a saturated RISE feedback control structure. Due to the lack of clarity regarding the driving mechanism behind LCO, common practice in literature and in Chapters 2 and 3 is to replicate the symptoms of LCO by including nonlinearities in the wing structure, typically a nonlinear torsional stiffness. To improve the accuracy of the system model a partial differential equation (PDE) model of a flexible wing is derived (see Appendix F) using Hamilton's principle. Chapters 4 and 5 are focused on developing boundary control strategies for regulating the bending and twisting deformations of the derived model. The contribution of Chapter 4 is the construction of a backstepping-based boundary control strategy for a linear PDE model of an aircraft wing. The backstepping-based strategy transforms the original system to a exponentially stable system. A Lyapunov-based stability

Análisis de estabilidad de controladores borrosos tipo Mamdani mediante el cálculo del exponente de Lyapunov

Directory of Open Access Journals (Sweden)

Leonardo-Alonso Martínez Rivera

2015-10-01

Full Text Available Resumen: Determinar la estabilidad de los controladores, ya sea mediante simulaciones o mediante técnicas analíticas, es vital en su diseño e implantación. El método analítico de estabilidad en el sentido de Lyapunov requiere encontrar una función candidata, como criterio suficiente pero no necesario para tal fin. Esta función candidata es elusiva para los controladores borrosos. Se propone, como posible solución a este problema, cuantificar la estabilidad de los controladores borrosos mediante el exponente de Lyapunov (EL calculado numéricamente. Las series de tiempo de la cuales se calculan los exponentes de Lyapunov son obtenidas de la salida de diversos controladores borrosos tipo Mamdani en lazo cerrado con la dinámica de la planta no lineal estabilizada en una región de operación admisible. Los experimentos fueron llevados al cabo mediante la implantación del método numérico en la plataforma MATLAB, integrándolo con datos provenientes de la simulación de diversos controladores borrosos. La planta a controlar es el sistema carro-péndulo invertido modelado con la formulación Euler Lagrange. En cada experimento se obtuvo la serie de tiempo correspondiente a la señal de control y se calculó el exponente de Lyapunov. Aunque se observan variaciones en magnitud, el exponente calculado resulta negativo en todos los casos. Esto indica que los controladores difusos tipo Mamdani empleados son sistemas disipativos. Como trabajo futuro se esboza el empleo del EL en control adaptable. Abstract: In order to design and implement any type of controller, their stability analysis is pivotal. At this regard, Lyapunov's analytical method consists in finding a candidate function as a sufficient but not necessary condition to validate the stability of the controller. In the case of fuzzy controllers such a candidate function is not always found, leading to an uncertainty about their stability. To

Using genetic programming to find Lyapunov functions

NARCIS (Netherlands)

Soute, I.A.C.; Molengraft, van de M.J.G.; Angelis, G.Z.; Ryan, C; Spector, L.

2001-01-01

In this paper Genetic Programming is used to find Lyapunov functions for (non)linear dif ferential equations of autonomous systems. As Lyapunov functions can be difficult to find, we use OP to make the decisions concerning the form of the Lyapunov function. As an e5cample two systems are taken to

Lyapunov-based distributed control of the safety-factor profile in a tokamak plasma

International Nuclear Information System (INIS)

Bribiesca Argomedo, Federico; Witrant, Emmanuel; Prieur, Christophe; Brémond, Sylvain; Nouailletas, Rémy; Artaud, Jean-François

2013-01-01

A real-time model-based controller is developed for the tracking of the distributed safety-factor profile in a tokamak plasma. Using relevant physical models and simplifying assumptions, theoretical stability and robustness guarantees were obtained using a Lyapunov function. This approach considers the couplings between the poloidal flux diffusion equation, the time-varying temperature profiles and an independent total plasma current control. The actuator chosen for the safety-factor profile tracking is the lower hybrid current drive, although the results presented can be easily extended to any non-inductive current source. The performance and robustness of the proposed control law is evaluated with a physics-oriented simulation code on Tore Supra experimental test cases. (paper)

A New Real Time Lyapunov Based Controller for Power Quality Improvement in Unified Power Flow Controllers Using Direct Matrix Converters

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Joaquim Monteiro

2017-06-01

Full Text Available This paper proposes a Direct Matrix Converter operating as a Unified Power Flow Controller (DMC-UPFC with an advanced control method for UPFC, based on the Lyapunov direct method, presenting good results in power quality assessment. This control method is used for real-time calculation of the appropriate matrix switching state, determining which switching state should be applied in the following sampling period. The control strategy takes into account active and reactive power flow references to choose the vector converter closest to the optimum. Theoretical principles for this new real-time vector modulation and control applied to the DMC-UPFC with input filter are established. The method needs DMC-UPFC dynamic equations to be solved just once in each control cycle, to find the required optimum vector, in contrast to similar control methods that need 27 vector estimations per control cycle. The designed controller’s performance was evaluated using Matlab/Simulink software. Controllers were also implemented using a digital signal processing (DSP system and matrix hardware. Simulation and experimental results show decoupled transmission line active (P and reactive (Q power control with zero theoretical error tracking and fast response. Output currents and voltages show small ripple and low harmonic content.

Lyapunov Function Synthesis - Algorithm and Software

DEFF Research Database (Denmark)

Leth, Tobias; Sloth, Christoffer; Wisniewski, Rafal

2016-01-01

In this paper we introduce an algorithm for the synthesis of polynomial Lyapunov functions for polynomial vector fields. The Lyapunov function is a continuous piecewisepolynomial defined on simplices, which compose a collection of simplices. The algorithm is elaborated and crucial features are ex...

Stability of dynamical systems on the role of monotonic and non-monotonic Lyapunov functions

CERN Document Server

Michel, Anthony N; Liu, Derong

2015-01-01

The second edition of this textbook provides a single source for the analysis of system models represented by continuous-time and discrete-time, finite-dimensional and infinite-dimensional, and continuous and discontinuous dynamical systems.  For these system models, it presents results which comprise the classical Lyapunov stability theory involving monotonic Lyapunov functions, as well as corresponding contemporary stability results involving non-monotonicLyapunov functions.Specific examples from several diverse areas are given to demonstrate the applicability of the developed theory to many important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, and artificial neural networks.   The authors cover the following four general topics:   -          Representation and modeling of dynamical systems of the types described above -          Presentation of Lyapunov and Lagrange stability theory for dynamical sy...

Control of chaos in permanent magnet synchronous motor by using optimal Lyapunov exponents placement

Energy Technology Data Exchange (ETDEWEB)

Ataei, Mohammad, E-mail: ataei@eng.ui.ac.i [Department of Electrical Engineering, Faculty of Engineering, University of Isfahan, Hezar-Jerib St., Postal Code 8174673441, Isfahan (Iran, Islamic Republic of); Kiyoumarsi, Arash, E-mail: kiyoumarsi@eng.ui.ac.i [Department of Electrical Engineering, Faculty of Engineering, University of Isfahan, Hezar-Jerib St., Postal Code 8174673441, Isfahan (Iran, Islamic Republic of); Ghorbani, Behzad, E-mail: behzad.ghorbani63@gmail.co [Department of Control Engineering, Najafabad Azad University, Najafabad, Isfahan (Iran, Islamic Republic of)

2010-09-13

Permanent Magnet Synchronous Motor (PMSM) experiences chaotic behavior for a certain range of its parameters. In this case, since the performance of the PMSM degrades, the chaos should be eliminated. In this Letter, the control of the undesirable chaos in PMSM using Lyapunov exponents (LEs) placement is proposed that is also improved by choosing optimal locations of the LEs in the sense of predefined cost function. Moreover, in order to provide the physical realization of the method, nonlinear parameter estimator for the system is suggested. Finally, to show the effectiveness of the proposed methodology, the simulation results for applying this control strategy are provided.

An algorithm for constructing Lyapunov functions

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Sigurdur Freyr Hafstein

2007-08-01

Full Text Available In this monograph we develop an algorithm for constructing Lyapunov functions for arbitrary switched dynamical systems $dot{mathbf{x}} = mathbf{f}_sigma(t,mathbf{x}$, possessing a uniformly asymptotically stable equilibrium. Let $dot{mathbf{x}}=mathbf{f}_p(t,mathbf{x}$, $pinmathcal{P}$, be the collection of the ODEs, to which the switched system corresponds. The number of the vector fields $mathbf{f}_p$ on the right-hand side of the differential equation is assumed to be finite and we assume that their components $f_{p,i}$ are $mathcal{C}^2$ functions and that we can give some bounds, not necessarily close, on their second-order partial derivatives. The inputs of the algorithm are solely a finite number of the function values of the vector fields $mathbf{f}_p$ and these bounds. The domain of the Lyapunov function constructed by the algorithm is only limited by the size of the equilibrium's region of attraction. Note, that the concept of a Lyapunov function for the arbitrary switched system $dot{mathbf{x}} = mathbf{f}_sigma(t,mathbf{x}$ is equivalent to the concept of a common Lyapunov function for the systems $dot{mathbf{x}}=mathbf{f}_p(t,mathbf{x}$, $pinmathcal{P}$, and that if $mathcal{P}$ contains exactly one element, then the switched system is just a usual ODE $dot{mathbf{x}}=mathbf{f}(t,mathbf{x}$. We give numerous examples of Lyapunov functions constructed by our method at the end of this monograph.

Homogeneous Stabilizer by State Feedback for Switched Nonlinear Systems Using Multiple Lyapunov Functions’ Approach

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Hui Ye

2017-01-01

Full Text Available This paper investigates the problem of global stabilization for a class of switched nonlinear systems using multiple Lyapunov functions (MLFs. The restrictions on nonlinearities are neither linear growth condition nor Lipschitz condition with respect to system states. Based on adding a power integrator technique, we design homogeneous state feedback controllers of all subsystems and a switching law to guarantee that the closed-loop system is globally asymptotically stable. Finally, an example is given to illustrate the validity of the proposed control scheme.

Advanced Lyapunov control of a novel laser beam tracking system

Science.gov (United States)

Nikulin, Vladimir V.; Sofka, Jozef; Skormin, Victor A.

2005-05-01

Laser communication systems developed for mobile platforms, such as satellites, aircraft, and terrain vehicles, require fast wide-range beam-steering devices to establish and maintain a communication link. Conventionally, the low-bandwidth, high-steering-range part of the beam-positioning task is performed by gimbals that inherently constitutes the system bottleneck in terms of reliability, accuracy and dynamic performance. Omni-WristTM, a novel robotic sensor mount capable of carrying a payload of 5 lb and providing a full 180-deg hemisphere of azimuth/declination motion is known to be free of most of the deficiencies of gimbals. Provided with appropriate controls, it has the potential to become a new generation of gimbals systems. The approach we demonstrate describes an adaptive controller enabling Omni-WristTM to be utilized as a part of a laser beam positioning system. It is based on a Lyapunov function that ensures global asymptotic stability of the entire system while achieving high tracking accuracy. The proposed scheme is highly robust, does not require knowledge of complex system dynamics, and facilitates independent control of each channel by full decoupling of the Omni-WristTM dynamics. We summarize the basic algorithm and demonstrate the results obtained in the simulation environment.

Anti-windup adaptive PID control design for a class of uncertain chaotic systems with input saturation.

Science.gov (United States)

Tahoun, A H

2017-01-01

In this paper, the stabilization problem of actuators saturation in uncertain chaotic systems is investigated via an adaptive PID control method. The PID control parameters are auto-tuned adaptively via adaptive control laws. A multi-level augmented error is designed to account for the extra terms appearing due to the use of PID and saturation. The proposed control technique uses both the state-feedback and the output-feedback methodologies. Based on Lyapunov׳s stability theory, new anti-windup adaptive controllers are proposed. Demonstrative examples with MATLAB simulations are studied. The simulation results show the efficiency of the proposed adaptive PID controllers. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Lyapunov functionals and stability of stochastic functional differential equations

CERN Document Server

Shaikhet, Leonid

2013-01-01

Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for discrete- and continuous-time difference equations. The text begins with a description of the peculiarities of deterministic and stochastic functional differential equations. There follow basic definitions for stability theory of stochastic hereditary systems, and a formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of di...

Chaos control of chaotic dynamical systems using backstepping design

International Nuclear Information System (INIS)

Yassen, M.T.

2006-01-01

This work presents chaos control of chaotic dynamical systems by using backstepping design method. This technique is applied to achieve chaos control for each of the dynamical systems Lorenz, Chen and Lue systems. Based on Lyapunov stability theory, control laws are derived. We used the same technique to enable stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory to be achieved in a systematic way. Numerical simulations are shown to verify the results

Covariant Lyapunov vectors

International Nuclear Information System (INIS)

Ginelli, Francesco; Politi, Antonio; Chaté, Hugues; Livi, Roberto

2013-01-01

Recent years have witnessed a growing interest in covariant Lyapunov vectors (CLVs) which span local intrinsic directions in the phase space of chaotic systems. Here, we review the basic results of ergodic theory, with a specific reference to the implications of Oseledets’ theorem for the properties of the CLVs. We then present a detailed description of a ‘dynamical’ algorithm to compute the CLVs and show that it generically converges exponentially in time. We also discuss its numerical performance and compare it with other algorithms presented in the literature. We finally illustrate how CLVs can be used to quantify deviations from hyperbolicity with reference to a dissipative system (a chain of Hénon maps) and a Hamiltonian model (a Fermi–Pasta–Ulam chain). This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)

Controlling and tracking hyperchaotic Roessler system via active backstepping design

International Nuclear Information System (INIS)

Zhang Hao; Ma Xikui; Li Ming; Zou Jianlong

2005-01-01

This paper presents a novel active backstepping control approach for controlling hyperchaotic Roessler system to a steady state as well as tracking of any desire trajectory to be achieved in a systematic way. The proposed method is a systematic design approach and consists in a recursive procedure that interlaces the choice of a Lyapunov function with the design of active control. Numerical results show that the controller is singularity free and the closed-loop system is stable globally. Especially, the main feature of this technique is that it gives the flexibility to construct a control law. Finally, numerical experiments verify the feasibility and effectiveness of the proposed control technique

Stability Analysis of Interconnected Fuzzy Systems Using the Fuzzy Lyapunov Method

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Ken Yeh

2010-01-01

Full Text Available The fuzzy Lyapunov method is investigated for use with a class of interconnected fuzzy systems. The interconnected fuzzy systems consist of J interconnected fuzzy subsystems, and the stability analysis is based on Lyapunov functions. Based on traditional Lyapunov stability theory, we further propose a fuzzy Lyapunov method for the stability analysis of interconnected fuzzy systems. The fuzzy Lyapunov function is defined in fuzzy blending quadratic Lyapunov functions. Some stability conditions are derived through the use of fuzzy Lyapunov functions to ensure that the interconnected fuzzy systems are asymptotically stable. Common solutions can be obtained by solving a set of linear matrix inequalities (LMIs that are numerically feasible. Finally, simulations are performed in order to verify the effectiveness of the proposed stability conditions in this paper.

Energy-Based Controller Design of Stochastic Magnetic Levitation System

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Weiwei Sun

2017-01-01

Full Text Available This paper investigates the control problem of magnetic levitation system, in which velocity feedback signal is influenced by stochastic disturbance. Firstly, single-degree-freedom magnetic levitation is regarded as an energy-transform action device. From the view of energy-balance relation, the magnetic levitation system is transformed into port-controlled Hamiltonian system model. Next, based on the Hamiltonian structure, the control law of magnetic levitation system is designed by applying Lyapunov theory. Finally, the simulation verifies the correctness of the proposed results.

Hall magnetohydrodynamics: Conservation laws and Lyapunov stability

International Nuclear Information System (INIS)

Holm, D.D.

1987-01-01

Hall electric fields produce circulating mass flow in confined ideal-fluid plasmas. The conservation laws, Hamiltonian structure, equilibrium state relations, and Lyapunov stability conditions are presented here for ideal Hall magnetohydrodynamics (HMHD) in two and three dimensions. The approach here is to use the remarkable array of nonlinear conservation laws for HMHD that follow from its Hamiltonian structure in order to construct explicit Lyapunov functionals for the HMHD equilibrium states. In this way, the Lyapunov stability analysis provides classes of HMHD equilibria that are stable and whose linearized initial-value problems are well posed (in the sense of possessing continuous dependence on initial conditions). Several examples are discussed in both two and three dimensions

Estabilización del Péndulo Invertido Sobre Dos Ruedas mediante el método de Lyapunov

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O. Octavio Gutiérrez Frías

2013-01-01

Full Text Available Resumen: En este trabajo, se presenta un controlador no lineal para estabilizar el sistema Péndulo Invertido Sobre Dos Ruedas. Como primera etapa la estrategia de control, se basa en una linealización parcial por realimentación, para posteriormente proponer una función candidata de Lyapunov en combinación con el principio de invariancia de LaSalle con el fin de obtener el controlador esta- bilizador. El sistema en lazo cerrado obtenido es asintóticamente estable localmente alrededor del punto de equilibrio inestable, con un dominio de atracción calculable. Abstract: In this paper, a nonlinear controller is presented for the stabilization of the two wheels inverted pendulum. The control strategy is based on partial feedback linealization, in first stage and then a suitable function Lyapunov in conjunction with LaSalle's invariance principle is formed to obtain a stabilizing feedback controller. The obtained closed-loop system is locally asymptotically stable around its unstable equilibrium point, with a computable domain of attraction. Palabras clave: Sistema Subactuado, Péndulo Invertido Sobre Dos Ruedas, Método de Lyapunov, Control No Lineal, Keywords: Under Actuated System, Two Wheels Inverted Pendulum, Lyapunov Approach, Non-Linear Control

Full spectrum of Lyapunov exponents in gauge field theories

International Nuclear Information System (INIS)

Biro, T.S.; Markum, H.; Pullirsch, R.

2003-01-01

Full text: Results are presented for the full spectrum of Lyapunov exponents of the compact U(1) gauge system in classical field theory. Instead of the determination of the largest Lyapunov exponent by the rescaling method we now use the monodromy matrix approach. The Lyapunov spectrum L i is expressed in terms of the eigenvalues Λ i of the monodromy matrix M. In the confinement phase the eigenvalues lie on either the real or on the imaginary axes. This is a nice illustration of a strange attractor of a chaotic system. Positive Lyapunov exponents eject the trajectories from oscillating orbits provided by the imaginary eigenvalues. Negative Lyapunov exponents attract the trajectories keeping them confined in the basin. Latest studies concern the time (in)dependence of the monodromy matrix. Further, we show that monopoles are created and annihilated in pairs as a function of real time in access to a fixed average monopole number. (author)

Lyapunov exponents and smooth ergodic theory

CERN Document Server

Barreira, Luis

2001-01-01

This book is a systematic introduction to smooth ergodic theory. The topics discussed include the general (abstract) theory of Lyapunov exponents and its applications to the stability theory of differential equations, stable manifold theory, absolute continuity, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents (including geodesic flows). The authors consider several non-trivial examples of dynamical systems with nonzero Lyapunov exponents to illustrate some basic methods and ideas of the theory. This book is self-contained. The reader needs a basic knowledge of real analysis, measure theory, differential equations, and topology. The authors present basic concepts of smooth ergodic theory and provide complete proofs of the main results. They also state some more advanced results to give readers a broader view of smooth ergodic theory. This volume may be used by those nonexperts who wish to become familiar with the field.

Evaluating Lyapunov exponent spectra with neural networks

International Nuclear Information System (INIS)

Maus, A.; Sprott, J.C.

2013-01-01

Highlights: • Cross-correlation is employed to remove spurious Lyapunov exponents from a spectrum. • Neural networks are shown to accurately model Lyapunov exponent spectra. • Neural networks compare favorably to local linear fits in modeling Lyapunov exponents. • Numerical experiments are performed with time series of varying length and noise. • Methods perform reasonably well on discrete time series. -- Abstract: A method using discrete cross-correlation for identifying and removing spurious Lyapunov exponents when embedding experimental data in a dimension greater than the original system is introduced. The method uses a distribution of calculated exponent values produced by modeling a single time series many times or multiple instances of a time series. For this task, global models are shown to compare favorably to local models traditionally used for time series taken from the Hénon map and delayed Hénon map, especially when the time series are short or contaminated by noise. An additional merit of global modeling is its ability to estimate the dynamical and geometrical properties of the original system such as the attractor dimension, entropy, and lag space, although consideration must be taken for the time it takes to train the global models

Behaviour of Lyapunov exponents near crisis points in the dissipative standard map

Science.gov (United States)

Pompe, B.; Leven, R. W.

1988-11-01

We numerically study the behaviour of the largest Lyapunov characteristic exponent λ1 in dependence on a control parameter in the 2D standard map with dissipation. In order to investigate the system's motion in parameter intervals slightly above crisis points we introduce "partial" Lyapunov exponents which characterize the average exponential divergence of nearby orbits on a semi-attractor at a boundary crisis and on distinct parts of a "large" chaotic attractor near an interior crisis. In the former case we find no significant difference between λ1 in the pre-crisis regime and the partial Lyapunov exponent describing transient chaotic motions slightly above the crisis. For the latter case we give a quantitative description of the drastic increase of λ1. Moreover, a formula which connects the critical exponent of a chaotic transient above a boundary crisis with a pointwise dimension is derived.

Attitude Control of a Single Tilt Tri-Rotor UAV System: Dynamic Modeling and Each Channel's Nonlinear Controllers Design

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Juing-Shian Chiou

2013-01-01

Full Text Available This paper has implemented nonlinear control strategy for the single tilt tri-rotor aerial robot. Based on Newton-Euler’s laws, the linear and nonlinear mathematical models of tri-rotor UAVs are obtained. A numerical analysis using Newton-Raphson method is chosen for finding hovering equilibrium point. Back-stepping nonlinear controller design is based on constructing Lyapunov candidate function for closed-loop system. By imitating the linguistic logic of human thought, fuzzy logic controllers (FLCs are designed based on control rules and membership functions, which are much less rigid than the calculations computers generally perform. Effectiveness of the controllers design scheme is shown through nonlinear simulation model on each channel.

Lyapunov stability and thermal stability of partially relaxed fluids and plasmas

International Nuclear Information System (INIS)

Elsaesser, K.; Spiess, P.

1996-01-01

The relation between the Lyapunov stability of a Hamiltonian system and the thermal stability of a fluid whose temperature is controlled from outside is explored: The free energy as a functional of the correct variables (specific volume, local entropy, and some Clebsch potentials of the velocity) may serve as a Lyapunov functional, depending on the open-quote open-quote Casimirs close-quote close-quote as exchanged quantities. For a multi-species plasma one obtains a sufficient condition for stability: γ(v 2 /c 2 s )-1 s the sound speed. Some features of partially relaxed (T=const) cylindrical plasmas are also discussed. copyright 1996 American Institute of Physics

Terminal Sliding Mode Tracking Controller Design for Automatic Guided Vehicle

Science.gov (United States)

Chen, Hongbin

2018-03-01

Based on sliding mode variable structure control theory, the path tracking problem of automatic guided vehicle is studied, proposed a controller design method based on the terminal sliding mode. First of all, through analyzing the characteristics of the automatic guided vehicle movement, the kinematics model is presented. Then to improve the traditional expression of terminal sliding mode, design a nonlinear sliding mode which the convergence speed is faster than the former, verified by theoretical analysis, the design of sliding mode is steady and fast convergence in the limited time. Finally combining Lyapunov method to design the tracking control law of automatic guided vehicle, the controller can make the automatic guided vehicle track the desired trajectory in the global sense as well as in finite time. The simulation results verify the correctness and effectiveness of the control law.

Lyapunov functions for the fixed points of the Lorenz model

International Nuclear Information System (INIS)

Bakasov, A.A.; Govorkov, B.B. Jr.

1992-11-01

We have shown how the explicit Lyapunov functions can be constructed in the framework of a regular procedure suggested and completed by Lyapunov a century ago (''method of critical cases''). The method completely covers all practically encountering subtle cases of stability study for ordinary differential equations when the linear stability analysis fails. These subtle cases, ''the critical cases'', according to Lyapunov, include both bifurcations of solutions and solutions of systems with symmetry. Being properly specialized and actually powerful in case of ODE's, this Lyapunov's method is formulated in simple language and should attract a wide interest of the physical audience. The method leads to inevitable construction of the explicit Lyapunov function, takes automatically into account the Fredholm alternative and avoids infinite step calculations. Easy and apparent physical interpretation of the Lyapunov function as a potential or as a time-dependent entropy provides one with more details about the local dynamics of the system at non-equilibrium phase transition points. Another advantage is that this Lyapunov's method consists of a set of very detailed explicit prescriptions which allow one to easy programmize the method for a symbolic processor. The application of the Lyapunov theory for critical cases has been done in this work to the real Lorenz equations and it is shown, in particular, that increasing σ at the Hopf bifurcation point suppresses the contribution of one of the variables to the destabilization of the system. The relation of the method to contemporary methods and its place among them have been clearly and extensively discussed. Due to Appendices, the paper is self-contained and does not require from a reader to approach results published only in Russian. (author). 38 refs

Sliding Mode Controller and Lyapunov Redesign Controller to Improve Microgrid Stability: A Comparative Analysis with CPL Power Variation

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Eklas Hossain

2017-11-01

Full Text Available To mitigate the microgrid instability despite the presence of dense Constant Power Load (CPL loads in the system, a number of compensation techniques have already been gone through extensive research, proposed, and implemented around the world. In this paper, a storage based load side compensation technique is used to enhance stability of microgrids. Besides adopting this technique here, Sliding Mode Controller (SMC and Lyapunov Redesign Controller (LRC, two of the most prominent nonlinear control techniques, are individually implemented to control microgrid system stability with desired robustness. CPL power is then varied to compare robustness of these two control techniques. This investigation revealed the better performance of the LRC system compared to SMC to retain stability in microgrid with dense CPL load. All the necessary results are simulated in Matlab/Simulink platform for authentic verification. Reasons behind inferior SMC performance and ways to mitigate that are also discussed. Finally, the effectiveness of SMC and LRC systems to attain stability in real microgrids is verified by numerical analysis.

Impulsive Controller Design for Complex Nonlinear Singular Networked Systems with Packet Dropouts

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Xian-Lin Zhao

2013-01-01

Full Text Available Globally exponential stability of Complex (with coupling Nonlinear Singular Impulsive Networked Control Systems (CNSINCS with packet dropouts and time-delay is investigated. Firstly, the mathematic model of CNSINCS is established. Then, by employing the method of Lyapunov functional, exponential stability criteria are obtained and the impulsive controller design method is given. Finally, some simulation results are provided to demonstrate the effectiveness of the proposed method.

A new two-scroll chaotic attractor with three quadratic nonlinearities, its adaptive control and circuit design

Science.gov (United States)

Lien, C.-H.; Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Sanjaya, W. S. M.; Subiyanto

2018-03-01

A 3-D new two-scroll chaotic attractor with three quadratic nonlinearities is investigated in this paper. First, the qualitative and dynamical properties of the new two-scroll chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new two-scroll dissipative chaotic system has three unstable equilibrium points. As an engineering application, global chaos control of the new two-scroll chaotic system with unknown system parameters is designed via adaptive feedback control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic two-scroll attractor model.

Lyapunov spectra of density fluctuations in TBR-1

International Nuclear Information System (INIS)

Oiwa, N.N.; Fidler-Ferrara, N.

1993-01-01

The results for the Lyapunov exponents associated with density fluctuations measured by Langmuir probes placed in the scrape-off layer of the Tokamak TBR-1 are reported. By a judicious use of the Sano-Sawada and Eckmann-Ruelle algorithms conclusive values for the positive Lyapunov exponents for most of the analysed signals are used showing evidences of chaotic behavior. (author)

Lyapunov analysis: from dynamical systems theory to applications

Science.gov (United States)

Cencini, Massimo; Ginelli, Francesco

2013-06-01

The study of deterministic laws of evolution has characterized the development of science since Newton's times. Chaos, namely the manifestation of irregular and unpredictable dynamics (not random but look random [1]), entered the debate on determinism at the end of the 19th century with the discovery of sensitivity to initial conditions, meaning that small infinitesimal differences in the initial state might lead to dramatic differences at later times. Poincaré [2, 3] was the first to realize that solutions of the three-body problem are generically highly sensitive to initial conditions. At about the same time, this property was recognized in geodesic flows with negative curvature by Hadamard [4]. One of the first experimental observations of chaos, as understood much later, was when irregular noise was heard by Van der Pol in 1927 [5] while studying a periodically forced nonlinear oscillator. Nevertheless, it was only with the advent of digital computing that chaos started to attract the interest of the wider scientific community. After the pioneering investigation of ergodicity in a chain of nonlinear oscillators by Fermi, Pasta and Ulam in 1955 [6], it was in the early 1960s that the numerical studies of Lorenz [7] and Hénon and Heiles [8] revealed that irregular and unpredictable motions are a generic feature of low-dimensional nonlinear deterministic systems. The existence and onset of chaos was then rigorously analyzed in several systems. While an exhaustive list of such mathematical proofs is beyond the scope of this preface, one should mention the contributions of Kolmogorov [9, 10], Chirikov [11], Smale [12], Ruelle and Takens [13], Li and Yorke [14] and Feigenbaum [15]. The characteristic Lyapunov exponents introduced by Oseledets in 1968 [16] are the fundamental quantities for measuring the sensitivity to initial conditions. Oseledets' work generalized the concept of Lyapunov stability to irregular trajectories building upon earlier studies of Birkhoff

Design of Distributed Engine Control Systems with Uncertain Delay.

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Xiaofeng Liu

Full Text Available Future gas turbine engine control systems will be based on distributed architecture, in which, the sensors and actuators will be connected to the controllers via a communication network. The performance of the distributed engine control (DEC is dependent on the network performance. This study introduces a distributed control system architecture based on a networked cascade control system (NCCS. Typical turboshaft engine-distributed controllers are designed based on the NCCS framework with a H∞ output feedback under network-induced time delays and uncertain disturbances. The sufficient conditions for robust stability are derived via the Lyapunov stability theory and linear matrix inequality approach. Both numerical and hardware-in-loop simulations illustrate the effectiveness of the presented method.

Design of Distributed Engine Control Systems with Uncertain Delay.

Science.gov (United States)

Liu, Xiaofeng; Li, Yanxi; Sun, Xu

Future gas turbine engine control systems will be based on distributed architecture, in which, the sensors and actuators will be connected to the controllers via a communication network. The performance of the distributed engine control (DEC) is dependent on the network performance. This study introduces a distributed control system architecture based on a networked cascade control system (NCCS). Typical turboshaft engine-distributed controllers are designed based on the NCCS framework with a H∞ output feedback under network-induced time delays and uncertain disturbances. The sufficient conditions for robust stability are derived via the Lyapunov stability theory and linear matrix inequality approach. Both numerical and hardware-in-loop simulations illustrate the effectiveness of the presented method.

Analysis and design of hybrid control systems

Energy Technology Data Exchange (ETDEWEB)

Malmborg, J.

1998-05-01

Different aspects of hybrid control systems are treated: analysis, simulation, design and implementation. A systematic methodology using extended Lyapunov theory for design of hybrid systems is developed. The methodology is based on conventional control designs in separate regions together with a switching strategy. Dynamics are not well defined if the control design methods lead to fast mode switching. The dynamics depend on the salient features of the implementation of the mode switches. A theorem for the stability of second order switching together with the resulting dynamics is derived. The dynamics on an intersection of two sliding sets are defined for two relays working on different time scales. The current simulation packages have problems modeling and simulating hybrid systems. It is shown how fast mode switches can be found before or during simulation. The necessary analysis work is a very small overhead for a modern simulation tool. To get some experience from practical problems with hybrid control the switching strategy is implemented in two different software environments. In one of them a time-optimal controller is added to an existing PID controller on a commercial control system. Successful experiments with this hybrid controller shows the practical use of the method 78 refs, 51 figs, 2 tabs

Diagonal recurrent neural network based adaptive control of nonlinear dynamical systems using lyapunov stability criterion.

Science.gov (United States)

Kumar, Rajesh; Srivastava, Smriti; Gupta, J R P

2017-03-01

In this paper adaptive control of nonlinear dynamical systems using diagonal recurrent neural network (DRNN) is proposed. The structure of DRNN is a modification of fully connected recurrent neural network (FCRNN). Presence of self-recurrent neurons in the hidden layer of DRNN gives it an ability to capture the dynamic behaviour of the nonlinear plant under consideration (to be controlled). To ensure stability, update rules are developed using lyapunov stability criterion. These rules are then used for adjusting the various parameters of DRNN. The responses of plants obtained with DRNN are compared with those obtained when multi-layer feed forward neural network (MLFFNN) is used as a controller. Also, in example 4, FCRNN is also investigated and compared with DRNN and MLFFNN. Robustness of the proposed control scheme is also tested against parameter variations and disturbance signals. Four simulation examples including one-link robotic manipulator and inverted pendulum are considered on which the proposed controller is applied. The results so obtained show the superiority of DRNN over MLFFNN as a controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Modern linear control design a time-domain approach

CERN Document Server

Caravani, Paolo

2013-01-01

This book offers a compact introduction to modern linear control design.  The simplified overview presented of linear time-domain methodology paves the road for the study of more advanced non-linear techniques. Only rudimentary knowledge of linear systems theory is assumed - no use of Laplace transforms or frequency design tools is required. Emphasis is placed on assumptions and logical implications, rather than abstract completeness; on interpretation and physical meaning, rather than theoretical formalism; on results and solutions, rather than derivation or solvability.  The topics covered include transient performance and stabilization via state or output feedback; disturbance attenuation and robust control; regional eigenvalue assignment and constraints on input or output variables; asymptotic regulation and disturbance rejection. Lyapunov theory and Linear Matrix Inequalities (LMI) are discussed as key design methods. All methods are demonstrated with MATLAB to promote practical use and comprehension. ...

H-Infinity robust controller design for the synchronization of master-slave chaotic systems with disturbance input

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Hamid Reza Karimi

2012-01-01

Full Text Available This paper is concerned with the robust control problems for the synchronization of master-slave chaotic systems with disturbance input. By constructing a series of Lyapunov functions, novel H-Infinity robust synchronization controllers are designed, whose control regulation possess the characteristic of simpleness and explicitness. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed techniques.

Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data

Science.gov (United States)

Pathak, Jaideep; Lu, Zhixin; Hunt, Brian R.; Girvan, Michelle; Ott, Edward

2017-12-01

We use recent advances in the machine learning area known as "reservoir computing" to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process. The technique uses a limited time series of measurements as input to a high-dimensional dynamical system called a "reservoir." After the reservoir's response to the data is recorded, linear regression is used to learn a large set of parameters, called the "output weights." The learned output weights are then used to form a modified autonomous reservoir designed to be capable of producing an arbitrarily long time series whose ergodic properties approximate those of the input signal. When successful, we say that the autonomous reservoir reproduces the attractor's "climate." Since the reservoir equations and output weights are known, we can compute the derivatives needed to determine the Lyapunov exponents of the autonomous reservoir, which we then use as estimates of the Lyapunov exponents for the original input generating system. We illustrate the effectiveness of our technique with two examples, the Lorenz system and the Kuramoto-Sivashinsky (KS) equation. In the case of the KS equation, we note that the high dimensional nature of the system and the large number of Lyapunov exponents yield a challenging test of our method, which we find the method successfully passes.

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

A Lyapunov based approach to energy maximization in renewable energy technologies

Science.gov (United States)

Iyasere, Erhun

This dissertation describes the design and implementation of Lyapunov-based control strategies for the maximization of the power captured by renewable energy harnessing technologies such as (i) a variable speed, variable pitch wind turbine, (ii) a variable speed wind turbine coupled to a doubly fed induction generator, and (iii) a solar power generating system charging a constant voltage battery. First, a torque control strategy is presented to maximize wind energy captured in variable speed, variable pitch wind turbines at low to medium wind speeds. The proposed strategy applies control torque to the wind turbine pitch and rotor subsystems to simultaneously control the blade pitch and tip speed ratio, via the rotor angular speed, to an optimum point at which the capture efficiency is maximum. The control method allows for aerodynamic rotor power maximization without exact knowledge of the wind turbine model. A series of numerical results show that the wind turbine can be controlled to achieve maximum energy capture. Next, a control strategy is proposed to maximize the wind energy captured in a variable speed wind turbine, with an internal induction generator, at low to medium wind speeds. The proposed strategy controls the tip speed ratio, via the rotor angular speed, to an optimum point at which the efficiency constant (or power coefficient) is maximal for a particular blade pitch angle and wind speed by using the generator rotor voltage as a control input. This control method allows for aerodynamic rotor power maximization without exact wind turbine model knowledge. Representative numerical results demonstrate that the wind turbine can be controlled to achieve near maximum energy capture. Finally, a power system consisting of a photovoltaic (PV) array panel, dc-to-dc switching converter, charging a battery is considered wherein the environmental conditions are time-varying. A backstepping PWM controller is developed to maximize the power of the solar generating

Lyapunov spectra and conjugate-pairing rule for confined atomic fluids

DEFF Research Database (Denmark)

Bernadi, Stefano; Todd, B.D.; Hansen, Jesper Schmidt

2010-01-01

In this work we present nonequilibrium molecular dynamics simulation results for the Lyapunov spectra of atomic fluids confined in narrow channels of the order of a few atomic diameters. We show the effect that realistic walls have on the Lyapunov spectra. All the degrees of freedom of the confin...... evolved Lyapunov vectors projected into a reduced dimensional phase space. We finally observe that the phase-space compression due to the thermostat remains confined into the wall region and does not significantly affect the purely Newtonian fluid region....

Lyapunov, attractors and exponents

International Nuclear Information System (INIS)

Oliveira, C.R. de.

1987-01-01

Based on the fundamental principles of statistical mechanics and ergodic theory a definition is given to atractor, as an invariant measure. Many results which reinforce this definition are demonstrated. Chaos is related to the presence of an atractor with entropy above zero. The role of Lyapunov exponents is analyzed. (A.C.A.S.) [pt

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.

Science.gov (United States)

Ott, William; Rivas, Mauricio A; West, James

2015-12-01

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ N using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C 1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time- T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).

Using Covariant Lyapunov Vectors to Understand Spatiotemporal Chaos in Fluids

Science.gov (United States)

Paul, Mark; Xu, Mu; Barbish, Johnathon; Mukherjee, Saikat

2017-11-01

The spatiotemporal chaos of fluids present many difficult and fascinating challenges. Recent progress in computing covariant Lyapunov vectors for a variety of model systems has made it possible to probe fundamental ideas from dynamical systems theory including the degree of hyperbolicity, the fractal dimension, the dimension of the inertial manifold, and the decomposition of the dynamics into a finite number of physical modes and spurious modes. We are interested in building upon insights such as these for fluid systems. We first demonstrate the power of covariant Lyapunov vectors using a system of maps on a lattice with a nonlinear coupling. We then compute the covariant Lyapunov vectors for chaotic Rayleigh-Bénard convection for experimentally accessible conditions. We show that chaotic convection is non-hyperbolic and we quantify the spatiotemporal features of the spectrum of covariant Lyapunov vectors. NSF DMS-1622299 and DARPA/DSO Models, Dynamics, and Learning (MoDyL).

Large-Signal Lyapunov-Based Stability Analysis of DC/AC Inverters and Inverter-Based Microgrids

Science.gov (United States)

Kabalan, Mahmoud

study. This will enable future studies to save computational effort and produce the most accurate results according to the needs of the study being performed. Moreover, the effect of grid (line) impedance on the accuracy of droop control is explored using the 5th order model. Simulation results show that traditional droop control is valid up to R/X line impedance value of 2. Furthermore, the 3rd order nonlinear model improves the currently available inverter-infinite bus models by accounting for grid impedance, active power-frequency droop and reactive power-voltage droop. Results show the 3rd order model's ability to account for voltage and reactive power changes during a transient event. Finally, the large-signal Lyapunov-based stability analysis is completed for a 3 bus microgrid system (made up of 2 inverters and 1 linear load). The thesis provides a systematic state space large-signal nonlinear mathematical modeling method of inverter-based microgrids. The inverters include the dc-side dynamics associated with dc sources. The mathematical model is then used to estimate the domain of asymptotic stability of the 3 bus microgrid. The three bus microgrid system was used as a case study to highlight the design and optimization capability of a large-signal-based approach. The study explores the effect of system component sizing, load transient and generation variations on the asymptotic stability of the microgrid. Essentially, this advancement gives microgrid designers and engineers the ability to manipulate the domain of asymptotic stability depending on performance requirements. Especially important, this research was able to couple the domain of asymptotic stability of the ac microgrid with that of the dc side voltage source. Time domain simulations were used to demonstrate the mathematical nonlinear analysis results.

Lyapunov Functions to Caputo Fractional Neural Networks with Time-Varying Delays

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Ravi Agarwal

2018-05-01

Full Text Available One of the main properties of solutions of nonlinear Caputo fractional neural networks is stability and often the direct Lyapunov method is used to study stability properties (usually these Lyapunov functions do not depend on the time variable. In connection with the Lyapunov fractional method we present a brief overview of the most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. These derivatives are applied to various types of neural networks with variable coefficients and time-varying delays. We show that quadratic Lyapunov functions and their Caputo fractional derivatives are not applicable in some cases when one studies stability properties. Some sufficient conditions for stability of equilibrium of nonlinear Caputo fractional neural networks with time dependent transmission delays, time varying self-regulating parameters of all units and time varying functions of the connection between two neurons in the network are obtained. The cases of time varying Lipschitz coefficients as well as nonLipschitz activation functions are studied. We illustrate our theory on particular nonlinear Caputo fractional neural networks.

Heat conduction in one-dimensional chains and nonequilibrium Lyapunov spectrum

International Nuclear Information System (INIS)

Posch, H.A.; Hoover, W.G.

1998-01-01

We define and study the heat conductivity κ and the Lyapunov spectrum for a modified 'ding-a-ling' chain undergoing steady heat flow. Free and bound particles alternate along a chain. In the present work, we use a linear gravitational potential to bind all the even-numbered particles to their lattice sites. The chain is bounded by two stochastic heat reservoirs, one hot and one cold. The Fourier conductivity of the chain decreases smoothly to a finite large-system limit. Special treatment of satellite collisions with the stochastic boundaries is required to obtain Lyapunov spectra. The summed spectra are negative, and correspond to a relatively small contraction in phase space, with the formation of a multifractal strange attractor. The largest of the Lyapunov exponents for the ding-a-ling chain appears to converge to a limiting value with increasing chain length, so that the large-system Lyapunov spectrum has a finite limit. copyright 1998 The American Physical Society

Analysis of Human Standing Balance by Largest Lyapunov Exponent

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Kun Liu

2015-01-01

Full Text Available The purpose of this research is to analyse the relationship between nonlinear dynamic character and individuals’ standing balance by the largest Lyapunov exponent, which is regarded as a metric for assessing standing balance. According to previous study, the largest Lyapunov exponent from centre of pressure time series could not well quantify the human balance ability. In this research, two improvements were made. Firstly, an external stimulus was applied to feet in the form of continuous horizontal sinusoidal motion by a moving platform. Secondly, a multiaccelerometer subsystem was adopted. Twenty healthy volunteers participated in this experiment. A new metric, coordinated largest Lyapunov exponent was proposed, which reflected the relationship of body segments by integrating multidimensional largest Lyapunov exponent values. By using this metric in actual standing performance under sinusoidal stimulus, an obvious relationship between the new metric and the actual balance ability was found in the majority of the subjects. These results show that the sinusoidal stimulus can make human balance characteristics more obvious, which is beneficial to assess balance, and balance is determined by the ability of coordinating all body segments.

Lyapunov exponents

CERN Document Server

Barreira, Luís

2017-01-01

This book offers a self-contained introduction to the theory of Lyapunov exponents and its applications, mainly in connection with hyperbolicity, ergodic theory and multifractal analysis. It discusses the foundations and some of the main results and main techniques in the area, while also highlighting selected topics of current research interest. With the exception of a few basic results from ergodic theory and the thermodynamic formalism, all the results presented include detailed proofs. The book is intended for all researchers and graduate students specializing in dynamical systems who are looking for a comprehensive overview of the foundations of the theory and a sample of its applications.

TS Fuzzy Model-Based Controller Design for a Class of Nonlinear Systems Including Nonsmooth Functions

DEFF Research Database (Denmark)

Vafamand, Navid; Asemani, Mohammad Hassan; Khayatiyan, Alireza

2018-01-01

This paper proposes a novel robust controller design for a class of nonlinear systems including hard nonlinearity functions. The proposed approach is based on Takagi-Sugeno (TS) fuzzy modeling, nonquadratic Lyapunov function, and nonparallel distributed compensation scheme. In this paper, a novel...... criterion, new robust controller design conditions in terms of linear matrix inequalities are derived. Three practical case studies, electric power steering system, a helicopter model and servo-mechanical system, are presented to demonstrate the importance of such class of nonlinear systems comprising...

Determining the Lyapunov Spectrum of Continuous-Time 1D and 2D Multiscroll Chaotic Oscillators via the Solution of m-PWL Variational Equations

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Jesus Manuel Munoz-Pacheco

2013-01-01

Full Text Available An algorithm to compute the Lyapunov exponents of piecewise linear function-based multidirectional multiscroll chaotic oscillators is reported. Based on the m regions in the piecewise linear functions, the suggested algorithm determines the individual expansion rate of Lyapunov exponents from m-piecewise linear variational equations and their associated m-Jacobian matrices whose entries remain constant during all computation cycles. Additionally, by considering OpAmp-based chaotic oscillators, we study the impact of two analog design procedures on the magnitude of Lyapunov exponents. We focus on analyzing variations of both frequency bandwidth and voltage/current dynamic range of the chaotic signals at electronic system level. As a function of the design parameters, a renormalization factor is proposed to estimate correctly the Lyapunov spectrum. Numerical simulation results in a double-scroll type chaotic oscillator and complex chaotic oscillators generating multidirectional multiscroll chaotic attractors on phase space confirm the usefulness of the reported algorithm.

Nonlinear Power Flow Control Design Utilizing Exergy, Entropy, Static and Dynamic Stability, and Lyapunov Analysis

CERN Document Server

Robinett III, Rush D

2011-01-01

Nonlinear Powerflow Control Design presents an innovative control system design process motivated by renewable energy electric grid integration problems. The concepts developed result from the convergence of three research and development goals: • to create a unifying metric to compare the value of different energy sources – coal-burning power plant, wind turbines, solar photovoltaics, etc. – to be integrated into the electric power grid and to replace the typical metric of costs/profit; • to develop a new nonlinear control tool that applies power flow control, thermodynamics, and complex adaptive systems theory to the energy grid in a consistent way; and • to apply collective robotics theories to the creation of high-performance teams of people and key individuals in order to account for human factors in controlling and selling power into a distributed, decentralized electric power grid. All three of these goals have important concepts in common: exergy flow, limit cycles, and balance between compe...

Novel controller design demonstration for vibration alleviation of helicopter rotor blades

Science.gov (United States)

Ulker, Fatma Demet; Nitzsche, Fred

2012-04-01

This paper presents an advanced controller design methodology for vibration alleviation of helicopter rotor sys- tems. Particularly, vibration alleviation in a forward ight regime where the rotor blades experience periodically varying aerodynamic loading was investigated. Controller synthesis was carried out under the time-periodic H2 and H∞ framework and the synthesis problem was solved based on both periodic Riccati and Linear Matrix Inequality (LMI) formulations. The closed-loop stability was analyzed using Floquet-Lyapunov theory, and the controller's performance was validated by closed-loop high-delity aeroelastic simulations. To validate the con- troller's performance an actively controlled trailing edge ap strategy was implemented. Computational cost was compared for both formulations.

Fuzzy Networked Control Systems Design Considering Scheduling Restrictions

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H. Benítez-Pérez

2012-01-01

known a priory but from a dynamic real-time behavior. To do so, the use of priority dynamic Priority exchange scheduling is performed. The objective of this paper is to show a way to tackle multiple time delays that are bounded and the dynamic response from real-time scheduling approximation. The related control law is designed considering fuzzy logic approximation for nonlinear time delays coupling, where the main advantage is the integration of this behavior through extended state space representation keeping certain linear and bounded behavior and leading to a stable situation during events presentation by guaranteeing stability through Lyapunov.

Lyapunov Functions, Stationary Distributions, and Non-equilibrium Potential for Reaction Networks

DEFF Research Database (Denmark)

Anderson, David F; Craciun, Gheorghe; Gopalkrishnan, Manoj

2015-01-01

We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well-known Lyapunov function of reaction network theory as a scaling limit of the non-equilibrium potent...

Construction of Lyapunov Function for Dissipative Gyroscopic System

International Nuclear Information System (INIS)

Xu Wei; Ao Ping; Yuan Bo

2011-01-01

We introduce a force decomposition to construct a potential function in deterministic dynamics described by ordinary differential equations in the context of dissipative gyroscopic systems. Such a potential function serves as the corresponding Lyapunov function for the dynamics, hence it gives both quantitative and qualitative descriptions for stability of motion. As an example we apply our force decomposition to a four-dimensional dissipative gyroscopic system. We explicitly obtain the potential function for all parameter regimes in the linear limit, including those regimes where the Lyapunov function was previously believed not to exist. (general)

Anisotropies in magnetic field evolution and local Lyapunov exponents

International Nuclear Information System (INIS)

Tang, X.Z.; Boozer, A.H.

2000-01-01

The natural occurrence of small scale structures and the extreme anisotropy in the evolution of a magnetic field embedded in a conducting flow is interpreted in terms of the properties of the local Lyapunov exponents along the various local characteristic (un)stable directions for the Lagrangian flow trajectories. The local Lyapunov exponents and the characteristic directions are functions of Lagrangian coordinates and time, which are completely determined once the flow field is specified. The characteristic directions that are associated with the spatial anisotropy of the problem, are prescribed in both Lagrangian and Eulerian frames. Coordinate transformation techniques are employed to relate the spatial distributions of the magnetic field, the induced current density, and the Lorentz force, which are usually followed in Eulerian frame, to those of the local Lyapunov exponents, which are naturally defined in Lagrangian coordinates

Kinematics, dynamics and control design of 4WIS4WID mobile robots

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Ming-Han Lee

2015-01-01

Full Text Available Kinematic and dynamic modelling and corresponding control design of a four-wheel-independent steering and four-wheel-independent driving (4WIS4WID mobile robot are presented in this study. Different from the differential or car-like mobile robot, the 4WIS4WID mobile robot is controlled by four steering and four driving motors, so the control scheme should possess the ability to integrate and manipulate the four independent wheels. A trajectory tracking control scheme is developed for the 4WIS4WID mobile robot, where both non-linear kinematic control and dynamic sliding-mode control are designed. All of the stabilities of the kinematic and dynamic control laws are proved by Lyapunov stability analysis. Finally, the feasibility and validity of the proposed trajectory tracking control scheme are confirmed through computer simulations.

Image-Based Visual Servoing for Robotic Systems: A Nonlinear Lyapunov-Based Control Approach

International Nuclear Information System (INIS)

Dixon, Warren

2003-01-01

The objective of this project is to enable current and future EM robots with an increased ability to perceive and interact with unstructured and unknown environments through the use of camera-based visual servo controllers. The scientific goals of this research are to develop a new visual servo control methodology that: (1) adapts for the unknown camera calibration parameters (e.g., focal length, scaling factors, camera position, and orientation) and the physical parameters of the robotic system (e.g., mass, inertia, friction), (2) compensates for unknown depth information (extract 3D information from the 2D image), and (3) enables multi-uncalibrated cameras to be used as a means to provide a larger field-of-view. Nonlinear Lyapunov-based techniques in conjunction with results from projective geometry are being used to overcome the complex control issues and alleviate many of the restrictive assumptions that impact current visual servo controlled robotic systems. The potential relevance of this control methodology will be a plug-and-play visual servoing control module that can be utilized in conjunction with current technology such as feature extraction and recognition, to enable current EM robotic systems with the capabilities of increased accuracy, autonomy, and robustness, with a larger field of view (and hence a larger workspace). These capabilities will enable EM robots to significantly accelerate D and D operations by providing for improved robot autonomy and increased worker productivity, while also reducing the associated costs, removing the human operator from the hazardous environments, and reducing the burden and skill of the human operators

Image-Based Visual Servoing for Robotic Systems: A Nonlinear Lyapunov-Based Control Approach

International Nuclear Information System (INIS)

Dixon, Warren

2002-01-01

The objective of this project is to enable current and future EM robots with an increased ability to perceive and interact with unstructured and unknown environments through the use of camera-based visual servo controlled robots. The scientific goals of this research are to develop a new visual servo control methodology that: (1) adapts for the unknown camera calibration parameters (e.g., focal length, scaling factors, camera position and orientation) and the physical parameters of the robotic system (e.g., mass, inertia, friction), (2) compensates for unknown depth information (extract 3D information from the 2D image), and (3) enables multi-uncalibrated cameras to be used as a means to provide a larger field-of-view. Nonlinear Lyapunov-based techniques are being used to overcome the complex control issues and alleviate many of the restrictive assumptions that impact current visual servo controlled robotic systems. The potential relevance of this control methodology will be a plug-and-play visual servoing control module that can be utilized in conjunction with current technology such as feature extraction and recognition, to enable current EM robotic systems with the capabilities of increased accuracy, autonomy, and robustness, with a larger field of view (and hence a larger workspace). These capabilities will enable EM robots to significantly accelerate D and D operations by providing for improved robot autonomy and increased worker productivity, while also reducing the associated costs, removing the human operator from the hazardous environments, and reducing the burden and skill of the human operators

On the existence of polynomial Lyapunov functions for rationally stable vector fields

DEFF Research Database (Denmark)

Leth, Tobias; Wisniewski, Rafal; Sloth, Christoffer

2018-01-01

This paper proves the existence of polynomial Lyapunov functions for rationally stable vector fields. For practical purposes the existence of polynomial Lyapunov functions plays a significant role since polynomial Lyapunov functions can be found algorithmically. The paper extents an existing result...... on exponentially stable vector fields to the case of rational stability. For asymptotically stable vector fields a known counter example is investigated to exhibit the mechanisms responsible for the inability to extend the result further....

Motion Control Design for an Omnidirectional Mobile Robot Subject to Velocity Constraints

Directory of Open Access Journals (Sweden)

Ollin Peñaloza-Mejía

2015-01-01

Full Text Available A solution to achieve global asymptotic tracking with bounded velocities in an omnidirectional mobile robot is proposed in this paper. It is motivated by the need of having a useful in-practice motion control scheme, which takes into account the physical limits of the velocities. To this end, a passive nonlinear controller is designed and combined with a tracking controller in a negative feedback connection structure. By using Lyapunov theory and passivity tools, global asymptotic tracking with desired bounded velocities is proved. Simulations and experimental results are provided to show the effectiveness of the proposal.

Local Lyapunov exponents for dissipative continuous systems

International Nuclear Information System (INIS)

Grond, Florian; Diebner, Hans H.

2005-01-01

We analyze a recently proposed algorithm for computing Lyapunov exponents focusing on its capability to calculate reliable local values for chaotic attractors. The averaging process of local contributions to the global measure becomes interpretable, i.e. they are related to the local topological structure in phase space. We compare the algorithm with the commonly used Wolf algorithm by means of analyzing correlations between coordinates of the chaotic attractor and local values of the Lyapunov exponents. The correlations for the new algorithm turn out to be significantly stronger than those for the Wolf algorithm. Since the usage of scalar measures to capture complex structures can be questioned we discuss these entities along with a more phenomenological description of scatter plots

Lyapunov stability analysis of magnetohydrodynamic plasma equilibria with axisymmetric toroidal flow

International Nuclear Information System (INIS)

Almaguer, J.A.; Hameiri, E.; Herrera, J.; Holm, D.D.

1988-01-01

Lyapunov stability conditions for ideal magnetohydrodynamic (MHD) plasmas with mass flow in axisymmetric toroidal geometry are determined in the Eulerian representation. Axisymmetric equilibrium solutions of ideal MHD are associated to critical points of a nonlinearly conserved Lyapunov functional consisting of the sum of the total energy and the following flux-weighted quantities: the circulation along field lines, the angular momentum, the toroidal flux, and the mass content within each flux tube. Conditions sufficient for Lyapunov stability of these equilibria against axisymmetric perturbations are found by taking advantage of the Hamiltonian formalism for ideal MHD. In particular [see Eq. (60)], it is sufficient for Lyapunov stability under linearized dynamics that an axisymmetric equilibrium be subsonic in the appropriate rotating frame, lie in the first elliptic regime of the Bernoulli--Grad--Shafranov (BGS) system of equations, and satisfy one additional, more complicated, condition. Effects of boundary conditions, nonlinearity, and three-dimensionality on MHD stability are also discussed

Dynamical behaviors determined by the Lyapunov function in competitive Lotka-Volterra systems

Science.gov (United States)

Tang, Ying; Yuan, Ruoshi; Ma, Yian

2013-01-01

Dynamical behaviors of the competitive Lotka-Volterra system even for 3 species are not fully understood. In this paper, we study this problem from the perspective of the Lyapunov function. We construct explicitly the Lyapunov function using three examples of the competitive Lotka-Volterra system for the whole state space: (1) the general 2-species case, (2) a 3-species model, and (3) the model of May-Leonard. The basins of attraction for these examples are demonstrated, including cases with bistability and cyclical behavior. The first two examples are the generalized gradient system, where the energy dissipation may not follow the gradient of the Lyapunov function. In addition, under a new type of stochastic interpretation, the Lyapunov function also leads to the Boltzmann-Gibbs distribution on the final steady state when multiplicative noise is added.

A New Robust Tracking Control Design for Turbofan Engines: H∞/Leitmann Approach

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Muxuan Pan

2017-04-01

Full Text Available In this paper, a H ∞ /Leitmann approach to the robust tracking control design is presented for an uncertain dynamic system. This new method is developed in the following two steps. Firstly, a tracking dynamic system with simultaneous consideration of parameter uncertainty and noise is modeled based on a linear system and a reference model. Accordingly, a “nominal system” from the tracking system is defined and controlled by a H ∞ control to obtain the asymptotical stability and noise resistance. Secondly, by making use of a Lyapunov function and the norm boundedness, a new robust control with the “Leitmann approach” is designed to cope with the uncertainty. The two controls collaborate with each other to achieve “uniform tracking boundedness” and “uniform ultimate tracking boundedness”. The new approach is then applied to an aircraft turbofan control design, and the numerical simulation results show the prescribed performances of the closed-loop system and the advantage of the developed approach.

Design of passive fault-tolerant flight controller against actuator failures

Directory of Open Access Journals (Sweden)

Xiang Yu

2015-02-01

Full Text Available The problem of designing passive fault-tolerant flight controller is addressed when the normal and faulty cases are prescribed. First of all, the considered fault and fault-free cases are formed by polytopes. As considering that the safety of a post-fault system is directly related to the maximum values of physical variables in the system, peak-to-peak gain is selected to represent the relationships among the amplitudes of actuator outputs, system outputs, and reference commands. Based on the parameter dependent Lyapunov and slack methods, the passive fault-tolerant flight controllers in the absence/presence of system uncertainty for actuator failure cases are designed, respectively. Case studies of an airplane under actuator failures are carried out to validate the effectiveness of the proposed approach.

Inertia theorems for operator Lyapunov inequalities

NARCIS (Netherlands)

Sasane, AJ; Curtain, RF

2001-01-01

We study operator Lyapunov inequalities and equations for which the infinitesimal generator is not necessarily stable, but it satisfies the spectrum decomposition assumption and it has at most finitely many unstable eigenvalues. Moreover, the input or output operators are not necessarily bounded,

A statistical approach to estimate the LYAPUNOV spectrum in disc brake squeal

Science.gov (United States)

Oberst, S.; Lai, J. C. S.

2015-01-01

The estimation of squeal propensity of a brake system from the prediction of unstable vibration modes using the linear complex eigenvalue analysis (CEA) in the frequency domain has its fair share of successes and failures. While the CEA is almost standard practice for the automotive industry, time domain methods and the estimation of LYAPUNOV spectra have not received much attention in brake squeal analyses. One reason is the challenge in estimating the true LYAPUNOV exponents and their discrimination against spurious ones in experimental data. A novel method based on the application of the ECKMANN-RUELLE matrices is proposed here to estimate LYAPUNOV exponents by using noise in a statistical procedure. It is validated with respect to parameter variations and dimension estimates. By counting the number of non-overlapping confidence intervals for LYAPUNOV exponent distributions obtained by moving a window of increasing size over bootstrapped same-length estimates of an observation function, a dispersion measure's width is calculated and fed into a BAYESIAN beta-binomial model. Results obtained using this method for benchmark models of white and pink noise as well as the classical HENON map indicate that true LYAPUNOV exponents can be isolated from spurious ones with high confidence. The method is then applied to accelerometer and microphone data obtained from brake squeal tests. Estimated LYAPUNOV exponents indicate that the pad's out-of-plane vibration behaves quasi-periodically on the brink to chaos while the microphone's squeal signal remains periodic.

Lyapunov stability of ideal compressible and incompressible fluid equilibria in three dimensions

International Nuclear Information System (INIS)

Holm, D.D.

1985-08-01

Linearized stability of ideal compressible and incompressible fluid equilibria in three dimensions is analyzed using Lyapunov's direct method. An action principle is given for the Eulerian and Lagrangian fluid descriptions and the family of constants of motion due to symmetry under fluid-particle relabelling is derived in the form of Ertel's theorem for each description. In an augmented Euleriah description, the steady equilibrium flows of these two fluids theories are identified as critical points of the conserved Lyapunov functionals defined by the sum, H + C, of the energy H, and the Ertel constants of motion, C. It turns out that unconditional linear Lyapunov stability of these flows in the norm provided by the second variation of H + C is precluded by vortex-particle stretching, even for otherwise shear-stable flows. Conditional Lyapunov stability of these flows is discussed. 24 refs

Image-Based Visual Servoing for Robotic Systems: A Nonlinear Lyapunov-Based Control Approach

International Nuclear Information System (INIS)

Dixon, Warren

2004-01-01

There is significant motivation to provide robotic systems with improved autonomy as a means to significantly accelerate deactivation and decommissioning (DandD) operations while also reducing the associated costs, removing human operators from hazardous environments, and reducing the required burden and skill of human operators. To achieve improved autonomy, this project focused on the basic science challenges leading to the development of visual servo controllers. The challenge in developing these controllers is that a camera provides 2-dimensional image information about the 3-dimensional Euclidean-space through a perspective (range dependent) projection that can be corrupted by uncertainty in the camera calibration matrix and by disturbances such as nonlinear radial distortion. Disturbances in this relationship (i.e., corruption in the sensor information) propagate erroneous information to the feedback controller of the robot, leading to potentially unpredictable task execution. This research project focused on the development of a visual servo control methodology that targets compensating for disturbances in the camera model (i.e., camera calibration and the recovery of range information) as a means to achieve predictable response by the robotic system operating in unstructured environments. The fundamental idea is to use nonlinear Lyapunov-based techniques along with photogrammetry methods to overcome the complex control issues and alleviate many of the restrictive assumptions that impact current robotic applications. The outcome of this control methodology is a plug-and-play visual servoing control module that can be utilized in conjunction with current technology such as feature recognition and extraction to enable robotic systems with the capabilities of increased accuracy, autonomy, and robustness, with a larger field of view (and hence a larger workspace). The developed methodology has been reported in numerous peer-reviewed publications and the

A development of the direct Lyapunov method for the analysis of transient stability of a system of synchronous generators based on the determination of non- stable equilibria on a multidimensional sphere

Directory of Open Access Journals (Sweden)

A. V. Stepanov

2014-01-01

Full Text Available A development of the direct Lyapunov method for the analysis of transient stability of a system of synchronous generators based on the determination of non- stable equilibria on a multidimensional sphere.We consider the problem of transient stability analysis for a system of synchronous generators under the action of strong perturbations. The aim of our work is to develop methods to analyze a transient stability of the system of synchronous generators, which allow getting trustworthy results on reserve transient stability under different perturbations. For the analysis of transient stability, we use the direct Lyapunov method.One of the problems for this method application is to find the Lypunov function that well reflects the properties of a parallel system of synchronous generators. The most reliable results were obtained when the analysis of transient stability was performed with a Lyapunov function of energy type. Another problem for application of the direct Lyapunov method is to determine the critical value of the Lyapunov function, which requires finding the non-stable equilibria of the system. Determination of the non-stable equilibria requires studying the Lyapunov function in a multidimensional space in a neighborhood of a stable equilibrium for the post-breakdown system; this is a complicated non-linear problem.In the paper, we propose a method for determination of the non-stable equilibria on a multidimensional sphere. The method is based on a search of a minimum of the Lyapunov function on a multidimensional sphere the center of which is a stable equilibrium. Our method allows, comparing with the other, e.g., gradient methods, reliable finding a non-stable equilibrium and calculating the critical value. The reliability of our method is proved by numerical experiments. The developed methods and a program realized in a MATLAB package can be recommended for design of a post-breakdown control system of synchronous generators or as a

Nonlinear generalized synchronization of chaotic systems by pure error dynamics and elaborate nondiagonal Lyapunov function

International Nuclear Information System (INIS)

Ge Zhengming; Chang Chingming

2009-01-01

By applying pure error dynamics and elaborate nondiagonal Lyapunov function, the nonlinear generalized synchronization is studied in this paper. Instead of current mixed error dynamics in which master state variables and slave state variables are presented, the nonlinear generalized synchronization can be obtained by pure error dynamics without auxiliary numerical simulation. The elaborate nondiagonal Lyapunov function is applied rather than current monotonous square sum Lyapunov function deeply weakening the powerfulness of Lyapunov direct method. Both autonomous and nonautonomous double Mathieu systems are used as examples with numerical simulations.

Sum-of-squares-based fuzzy controller design using quantum-inspired evolutionary algorithm

Science.gov (United States)

Yu, Gwo-Ruey; Huang, Yu-Chia; Cheng, Chih-Yung

2016-07-01

In the field of fuzzy control, control gains are obtained by solving stabilisation conditions in linear-matrix-inequality-based Takagi-Sugeno fuzzy control method and sum-of-squares-based polynomial fuzzy control method. However, the optimal performance requirements are not considered under those stabilisation conditions. In order to handle specific performance problems, this paper proposes a novel design procedure with regard to polynomial fuzzy controllers using quantum-inspired evolutionary algorithms. The first contribution of this paper is a combination of polynomial fuzzy control and quantum-inspired evolutionary algorithms to undertake an optimal performance controller design. The second contribution is the proposed stability condition derived from the polynomial Lyapunov function. The proposed design approach is dissimilar to the traditional approach, in which control gains are obtained by solving the stabilisation conditions. The first step of the controller design uses the quantum-inspired evolutionary algorithms to determine the control gains with the best performance. Then, the stability of the closed-loop system is analysed under the proposed stability conditions. To illustrate effectiveness and validity, the problem of balancing and the up-swing of an inverted pendulum on a cart is used.

A sampling approach to constructing Lyapunov functions for nonlinear continuous–time systems

NARCIS (Netherlands)

Bobiti, R.V.; Lazar, M.

2016-01-01

The problem of constructing a Lyapunov function for continuous-time nonlinear dynamical systems is tackled in this paper via a sampling-based approach. The main idea of the sampling-based method is to verify a Lyapunov-type inequality for a finite number of points (known state vectors) in the

Statistical-mechanical formulation of Lyapunov exponents

International Nuclear Information System (INIS)

Tanase-Nicola, Sorin; Kurchan, Jorge

2003-01-01

We show how the Lyapunov exponents of a dynamic system can, in general, be expressed in terms of the free energy of a (non-Hermitian) quantum many-body problem. This puts their study as a problem of statistical mechanics, whose intuitive concepts and techniques of approximation can hence be borrowed

Thermodynamic stability of elementary chemical reactions proceeding at finite rates revisited using Lyapunov function analysis

International Nuclear Information System (INIS)

Burande, Chandrakant S.; Bhalekar, Anil A.

2005-01-01

The thermodynamic stability of a few representative elementary chemical reactions proceeding at finite rates has been investigated using the recently proposed thermodynamic Lyapunov function and following the steps of Lyapunov's second method (also termed as the direct method) of stability of motion. The thermodynamic Lyapunov function; L s , used herein is the excess rate of entropy production in the thermodynamic perturbation space, which thereby inherits the dictates of the second law of thermodynamics. This Lyapunov function is not the same as the excess entropy rate that one encounters in thermodynamic (irreversible) literature. The model chemical conversions studied in this presentation are A+B→v x X and A+B↔ν x X. For the sake of simplicity, the thermal effects of chemical reactions have been considered as not adding to the perturbation as our main aim was to demonstrate how one should use systematically the proposed thermodynamic Lyapunov function following the steps of Lyapunov's second method of stability of motion. The domains of thermodynamic stability under the constantly acting small disturbances, thermodynamic asymptotic stability and thermodynamic instability in these model systems get established

Critical behavior of the Lyapunov exponent in type-III intermittency

Energy Technology Data Exchange (ETDEWEB)

Alvarez-Llamoza, O. [Departamento de Fisica, FACYT, Universidad de Carabobo, Valencia (Venezuela); Centro de Fisica Fundamental, Grupo de Caos y Sistemas Complejos, Universidad de Los Andes, Merida 5251, Merida (Venezuela)], E-mail: llamoza@ula.ve; Cosenza, M.G. [Centro de Fisica Fundamental, Grupo de Caos y Sistemas Complejos, Universidad de Los Andes, Merida 5251, Merida (Venezuela); Ponce, G.A. [Departamento de Fisica, Universidad Nacional Autonoma de Honduras (Honduras); Departamento de Ciencias Naturales, Universidad Pedagogica Nacional Francisco Morazan, Tegucigalpa (Honduras)

2008-04-15

The critical behavior of the Lyapunov exponent near the transition to robust chaos via type-III intermittency is determined for a family of one-dimensional singular maps. Critical boundaries separating the region of robust chaos from the region where stable fixed points exist are calculated on the parameter space of the system. A critical exponent {beta} expressing the scaling of the Lyapunov exponent is calculated along the critical curve corresponding to the type-III intermittent transition to chaos. It is found that {beta} varies on the interval 0 {<=} {beta} < 1/2 as a function of the order of the singularity of the map. This contrasts with earlier predictions for the scaling behavior of the Lyapunov exponent in type-III intermittency. The variation of the critical exponent {beta} implies a continuous change in the nature of the transition to chaos via type-III intermittency, from a second-order, continuous transition to a first-order, discontinuous transition.

Critical behavior of the Lyapunov exponent in type-III intermittency

International Nuclear Information System (INIS)

Alvarez-Llamoza, O.; Cosenza, M.G.; Ponce, G.A.

2008-01-01

The critical behavior of the Lyapunov exponent near the transition to robust chaos via type-III intermittency is determined for a family of one-dimensional singular maps. Critical boundaries separating the region of robust chaos from the region where stable fixed points exist are calculated on the parameter space of the system. A critical exponent β expressing the scaling of the Lyapunov exponent is calculated along the critical curve corresponding to the type-III intermittent transition to chaos. It is found that β varies on the interval 0 ≤ β < 1/2 as a function of the order of the singularity of the map. This contrasts with earlier predictions for the scaling behavior of the Lyapunov exponent in type-III intermittency. The variation of the critical exponent β implies a continuous change in the nature of the transition to chaos via type-III intermittency, from a second-order, continuous transition to a first-order, discontinuous transition

Regeneration cycle and the covariant Lyapunov vectors in a minimal wall turbulence.

Science.gov (United States)

Inubushi, Masanobu; Takehiro, Shin-ichi; Yamada, Michio

2015-08-01

Considering a wall turbulence as a chaotic dynamical system, we study regeneration cycles in a minimal wall turbulence from the viewpoint of orbital instability by employing the covariant Lyapunov analysis developed by [F. Ginelli et al. Phys. Rev. Lett. 99, 130601 (2007)]. We divide the regeneration cycle into two phases and characterize them with the local Lyapunov exponents and the covariant Lyapunov vectors of the Navier-Stokes turbulence. In particular, we show numerically that phase (i) is dominated by instabilities related to the sinuous mode and the streamwise vorticity, and there is no instability in phase (ii). Furthermore, we discuss a mechanism of the regeneration cycle, making use of an energy budget analysis.

Evaluation-Function-based Model-free Adaptive Fuzzy Control

Directory of Open Access Journals (Sweden)

Agus Naba

2016-12-01

Full Text Available Designs of adaptive fuzzy controllers (AFC are commonly based on the Lyapunov approach, which requires a known model of the controlled plant. They need to consider a Lyapunov function candidate as an evaluation function to be minimized. In this study these drawbacks were handled by designing a model-free adaptive fuzzy controller (MFAFC using an approximate evaluation function defined in terms of the current state, the next state, and the control action. MFAFC considers the approximate evaluation function as an evaluative control performance measure similar to the state-action value function in reinforcement learning. The simulation results of applying MFAFC to the inverted pendulum benchmark verified the proposed scheme’s efficacy.

Data Driven Economic Model Predictive Control

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Masoud Kheradmandi

2018-04-01

Full Text Available This manuscript addresses the problem of data driven model based economic model predictive control (MPC design. To this end, first, a data-driven Lyapunov-based MPC is designed, and shown to be capable of stabilizing a system at an unstable equilibrium point. The data driven Lyapunov-based MPC utilizes a linear time invariant (LTI model cognizant of the fact that the training data, owing to the unstable nature of the equilibrium point, has to be obtained from closed-loop operation or experiments. Simulation results are first presented demonstrating closed-loop stability under the proposed data-driven Lyapunov-based MPC. The underlying data-driven model is then utilized as the basis to design an economic MPC. The economic improvements yielded by the proposed method are illustrated through simulations on a nonlinear chemical process system example.

Universality in chaos: Lyapunov spectrum and random matrix theory.

Science.gov (United States)

Hanada, Masanori; Shimada, Hidehiko; Tezuka, Masaki

2018-02-01

We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by random matrix theory. We demonstrate it by studying the finite-time Lyapunov exponents of the matrix model of a stringy black hole and the mass-deformed models. The massless limit, which has a dual string theory interpretation, is special in that the universal behavior can be seen already at t=0, while in other cases it sets in at late time. The same pattern is demonstrated also in the product of random matrices.

Generalized decompositions of dynamic systems and vector Lyapunov functions

Science.gov (United States)

Ikeda, M.; Siljak, D. D.

1981-10-01

The notion of decomposition is generalized to provide more freedom in constructing vector Lyapunov functions for stability analysis of nonlinear dynamic systems. A generalized decomposition is defined as a disjoint decomposition of a system which is obtained by expanding the state-space of a given system. An inclusion principle is formulated for the solutions of the expansion to include the solutions of the original system, so that stability of the expansion implies stability of the original system. Stability of the expansion can then be established by standard disjoint decompositions and vector Lyapunov functions. The applicability of the new approach is demonstrated using the Lotka-Volterra equations.

Universality in chaos: Lyapunov spectrum and random matrix theory

Science.gov (United States)

Hanada, Masanori; Shimada, Hidehiko; Tezuka, Masaki

2018-02-01

We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by random matrix theory. We demonstrate it by studying the finite-time Lyapunov exponents of the matrix model of a stringy black hole and the mass-deformed models. The massless limit, which has a dual string theory interpretation, is special in that the universal behavior can be seen already at t =0 , while in other cases it sets in at late time. The same pattern is demonstrated also in the product of random matrices.

Lyapunov exponent of the random frequency oscillator: cumulant expansion approach

International Nuclear Information System (INIS)

Anteneodo, C; Vallejos, R O

2010-01-01

We consider a one-dimensional harmonic oscillator with a random frequency, focusing on both the standard and the generalized Lyapunov exponents, λ and λ* respectively. We discuss the numerical difficulties that arise in the numerical calculation of λ* in the case of strong intermittency. When the frequency corresponds to a Ornstein-Uhlenbeck process, we compute analytically λ* by using a cumulant expansion including up to the fourth order. Connections with the problem of finding an analytical estimate for the largest Lyapunov exponent of a many-body system with smooth interactions are discussed.

New stability and stabilization for switched neutral control systems

International Nuclear Information System (INIS)

Xiong Lianglin; Zhong Shouming; Ye Mao; Wu Shiliang

2009-01-01

This paper concerns stability and stabilization issues for switched neutral systems and presents new classes of piecewise Lyapunov functionals and multiple Lyapunov functionals, based on which, two new switching rules are introduced to stabilize the neutral systems. One switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. The other is based on the determination of average dwell time computed from a new class of linear matrix inequalities (LMIs). And then, state-feedback control is derived for the switched neutral control system mainly based on the state switching rules. Finally, three examples are given to demonstrate the effectiveness of the proposed method.

International Congress NONLINEAR DYNAMICAL ANALYSIS 2007 dedicated to the 150th Anniversary of Academician A. M. Lyapunov

Science.gov (United States)

2010-05-14

Mikhailovich Lyapunov is discussed. Main attention is focused on the first Lyapunov method. LYAPUNOV BUNDLES IN CYCLIC FEEDBACK SYSTEMS WITH DELAYS George ...Lyapunov frequently discussed this problem with Henry Poincare (1854-1912) and George Darwin (1845 - 1912). They both considered the "pear-form" figure as... Cantor -type set. Neither can the existence of such systems be excluded. The results we present are discussed in a joint paper with K. Bjerkloev. МЕТОДЫ А.М

The Multivariate Largest Lyapunov Exponent as an Age-Related Metric of Quiet Standing Balance

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Kun Liu

2015-01-01

Full Text Available The largest Lyapunov exponent has been researched as a metric of the balance ability during human quiet standing. However, the sensitivity and accuracy of this measurement method are not good enough for clinical use. The present research proposes a metric of the human body’s standing balance ability based on the multivariate largest Lyapunov exponent which can quantify the human standing balance. The dynamic multivariate time series of ankle, knee, and hip were measured by multiple electrical goniometers. Thirty-six normal people of different ages participated in the test. With acquired data, the multivariate largest Lyapunov exponent was calculated. Finally, the results of the proposed approach were analysed and compared with the traditional method, for which the largest Lyapunov exponent and power spectral density from the centre of pressure were also calculated. The following conclusions can be obtained. The multivariate largest Lyapunov exponent has a higher degree of differentiation in differentiating balance in eyes-closed conditions. The MLLE value reflects the overall coordination between multisegment movements. Individuals of different ages can be distinguished by their MLLE values. The standing stability of human is reduced with the increment of age.

Lyapunov vs. geometrical stability analysis of the Kepler and the restricted three body problems

International Nuclear Information System (INIS)

Yahalom, A.; Levitan, J.; Lewkowicz, M.; Horwitz, L.

2011-01-01

In this Letter we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, the geometrical analysis of Horwitz et al. predicts the observed stability. This seems to us to provide evidence for both the incompleteness of the standard Lyapunov analysis and the strength of the geometrical analysis. Moreover, we apply this approach to the three body problem in which the third body is restricted to move on a circle of large radius which induces an adiabatic time dependent potential on the second body. This causes the second body to move in a very interesting and intricate but periodic trajectory; however, the standard Lyapunov analysis, as well as methods based on the parametric variation of curvature associated with the Jacobi metric, incorrectly predict chaotic behavior. The geometric approach predicts the correct stable motion in this case as well. - Highlights: → Lyapunov analysis predicts Kepler motion to be unstable. → Geometrical analysis predicts the observed stability. → Lyapunov analysis predicts chaotic behavior in restricted three body problem. → The geometric approach predicts the correct stable motion in restricted three body problem.

Lyapunov functionals and stability of stochastic difference equations

CERN Document Server

Shaikhet, Leonid

2011-01-01

This book offers a general method of Lyapunov functional construction which lets researchers analyze the degree to which the stability properties of differential equations are preserved in their difference analogues. Includes examples from physical systems.

On some properties of the discrete Lyapunov exponent

International Nuclear Information System (INIS)

Amigo, Jose M.; Kocarev, Ljupco; Szczepanski, Janusz

2008-01-01

One of the possible by-products of discrete chaos is the application of its tools, in particular of the discrete Lyapunov exponent, to cryptography. In this Letter we explore this question in a very general setting

H∞ Control for a Networked Control Model of Systems with Two Additive Time-Varying Delays

Directory of Open Access Journals (Sweden)

Hanyong Shao

2014-01-01

Full Text Available This paper is concerned with H∞ control for a networked control model of systems with two additive time-varying delays. A new Lyapunov functional is constructed to make full use of the information of the delays, and for the derivative of the Lyapunov functional a novel technique is employed to compute a tighter upper bound, which is dependent on the two time-varying delays instead of the upper bounds of them. Then the convex polyhedron method is proposed to check the upper bound of the derivative of the Lyapunov functional. The resulting stability criteria have fewer matrix variables but less conservatism than some existing ones. The stability criteria are applied to designing a state feedback controller, which guarantees that the closed-loop system is asymptotically stable with a prescribed H∞ disturbance attenuation level. Finally examples are given to show the advantages of the stability criteria and the effectiveness of the proposed control method.

Comparative study of adaptive controller using MIT rules and Lyapunov method for MPPT standalone PV systems

Science.gov (United States)

Tariba, N.; Bouknadel, A.; Haddou, A.; Ikken, N.; Omari, Hafsa El; Omari, Hamid El

2017-01-01

The Photovoltaic Generator have a nonlinear characteristic function relating the intensity at the voltage I = f (U) and depend on the variation of solar irradiation and temperature, In addition, its point of operation depends directly on the load that it supplies. To fix this drawback, and to extract the maximum power available to the terminal of the generator, an adaptation stage is introduced between the generator and the load to couple the two elements as perfectly as possible. The adaptation stage is associated with a command called MPPT MPPT (Maximum Power Point Tracker) whose is used to force the PVG to operate at the MPP (Maximum Power Point) under variation of climatic conditions and load variation. This paper presents a comparative study between the adaptive controller for PV Systems using MIT rules and Lyapunov method to regulate the PV voltage. The Incremental Conductance (IC) algorithm is used to extract the maximum power from the PVG by calculating the voltage Vref, and the adaptive controller is used to regulate and track quickly the PV voltage. The two methods of the adaptive controller will be compared to prove their performance by using the PSIM tools and experimental test, and the mathematical model of step-up with PVG model will be presented.

Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions

OpenAIRE

Bernal Reza, Miguel Ángel; Sala, Antonio; JAADARI, ABDELHAFIDH; Guerra, Thierry-Marie

2011-01-01

In this paper, the stability of continuous-time polynomial fuzzy models by means of a polynomial generalization of fuzzy Lyapunov functions is studied. Fuzzy Lyapunov functions have been fruitfully used in the literature for local analysis of Takagi-Sugeno models, a particular class of the polynomial fuzzy ones. Based on a recent Taylor-series approach which allows a polynomial fuzzy model to exactly represent a nonlinear model in a compact set of the state space, it is shown that a refinemen...

Multiscale Lyapunov exponent for 2-microlocal functions

International Nuclear Information System (INIS)

Dhifaoui, Zouhaier; Kortas, Hedi; Ammou, Samir Ben

2009-01-01

The Lyapunov exponent is an important indicator of chaotic dynamics. Using wavelet analysis, we define a multiscale representation of this exponent which we demonstrate the scale-wise dependence for functions belonging to C x 0 s,s ' spaces. An empirical study involving simulated processes and financial time series corroborates the theoretical findings.

Backstepping fuzzy-neural-network control design for hybrid maglev transportation system.

Science.gov (United States)

Wai, Rong-Jong; Yao, Jing-Xiang; Lee, Jeng-Dao

2015-02-01

This paper focuses on the design of a backstepping fuzzy-neural-network control (BFNNC) for the online levitated balancing and propulsive positioning of a hybrid magnetic levitation (maglev) transportation system. The dynamic model of the hybrid maglev transportation system including levitated hybrid electromagnets to reduce the suspension power loss and the friction force during linear movement and a propulsive linear induction motor based on the concepts of mechanical geometry and motion dynamics is first constructed. The ultimate goal is to design an online fuzzy neural network (FNN) control methodology to cope with the problem of the complicated control transformation and the chattering control effort in backstepping control (BSC) design, and to directly ensure the stability of the controlled system without the requirement of strict constraints, detailed system information, and auxiliary compensated controllers despite the existence of uncertainties. In the proposed BFNNC scheme, an FNN control is utilized to be the major control role by imitating the BSC strategy, and adaptation laws for network parameters are derived in the sense of projection algorithm and Lyapunov stability theorem to ensure the network convergence as well as stable control performance. The effectiveness of the proposed control strategy for the hybrid maglev transportation system is verified by experimental results, and the superiority of the BFNNC scheme is indicated in comparison with the BSC strategy and the backstepping particle-swarm-optimization control system in previous research.

Observer-Based Controller Design for a Class of Nonlinear Networked Control Systems with Random Time-Delays Modeled by Markov Chains

Directory of Open Access Journals (Sweden)

Yanfeng Wang

2017-01-01

Full Text Available This paper investigates the observer-based controller design problem for a class of nonlinear networked control systems with random time-delays. The nonlinearity is assumed to satisfy a global Lipschitz condition and two dependent Markov chains are employed to describe the time-delay from sensor to controller (S-C delay and the time-delay from controller to actuator (C-A delay, respectively. The transition probabilities of S-C delay and C-A delay are both assumed to be partly inaccessible. Sufficient conditions on the stochastic stability for the closed-loop systems are obtained by constructing proper Lyapunov functional. The methods of calculating the controller and the observer gain matrix are also given. Two numerical examples are used to illustrate the effectiveness of the proposed method.

Lyapunov exponents a tool to explore complex dynamics

CERN Document Server

Pikovsky, Arkady

2016-01-01

Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Utilising a pragmatic, physical approach, this self-contained book provides a comprehensive description of the concept. Beginning with the basic properties and numerical methods, it then guides readers through to the most recent advances in applications to complex systems. Practical algorithms are thoroughly reviewed and their performance is discussed, while a broad set of examples illustrate the wide range of potential applications. The description of various numerical and analytical techniques for the computation of Lyapunov exponents offers an extensive array of tools for the characterization of phenomena such as synchronization, weak and global chaos in low and high-dimensional set-ups, and localization. This text equips readers with all the investigative expertise needed to fully explore the dynamical properties of complex systems, making it ideal for both graduate students and experienced researchers...

On the relation between Lyapunov exponents and exponential decay of correlations

International Nuclear Information System (INIS)

Slipantschuk, Julia; Bandtlow, Oscar F; Just, Wolfram

2013-01-01

Chaotic dynamics with sensitive dependence on initial conditions may result in exponential decay of correlation functions. We show that for one-dimensional interval maps the corresponding quantities, that is, Lyapunov exponents and exponential decay rates, are related. More specifically, for piecewise linear expanding Markov maps observed via piecewise analytic functions, we show that the decay rate is bounded above by twice the Lyapunov exponent, that is, we establish lower bounds for the subleading eigenvalue of the corresponding Perron–Frobenius operator. In addition, we comment on similar relations for general piecewise smooth expanding maps. (paper)

Lyapunov equation for infinite-dimensional discrete bilinear systems

International Nuclear Information System (INIS)

Costa, O.L.V.; Kubrusly, C.S.

1991-03-01

Mean-square stability for discrete systems requires that uniform convergence is preserved between input and state correlation sequences. Such a convergence preserving property holds for an infinite-dimensional bilinear system if and only if the associate Lyapunov equation has a unique strictly positive solution. (author)

Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility

KAUST Repository

Korobeinikov, Andrei; Melnik, Andrey V.

2013-01-01

We consider global asymptotic properties for the SIR and SEIR age structured models for infectious diseases where the susceptibility depends on the age. Using the direct Lyapunov method with Volterra type Lyapunov functions, we establish conditions for the global stability of a unique endemic steady state and the infection-free steady state.

Tracking control of air-breathing hypersonic vehicles with non-affine dynamics via improved neural back-stepping design.

Science.gov (United States)

Bu, Xiangwei; He, Guangjun; Wang, Ke

2018-04-01

This study considers the design of a new back-stepping control approach for air-breathing hypersonic vehicle (AHV) non-affine models via neural approximation. The AHV's non-affine dynamics is decomposed into velocity subsystem and altitude subsystem to be controlled separately, and robust adaptive tracking control laws are developed using improved back-stepping designs. Neural networks are applied to estimate the unknown non-affine dynamics, which guarantees the addressed controllers with satisfactory robustness against uncertainties. In comparison with the existing control methodologies, the special contributions are that the non-affine issue is handled by constructing two low-pass filters based on model transformations, and virtual controllers are treated as intermediate variables such that they aren't needed for back-stepping designs any more. Lyapunov techniques are employed to show the uniformly ultimately boundedness of all closed-loop signals. Finally, simulation results are presented to verify the tracking performance and superiorities of the investigated control strategy. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Predicting Traffic Flow in Local Area Networks by the Largest Lyapunov Exponent

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Yan Liu

2016-01-01

Full Text Available The dynamics of network traffic are complex and nonlinear, and chaotic behaviors and their prediction, which play an important role in local area networks (LANs, are studied in detail, using the largest Lyapunov exponent. With the introduction of phase space reconstruction based on the time sequence, the high-dimensional traffic is projected onto the low dimension reconstructed phase space, and a reduced dynamic system is obtained from the dynamic system viewpoint. Then, a numerical method for computing the largest Lyapunov exponent of the low-dimensional dynamic system is presented. Further, the longest predictable time, which is related to chaotic behaviors in the system, is studied using the largest Lyapunov exponent, and the Wolf method is used to predict the evolution of the traffic in a local area network by both Dot and Interval predictions, and a reliable result is obtained by the presented method. As the conclusion, the results show that the largest Lyapunov exponent can be used to describe the sensitivity of the trajectory in the reconstructed phase space to the initial values. Moreover, Dot Prediction can effectively predict the flow burst. The numerical simulation also shows that the presented method is feasible and efficient for predicting the complex dynamic behaviors in LAN traffic, especially for congestion and attack in networks, which are the main two complex phenomena behaving as chaos in networks.

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.

Nonlinear robust hierarchical control for nonlinear uncertain systems

Directory of Open Access Journals (Sweden)

Leonessa Alexander

1999-01-01

Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.

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.

Modulational estimate for the maximal Lyapunov exponent in Fermi-Pasta-Ulam chains

Science.gov (United States)

Dauxois, Thierry; Ruffo, Stefano; Torcini, Alessandro

1997-12-01

In the framework of the Fermi-Pasta-Ulam (FPU) model, we show a simple method to give an accurate analytical estimation of the maximal Lyapunov exponent at high energy density. The method is based on the computation of the mean value of the modulational instability growth rates associated to unstable modes. Moreover, we show that the strong stochasticity threshold found in the β-FPU system is closely related to a transition in tangent space, the Lyapunov eigenvector being more localized in space at high energy.

Designing Hyperchaotic Cat Maps With Any Desired Number of Positive Lyapunov Exponents.

Science.gov (United States)

Hua, Zhongyun; Yi, Shuang; Zhou, Yicong; Li, Chengqing; Wu, Yue

2018-02-01

Generating chaotic maps with expected dynamics of users is a challenging topic. Utilizing the inherent relation between the Lyapunov exponents (LEs) of the Cat map and its associated Cat matrix, this paper proposes a simple but efficient method to construct an -dimensional ( -D) hyperchaotic Cat map (HCM) with any desired number of positive LEs. The method first generates two basic -D Cat matrices iteratively and then constructs the final -D Cat matrix by performing similarity transformation on one basic -D Cat matrix by the other. Given any number of positive LEs, it can generate an -D HCM with desired hyperchaotic complexity. Two illustrative examples of -D HCMs were constructed to show the effectiveness of the proposed method, and to verify the inherent relation between the LEs and Cat matrix. Theoretical analysis proves that the parameter space of the generated HCM is very large. Performance evaluations show that, compared with existing methods, the proposed method can construct -D HCMs with lower computation complexity and their outputs demonstrate strong randomness and complex ergodicity.

Adaptive Backstepping Controller Design for the Anti-Synchronization of Identical WINDMI Chaotic Systems with Unknown Parameters and its SPICE Implementation

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S. Vaidyanathan

2014-11-01

Full Text Available This paper derives new results for the adaptive backstepping controller design for the anti-synchronization of identical WINDMI systems (Wind-Magnetosphere-Ionosphere models with unknown parameters and also details the SPICE implementation of the proposed adaptive backstepping controller. In the anti-synchronization of chaotic systems, the sum of the outputs of master and slave systems is made to converge asymptotically to zero with time. The adaptive controller design for the anti-synchronization of identical WINDMI systems with unknown parameters has been established by applying Lyapunov stability theory. MATLAB simulations have been shown for the illustration of the adaptive anti-synchronizing backstepping controller for identical WINDMI chaotic systems. Finally, the proposed controller has been implemented using SPICE and circuit simulation results have been detailed.

Global chaos synchronization of new chaotic systems via nonlinear control

International Nuclear Information System (INIS)

Chen, H.-K.

2005-01-01

Nonlinear control is an effective method for making two identical chaotic systems or two different chaotic systems be synchronized. However, this method assumes that the Lyapunov function of error dynamic (e) of synchronization is always formed as V (e) = 1/2e T e. In this paper, modification based on Lyapunov stability theory to design a controller is proposed in order to overcome this limitation. The method has been applied successfully to make two identical new systems and two different chaotic systems (new system and Lorenz system) globally asymptotically synchronized. Since the Lyapunov exponents are not required for the calculation, this method is effective and convenient to synchronize two identical systems and two different chaotic systems. Numerical simulations are also given to validate the proposed synchronization approach

On the angle between the first and second Lyapunov vectors in spatio-temporal chaos

International Nuclear Information System (INIS)

Pazó, D; López, J M; Rodríguez, M A

2013-01-01

In a dynamical system the first Lyapunov vector (LV) is associated with the largest Lyapunov exponent and indicates—at any point on the attractor—the direction of maximal growth in tangent space. The LV corresponding to the second largest Lyapunov exponent generally points in a different direction, but tangencies between both vectors can in principle occur. Here we find that the probability density function (PDF) of the angle ψ spanned by the first and second LVs should be expected to be approximately symmetric around π/4 and to peak at 0 and π/2. Moreover, for small angles we uncover a scaling law for the PDF Q of ψ l = ln ψ with the system size L: Q(ψ l ) = L −1/2 f(ψ l L −1/2 ). We give a theoretical argument that justifies this scaling form and also explains why it should be universal (irrespective of the system details) for spatio-temporal chaos in one spatial dimension. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)

New prediction of chaotic time series based on local Lyapunov exponent

International Nuclear Information System (INIS)

Zhang Yong

2013-01-01

A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After reconstructing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction formula by using the definition of the local Lyapunov exponent. Numerical simulations are carried out to test its effectiveness and verify its higher precision over two older methods. The effects of the number of referential state vectors and added noise on forecasting accuracy are also studied numerically. (general)

An Isomorphism between Lyapunov Exponents and Shannon's Channel Capacity

Energy Technology Data Exchange (ETDEWEB)

Friedland, Gerald [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Metere, Alfredo [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2017-06-07

We demonstrate that discrete Lyapunov exponents are isomorphic to numeric overflows of the capacity of an arbitrary noiseless and memoryless channel in a Shannon communication model with feedback. The isomorphism allows the understanding of Lyapunov exponents in terms of Information Theory, rather than the traditional definitions in chaos theory. The result also implies alternative approaches to the calculation of related quantities, such as the Kolmogorov Sinai entropy which has been linked to thermodynamic entropy. This work provides a bridge between fundamental physics and information theory. It suggests, among other things, that machine learning and other information theory methods can be employed at the core of physics simulations.

Guaranteed cost control of polynomial fuzzy systems via a sum of squares approach.

Science.gov (United States)

Tanaka, Kazuo; Ohtake, Hiroshi; Wang, Hua O

2009-04-01

This paper presents the guaranteed cost control of polynomial fuzzy systems via a sum of squares (SOS) approach. First, we present a polynomial fuzzy model and controller that are more general representations of the well-known Takagi-Sugeno (T-S) fuzzy model and controller, respectively. Second, we derive a guaranteed cost control design condition based on polynomial Lyapunov functions. Hence, the design approach discussed in this paper is more general than the existing LMI approaches (to T-S fuzzy control system designs) based on quadratic Lyapunov functions. The design condition realizes a guaranteed cost control by minimizing the upper bound of a given performance function. In addition, the design condition in the proposed approach can be represented in terms of SOS and is numerically (partially symbolically) solved via the recent developed SOSTOOLS. To illustrate the validity of the design approach, two design examples are provided. The first example deals with a complicated nonlinear system. The second example presents micro helicopter control. Both the examples show that our approach provides more extensive design results for the existing LMI approach.

Lyapunov Functions and Solutions of the Lyapunov Matrix Equation for Marginally Stable Systems

DEFF Research Database (Denmark)

Kliem, Wolfhard; Pommer, Christian

2000-01-01

We consider linear systems of differential equations $I \\ddot{x}+B \\dot{x}+C{x}={0}$ where $I$ is the identity matrix and $B$ and $C$ are general complex $n$ x $n$ matrices. Our main interest is to determine conditions for complete marginalstability of these systems. To this end we find solutions...... of the Lyapunov matrix equation and characterize the set of matrices $(B, C)$ which guarantees marginal stability. The theory is applied to gyroscopic systems, to indefinite damped systems, and to circulatory systems, showing how to choose certain parameter matrices to get sufficient conditions for marginal...... stability.Comparison is made with some known results for equations with real system matrices.Moreover more general cases are investigated and several examples are given....

Extending the length and time scales of Gram–Schmidt Lyapunov vector computations

Energy Technology Data Exchange (ETDEWEB)

Costa, Anthony B., E-mail: acosta@northwestern.edu [Department of Chemistry, Northwestern University, Evanston, IL 60208 (United States); Green, Jason R., E-mail: jason.green@umb.edu [Department of Chemistry, Northwestern University, Evanston, IL 60208 (United States); Department of Chemistry, University of Massachusetts Boston, Boston, MA 02125 (United States)

2013-08-01

Lyapunov vectors have found growing interest recently due to their ability to characterize systems out of thermodynamic equilibrium. The computation of orthogonal Gram–Schmidt vectors requires multiplication and QR decomposition of large matrices, which grow as N{sup 2} (with the particle count). This expense has limited such calculations to relatively small systems and short time scales. Here, we detail two implementations of an algorithm for computing Gram–Schmidt vectors. The first is a distributed-memory message-passing method using Scalapack. The second uses the newly-released MAGMA library for GPUs. We compare the performance of both codes for Lennard–Jones fluids from N=100 to 1300 between Intel Nahalem/Infiniband DDR and NVIDIA C2050 architectures. To our best knowledge, these are the largest systems for which the Gram–Schmidt Lyapunov vectors have been computed, and the first time their calculation has been GPU-accelerated. We conclude that Lyapunov vector calculations can be significantly extended in length and time by leveraging the power of GPU-accelerated linear algebra.

Extending the length and time scales of Gram–Schmidt Lyapunov vector computations

International Nuclear Information System (INIS)

Costa, Anthony B.; Green, Jason R.

2013-01-01

Lyapunov vectors have found growing interest recently due to their ability to characterize systems out of thermodynamic equilibrium. The computation of orthogonal Gram–Schmidt vectors requires multiplication and QR decomposition of large matrices, which grow as N 2 (with the particle count). This expense has limited such calculations to relatively small systems and short time scales. Here, we detail two implementations of an algorithm for computing Gram–Schmidt vectors. The first is a distributed-memory message-passing method using Scalapack. The second uses the newly-released MAGMA library for GPUs. We compare the performance of both codes for Lennard–Jones fluids from N=100 to 1300 between Intel Nahalem/Infiniband DDR and NVIDIA C2050 architectures. To our best knowledge, these are the largest systems for which the Gram–Schmidt Lyapunov vectors have been computed, and the first time their calculation has been GPU-accelerated. We conclude that Lyapunov vector calculations can be significantly extended in length and time by leveraging the power of GPU-accelerated linear algebra

LYAPUNOV-Based Sensor Failure Detection and Recovery for the Reverse Water Gas Shift Process

Science.gov (United States)

Haralambous, Michael G.

2002-01-01

Livingstone, a model-based AI software system, is planned for use in the autonomous fault diagnosis, reconfiguration, and control of the oxygen-producing reverse water gas shift (RWGS) process test-bed located in the Applied Chemistry Laboratory at KSC. In this report the RWGS process is first briefly described and an overview of Livingstone is given. Next, a Lyapunov-based approach for detecting and recovering from sensor failures, differing significantly from that used by Livingstone, is presented. In this new method, models used are in t e m of the defining differential equations of system components, thus differing from the qualitative, static models used by Livingstone. An easily computed scalar inequality constraint, expressed in terms of sensed system variables, is used to determine the existence of sensor failures. In the event of sensor failure, an observer/estimator is used for determining which sensors have failed. The theory underlying the new approach is developed. Finally, a recommendation is made to use the Lyapunov-based approach to complement the capability of Livingstone and to use this combination in the RWGS process.

Generalized Synchronization of Nonlinear Chaotic Systems through Natural Bioinspired Controlling Strategy

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Shih-Yu Li

2015-01-01

Full Text Available A novel bioinspired control strategy design is proposed for generalized synchronization of nonlinear chaotic systems, combining the bioinspired stability theory, fuzzy modeling, and a novel, simple-form Lyapunov control function design of derived high efficient, heuristic and bioinspired controllers. Three main contributions are concluded: (1 apply the bioinspired stability theory to further analyze the stability of fuzzy error systems; the high performance of controllers has been shown in previous study by Li and Ge 2009, (2 a new Lyapunov control function based on bioinspired stability theory is designed to achieve synchronization without using traditional LMI method, which is a simple linear homogeneous function of states and the process of designing controller to synchronize two fuzzy chaotic systems becomes much simpler, and (3 three different situations of synchronization are proposed; classical master and slave Lorenz systems, slave Chen’s system, and Rossler’s system as functional system are illustrated to further show the effectiveness and feasibility of our novel strategy. The simulation results show that our novel control strategy can be applied to different and complicated control situations with high effectiveness.

Stabilization with guaranteed safety using Control Lyapunov–Barrier Function

NARCIS (Netherlands)

Romdlony, Muhammad Zakiyullah; Jayawardhana, Bayu

2016-01-01

We propose a novel nonlinear control method for solving the problem of stabilization with guaranteed safety for nonlinear systems. The design is based on the merging of the well-known Control Lyapunov Function (CLF) and the recent concept of Control Barrier Function (CBF). The proposed control

State control of discrete-time linear systems to be bound in state variables by equality constraints

International Nuclear Information System (INIS)

Filasová, Anna; Krokavec, Dušan; Serbák, Vladimír

2014-01-01

The paper is concerned with the problem of designing the discrete-time equivalent PI controller to control the discrete-time linear systems in such a way that the closed-loop state variables satisfy the prescribed equality constraints. Since the problem is generally singular, using standard form of the Lyapunov function and a symmetric positive definite slack matrix, the design conditions are proposed in the form of the enhanced Lyapunov inequality. The results, offering the conditions of the control existence and the optimal performance with respect to the prescribed equality constraints for square discrete-time linear systems, are illustrated with the numerical example to note effectiveness and applicability of the considered approach

H∞ Excitation Control Design for Stochastic Power Systems with Input Delay Based on Nonlinear Hamiltonian System Theory

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Weiwei Sun

2015-01-01

Full Text Available This paper presents H∞ excitation control design problem for power systems with input time delay and disturbances by using nonlinear Hamiltonian system theory. The impact of time delays introduced by remote signal transmission and processing in wide-area measurement system (WAMS is well considered. Meanwhile, the systems under investigation are disturbed by random fluctuation. First, under prefeedback technique, the power systems are described as a nonlinear Hamiltonian system. Then the H∞ excitation controller of generators connected to distant power systems with time delay and stochasticity is designed. Based on Lyapunov functional method, some sufficient conditions are proposed to guarantee the rationality and validity of the proposed control law. The closed-loop systems under the control law are asymptotically stable in mean square independent of the time delay. And we through a simulation of a two-machine power system prove the effectiveness of the results proposed in this paper.

Hyperchaos of four state autonomous system with three positive Lyapunov exponents

International Nuclear Information System (INIS)

Ge Zhengming; Yang, C-H.

2009-01-01

This Letter gives the results of numerical simulations of Quantum Cellular Neural Network (Quantum-CNN) autonomous system with four state variables. Three positive Lyapunov exponents confirm hyperchaotic nature of its dynamics

Predictor-Based Model Reference Adaptive Control

Science.gov (United States)

Lavretsky, Eugene; Gadient, Ross; Gregory, Irene M.

2010-01-01

This paper is devoted to the design and analysis of a predictor-based model reference adaptive control. Stable adaptive laws are derived using Lyapunov framework. The proposed architecture is compared with the now classical model reference adaptive control. A simulation example is presented in which numerical evidence indicates that the proposed controller yields improved transient characteristics.

Lyapunov exponent and criticality in the Hamiltonian mean field model

Science.gov (United States)

Filho, L. H. Miranda; Amato, M. A.; Rocha Filho, T. M.

2018-03-01

We investigate the dependence of the largest Lyapunov exponent (LLE) of an N-particle self-gravitating ring model at equilibrium with respect to the number of particles and its dependence on energy. This model has a continuous phase-transition from a ferromagnetic to homogeneous phase, and we numerically confirm with large scale simulations the existence of a critical exponent associated to the LLE, although at variance with the theoretical estimate. The existence of strong chaos in the magnetized state evidenced by a positive Lyapunov exponent is explained by the coupling of individual particle oscillations to the diffusive motion of the center of mass of the system and also results in a change of the scaling of the LLE with the number of particles. We also discuss thoroughly for the model the validity and limits of the approximations made by a geometrical model for their analytic estimate.

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

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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.

New zero-input overflow stability proofs based on Lyapunov theory

NARCIS (Netherlands)

Werter, M.J.; Ritzerfeld, J.H.F.

1989-01-01

The authors demonstrate some proofs of zero-input overflow-oscillation suppression in recursive digital filters. The proofs are based on the second method of Lyapunov. For second-order digital filters with complex conjugated poles, the state describes a trajectory in the phase plane, spiraling

A New Approach to the Method of Lyapunov Functionals and Its Applications

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Yunguo Jin

2013-01-01

Full Text Available We show some results which can replace the graph theory used to construct global Lyapunov functions in some coupled systems of differential equations. We present an example of an epidemic model with stage structure and latency spreading in a heterogeneous host population and obtain a more general threshold for the extinction and persistence of a disease. Using some results obtained by mathematical induction and suitable Lyapunov functionals, we prove the global stability of the endemic equilibrium. For some coupled systems of differential equations, by a similar approach to the discussion of the epidemic model, the conditions of threshold property or global stability can be established without the assumption that the relative matrix is irreducible.

Containment control of networked autonomous underwater vehicles: A predictor-based neural DSC design.

Science.gov (United States)

Peng, Zhouhua; Wang, Dan; Wang, Wei; Liu, Lu

2015-11-01

This paper investigates the containment control problem of networked autonomous underwater vehicles in the presence of model uncertainty and unknown ocean disturbances. A predictor-based neural dynamic surface control design method is presented to develop the distributed adaptive containment controllers, under which the trajectories of follower vehicles nearly converge to the dynamic convex hull spanned by multiple reference trajectories over a directed network. Prediction errors, rather than tracking errors, are used to update the neural adaptation laws, which are independent of the tracking error dynamics, resulting in two time-scales to govern the entire system. The stability property of the closed-loop network is established via Lyapunov analysis, and transient property is quantified in terms of L2 norms of the derivatives of neural weights, which are shown to be smaller than the classical neural dynamic surface control approach. Comparative studies are given to show the substantial improvements of the proposed new method. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Lyapunov functions for a dengue disease transmission model

International Nuclear Information System (INIS)

Tewa, Jean Jules; Dimi, Jean Luc; Bowong, Samuel

2009-01-01

In this paper, we study a model for the dynamics of dengue fever when only one type of virus is present. For this model, Lyapunov functions are used to show that when the basic reproduction ratio is less than or equal to one, the disease-free equilibrium is globally asymptotically stable, and when it is greater than one there is an endemic equilibrium which is also globally asymptotically stable.

Lyapunov functions for a dengue disease transmission model

Energy Technology Data Exchange (ETDEWEB)

Tewa, Jean Jules [Department of Mathematics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde (Cameroon)], E-mail: tewa@univ-metz.fr; Dimi, Jean Luc [Department of Mathematics, Faculty of Science, University Marien Ngouabi, P.O. Box 69, Brazzaville (Congo, The Democratic Republic of the)], E-mail: jldimi@yahoo.fr; Bowong, Samuel [Department of Mathematics and Computer Science, Faculty of Science, University of Douala, P.O. Box 24157, Douala (Cameroon)], E-mail: samuelbowong@yahoo.fr

2009-01-30

In this paper, we study a model for the dynamics of dengue fever when only one type of virus is present. For this model, Lyapunov functions are used to show that when the basic reproduction ratio is less than or equal to one, the disease-free equilibrium is globally asymptotically stable, and when it is greater than one there is an endemic equilibrium which is also globally asymptotically stable.

Un algoritmo de replanificación en tiempo real basado en un índice de estabilidad de Lyapunov para líneas de metro

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A. Berbey

2014-04-01

Full Text Available Resumen: En este trabajo, se propone un nuevo índice basado en el método directo de Lyapunov para el diseño de un algoritmo de reprogramación en tiempo real para líneas de metro. En este estudio se utiliza una versión modificada de un modelo de espacio de estados en tiempo real discreto, que considera los efectos de saturación en la línea de metro. Una vez que el modelo de espacio de estados se ha obtenido, el método directo de Lyapunov se aplica con el fin de analizar la estabilidad del sistema de la línea de metro. Como resultado de este análisis no sólo se propone un nuevo índice de estabilidad, sino también la creación de tres zonas de estabilidad para indicar el estado actual del sistema. Finalmente, se presenta un nuevo algoritmo que permite la reprogramación del calendario de los trenes en tiempo real en presencia de perturbaciones medianas. Abstract: A new Lyapunov-based index for designing a rescheduling algorithm in real time for metro lines has been proposed in this paper. A modified real time discrete space state model which considers saturation effects in the metro line has been utilized in this study. Once the space state model has been obtained, the direct method of Lyapunov is applied in order to analyze the stability of the metro line system. As a result of this analysis not only a new stability index is proposed, but also the establishment of three stability zones to indicate the current state of the system. Finally, a new algorithm which allows the rescheduling of the timetable in the real time of the trains under presence of medium disturbances has been presented. Palabras clave: Sistema de metro, estabilidad de Lyapunov, planificación en tiempo real, Keywords: Metro system, Lyapunov stability, real time planning, traffic regulation

Control Strategy of an Impulse Turbine for an Oscillating Water Column-Wave Energy Converter in Time-Domain Using Lyapunov Stability Method

Directory of Open Access Journals (Sweden)

Seung Kwan Song

2016-10-01

Full Text Available We present two control strategies for an oscillating water column-wave energy converter (OWC-WEC in the time domain. We consider a fixed OWC-WEC on the open sea with an impulse turbine module. This system mainly consists of a chamber, turbine and electric generator. For the time domain analysis, all of the conversion stages considering mutualities among them should be analyzed based on the Newtonian mechanics. According to the analysis of Newtonian mechanics, the hydrodynamics of wave energy absorption in the chamber and the turbine aerodynamic performance are directly coupled and share the internal air pressure term via the incompressible air assumption. The turbine aerodynamics and the dynamics of the electric generator are connected by torque load through the rotor shaft, which depends on an electric terminal load that acts as a control input. The proposed control strategies are an instant maximum turbine efficiency tracking control and a constant angular velocity of the turbine rotor control methods. Both are derived by Lyapunov stability analysis. Numerical simulations are carried out under irregular waves with various heights and periods in the time domain, and the results with the controllers are analyzed. We then compare these results with simulations carried out in the absence of the control strategy in order to prove the performance of the controllers.

Switching LPV Control with Double-Layer LPV Model for Aero-Engines

Science.gov (United States)

Tang, Lili; Huang, Jinquan; Pan, Muxuan

2017-11-01

To cover the whole range of operating conditions of aero-engine, a double-layer LPV model is built so as to take into account of the variability due to the flight altitude, Mach number and the rotational speed. With this framework, the problem of designing LPV state-feedback robust controller that guarantees desired bounds on both H_∞ and H_2 performances is considered. Besides this, to reduce the conservativeness caused by a single LPV controller of the whole flight envelope and the common Lyapunov function method, a new method is proposed to design a family of LPV switching controllers. The switching LPV controllers can ensure that the closed-loop system remains stable in the sense of Lyapunov under arbitrary switching logic. Meanwhile, the switching LPV controllers can ensure the parameters change smoothly. The validity and performance of the theoretical results are demonstrated through a numerical example.

The control of an optical hyper-chaotic system

International Nuclear Information System (INIS)

Jiang Shumin; Tian Lixin; Wang Xuedi

2007-01-01

This paper discusses the problem of hyper-chaos control of an optical system. Based on Lyapunov stability theory, a non-autonomous feedback controller is designed. The proposed controller ensures that the hyper-chaotic system will be asymptotically stable. Numerical simulation of the original and the controlled system is provided to show the effectiveness of our method

Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation

NARCIS (Netherlands)

Maschke, Bernhard M.J.; Ortega, Romeo; Schaft, Arjan J. van der

1998-01-01

It is well known that the total energy is a suitable Lyapunov function to study the stability of the trivial equilibrium of an isolated standard Hamiltonian system. In many practical instances, however, the system is in interaction with its environment through some constant forcing terms. This gives

Economic model predictive control theory, formulations and chemical process applications

CERN Document Server

Ellis, Matthew; Christofides, Panagiotis D

2017-01-01

This book presents general methods for the design of economic model predictive control (EMPC) systems for broad classes of nonlinear systems that address key theoretical and practical considerations including recursive feasibility, closed-loop stability, closed-loop performance, and computational efficiency. Specifically, the book proposes: Lyapunov-based EMPC methods for nonlinear systems; two-tier EMPC architectures that are highly computationally efficient; and EMPC schemes handling explicitly uncertainty, time-varying cost functions, time-delays and multiple-time-scale dynamics. The proposed methods employ a variety of tools ranging from nonlinear systems analysis, through Lyapunov-based control techniques to nonlinear dynamic optimization. The applicability and performance of the proposed methods are demonstrated through a number of chemical process examples. The book presents state-of-the-art methods for the design of economic model predictive control systems for chemical processes. In addition to being...

Reinforcement-Learning-Based Robust Controller Design for Continuous-Time Uncertain Nonlinear Systems Subject to Input Constraints.

Science.gov (United States)

Liu, Derong; Yang, Xiong; Wang, Ding; Wei, Qinglai

2015-07-01

The design of stabilizing controller for uncertain nonlinear systems with control constraints is a challenging problem. The constrained-input coupled with the inability to identify accurately the uncertainties motivates the design of stabilizing controller based on reinforcement-learning (RL) methods. In this paper, a novel RL-based robust adaptive control algorithm is developed for a class of continuous-time uncertain nonlinear systems subject to input constraints. The robust control problem is converted to the constrained optimal control problem with appropriately selecting value functions for the nominal system. Distinct from typical action-critic dual networks employed in RL, only one critic neural network (NN) is constructed to derive the approximate optimal control. Meanwhile, unlike initial stabilizing control often indispensable in RL, there is no special requirement imposed on the initial control. By utilizing Lyapunov's direct method, the closed-loop optimal control system and the estimated weights of the critic NN are proved to be uniformly ultimately bounded. In addition, the derived approximate optimal control is verified to guarantee the uncertain nonlinear system to be stable in the sense of uniform ultimate boundedness. Two simulation examples are provided to illustrate the effectiveness and applicability of the present approach.

Lyapunov exponent as a metric for assessing the dynamic content and predictability of large-eddy simulations

Science.gov (United States)

Nastac, Gabriel; Labahn, Jeffrey W.; Magri, Luca; Ihme, Matthias

2017-09-01

Metrics used to assess the quality of large-eddy simulations commonly rely on a statistical assessment of the solution. While these metrics are valuable, a dynamic measure is desirable to further characterize the ability of a numerical simulation for capturing dynamic processes inherent in turbulent flows. To address this issue, a dynamic metric based on the Lyapunov exponent is proposed which assesses the growth rate of the solution separation. This metric is applied to two turbulent flow configurations: forced homogeneous isotropic turbulence and a turbulent jet diffusion flame. First, it is shown that, despite the direct numerical simulation (DNS) and large-eddy simulation (LES) being high-dimensional dynamical systems with O (107) degrees of freedom, the separation growth rate qualitatively behaves like a lower-dimensional dynamical system, in which the dimension of the Lyapunov system is substantially smaller than the discretized dynamical system. Second, a grid refinement analysis of each configuration demonstrates that as the LES filter width approaches the smallest scales of the system the Lyapunov exponent asymptotically approaches a plateau. Third, a small perturbation is superimposed onto the initial conditions of each configuration, and the Lyapunov exponent is used to estimate the time required for divergence, thereby providing a direct assessment of the predictability time of simulations. By comparing inert and reacting flows, it is shown that combustion increases the predictability of the turbulent simulation as a result of the dilatation and increased viscosity by heat release. The predictability time is found to scale with the integral time scale in both the reacting and inert jet flows. Fourth, an analysis of the local Lyapunov exponent is performed to demonstrate that this metric can also determine flow-dependent properties, such as regions that are sensitive to small perturbations or conditions of large turbulence within the flow field. Finally

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.

Novel stability criteria for uncertain delayed Cohen-Grossberg neural networks using discretized Lyapunov functional

International Nuclear Information System (INIS)

Souza, Fernando O.; Palhares, Reinaldo M.; Ekel, Petr Ya.

2009-01-01

This paper deals with the stability analysis of delayed uncertain Cohen-Grossberg neural networks (CGNN). The proposed methodology consists in obtaining new robust stability criteria formulated as linear matrix inequalities (LMIs) via the Lyapunov-Krasovskii theory. Particularly one stability criterion is derived from the selection of a parameter-dependent Lyapunov-Krasovskii functional, which allied with the Gu's discretization technique and a simple strategy that decouples the system matrices from the functional matrices, assures a less conservative stability condition. Two computer simulations are presented to support the improved theoretical results.

Analysis and design of singular Markovian jump systems

CERN Document Server

Wang, Guoliang; Yan, Xinggang

2014-01-01

This monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H∞ control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat's Lemma, among other techniques.Features of the book include:·???????? study of the stability pr

Hyperchaos Numerical Simulation and Control in a 4D Hyperchaotic System

Directory of Open Access Journals (Sweden)

Junhai Ma

2013-01-01

Full Text Available A hyperchaotic system is introduced, and the complex dynamical behaviors of such system are investigated by means of numerical simulations. The bifurcation diagrams, Lyapunov exponents, hyperchaotic attractors, the power spectrums, and time charts are mapped out through the theory analysis and dynamic simulations. The chaotic and hyper-chaotic attractors exist and alter over a wide range of parameters according to the variety of Lyapunov exponents and bifurcation diagrams. Furthermore, linear feedback controllers are designed for stabilizing the hyperchaos to the unstable equilibrium points; thus, we achieve the goal of a second control which is more useful in application.

The brief time-reversibility of the local Lyapunov exponents for a small chaotic Hamiltonian system

International Nuclear Information System (INIS)

Waldner, Franz; Hoover, William G.; Hoover, Carol G.

2014-01-01

Highlights: •We consider the local Lyapunov spectrum for a four-dimensional Hamilton system. •Its stable periodic motion can be reversed for long times. •In the chaotic motion, time reversal occurs only for a short time. •Perturbations will change this short unstable case into a different stable case. •These observations might relate chaos to the Second Law of Thermodynamics. - Abstract: We consider the local (instantaneous) Lyapunov spectrum for a four-dimensional Hamiltonian system. Its stable periodic motion can be reversed for long times. Its unstable chaotic motion, with two symmetric pairs of exponents, cannot. In the latter case reversal occurs for more than a thousand fourth-order Runge–Kutta time steps, followed by a transition to a new set of paired Lyapunov exponents, unrelated to those seen in the forward time direction. The relation of the observed chaotic dynamics to the Second Law of Thermodynamics is discussed

Hyperbolicity and integral expression of the Lyapunov exponents for linear cocycles

Science.gov (United States)

Dai, Xiongping

Consider in this paper a linear skew-product system (θ,Θ) :T×W×R→W×R; (t,w,x)↦(tw,Θ(t,w)ṡx) where T=R or Z, and θ :(t,w)↦tw is a topological dynamical system on a compact metrizable space W, and where Θ(t,w)∈GL(n,R) satisfies the cocycle condition based on θ and is continuously differentiable in t if T=R. We show that 'semi λ-exponential dichotomy' of (θ,Θ) implies ' λ-exponential dichotomy.' Precisely, if Θ has no Lyapunov exponent λ and is almost uniformly λ-contracting along the λ-stable direction E(w;λ) and if dimE(w;λ) is constant a.e., then Θ is almost λ-exponentially dichotomous. To prove this, we first use Liao's spectrum theorem, which gives integral expression of the Lyapunov exponents, and then use the semi-uniform ergodic theorem by Sturman and Stark, which allows one to derive uniform estimates from nonuniform ones. As a consequence, we obtain the open-and-dense hyperbolicity of eventual GL(2,R)-cocycles based on a uniquely ergodic endomorphism, and of GL(2,R)-cocycles based on a uniquely ergodic equi-continuous endomorphism, respectively. On the other hand, in the sense of C-topology we obtain the density of SL(2,R)-cocycles having positive Lyapunov exponent based on a minimal subshift satisfying the Boshernitzan condition.

Nonlinear superheat and capacity control of a refrigeration plant

DEFF Research Database (Denmark)

Rasmussen, Henrik; Larsen, Lars F. S.

2009-01-01

This paper proposes a novel method for superheat and capacity control of refrigeration systems. A new low order nonlinear model of the evaporator is developed and used in a backstepping design of a nonlinear controller. The stability of the proposed method is validated theoretically by Lyapunov...

Application of Lyapunov's Second Method in the Stability Analysis of ...

African Journals Online (AJOL)

In this paper, Lyapunov's method for determining the stability of non-linear systems under dynamic states is presented. The paper highlights a practical application of the method to investigate the stability of crude oil/natural gas separation process. Mathematical state models for the separation process, used in the ...

Robust uniform persistence in discrete and continuous dynamical systems using Lyapunov exponents.

Science.gov (United States)

Salceanu, Paul L

2011-07-01

This paper extends the work of Salceanu and Smith [12, 13] where Lyapunov exponents were used to obtain conditions for uniform persistence ina class of dissipative discrete-time dynamical systems on the positive orthant of R(m), generated by maps. Here a united approach is taken, for both discrete and continuous time, and the dissipativity assumption is relaxed. Sufficient conditions are given for compact subsets of an invariant part of the boundary of R(m+) to be robust uniform weak repellers. These conditions require Lyapunov exponents be positive on such sets. It is shown how this leads to robust uniform persistence. The results apply to the investigation of robust uniform persistence of the disease in host populations, as shown in an application.

Dynamic surface tracking controller design for a constrained hypersonic vehicle based on disturbance observer

Directory of Open Access Journals (Sweden)

Fang Wang

2017-05-01

Full Text Available The tracking control problem of a flexible air-breathing hypersonic vehicle subjects to aerodynamic parameter uncertainty and input constraint is investigated by combining nonlinear disturbance observer and dynamic surface control. To design controller simply, a control-oriented model is firstly derived and divided into two subsystems, velocity subsystem and altitude subsystem based on the engineering backgrounds of flexible air-breathing hypersonic vehicle. In every subsystem, compounded disturbances are included to consider aerodynamic uncertainty and the effect of the flexible modes. Then, disturbance observer is not only used to handle the compounded disturbance but also to handle the input constraint, where the estimation error converges to a random small region through appropriately choosing the observer parameters. To sequel, the disturbance observer–based robust control scheme and the disturbance observer-based dynamic surface control scheme are developed for the velocity subsystem and altitude subsystem, respectively. Besides, novel filters are designed to alleviate the problem of “explosion of terms” induced by backstepping method. On the basis of Lyapunov stability theory, the presented control scheme can assure that tracking error converges to an arbitrarily small neighborhood around zero by rigorous theoretical analysis. At last, simulation result shows the effectiveness of the presented control method.

Estabilidad para un control borroso en modo deslizante aplicado a un robot paralelo neumático

Directory of Open Access Journals (Sweden)

Pablo J. Prieto

2015-10-01

Full Text Available Resumen: Se presenta un controlador borroso tipo Mamdani basado en técnicas en modo deslizante para el posicionamiento de un robot paralelo neumático de dos grados de libertad (2 GDL. Es probado que el sistema es asintóticamente estable en el sentido de Lyapunov y se presentan resultados numéricos y experimentales. Ma's aún, el controlador diseñado puede ser aplicado en control de trayectoria al ser retroalimentadas la velocidad y la aceleración del sistema. Se presentan adema's resultados satisfactorios obtenidos en forma experimental para el caso de seguimiento de trayectoria. Abstract: In this paper is reported a Mamdani type fuzzy controller based on sliding mode techniques applied to the regulation of a 2 DOF pneumatic parallel robot. Is is proved that the system is stable in Lyapunov sense, and numerical and experimental results are reported. Moreover, the designed controller can be applied to tracking control if speed and acceleration from the system are feedbacked. Also are reported satisfactory experimental results for the tracking case. Palabras clave: Control borroso, Control de robot, Estabilidad de Lyapunov, Modos deslizantes., Keywords: Fuzzy control, Robot control, Lyapunov stability, Sliding mode.

A New Robust Controller with Applications to Bioreactors

Directory of Open Access Journals (Sweden)

Alejandro Rincón

2014-01-01

Full Text Available In this work an anaerobic digester is controlled using input-output linearization and Lyapunov-like function methods. It is assumed that model parameters are unknown, time-varying, and bounded, and upper or lower bounds are also unknown. To tackle the effect of input saturation, a state observer is designed. The tracking and observer errors are defined in terms of the noisy measured output instead of ideal output, given by the mathematical model. The design of the observer mechanism and the update laws is based on the Lyapunov-like function technique, whereas the design of the control law is based on the input-output linearization method. In this paper two important properties of the controlled system are proven. First, the observer error converges asymptotically to a residual set whose size is user-defined, and such convergence is not disrupted, neither by the input saturation nor by the parameter uncertainties. Second, when the control input is nonsaturated the tracking error converges to a residual set whose size is user-defined. The model parameter uncertainties are included to prove the convergence of errors. Finally, a numerical example to validate the developed control is presented.

Design of adaptive switching control for hypersonic aircraft

Directory of Open Access Journals (Sweden)

Xin Jiao

2015-10-01

Full Text Available This article proposes a novel adaptive switching control of hypersonic aircraft based on type-2 Takagi–Sugeno–Kang fuzzy sliding mode control and focuses on the problem of stability and smoothness in the switching process. This method uses full-state feedback to linearize the nonlinear model of hypersonic aircraft. Combining the interval type-2 Takagi–Sugeno–Kang fuzzy approach with sliding mode control keeps the adaptive switching process stable and smooth. For rapid stabilization of the system, the adaptive laws use a direct constructive Lyapunov analysis together with an established type-2 Takagi–Sugeno–Kang fuzzy logic system. Simulation results indicate that the proposed control scheme can maintain the stability and smoothness of switching process for the hypersonic aircraft.

Bilinear Approximate Model-Based Robust Lyapunov Control for Parabolic Distributed Collectors

KAUST Repository

Elmetennani, Shahrazed; Laleg-Kirati, Taous-Meriem

2016-01-01

This brief addresses the control problem of distributed parabolic solar collectors in order to maintain the field outlet temperature around a desired level. The objective is to design an efficient controller to force the outlet fluid temperature

Quantum control theory and applications: A survey

OpenAIRE

Dong, Daoyi; Petersen, Ian R

2009-01-01

This paper presents a survey on quantum control theory and applications from a control systems perspective. Some of the basic concepts and main developments (including open-loop control and closed-loop control) in quantum control theory are reviewed. In the area of open-loop quantum control, the paper surveys the notion of controllability for quantum systems and presents several control design strategies including optimal control, Lyapunov-based methodologies, variable structure control and q...

Espectro de Lyapunov de un Oscilador Colpitts en Base Común

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Camilo Andrés Florez

2013-09-01

Full Text Available En el presente documento se presenta la definición de exponentes de Lyapunov de un sistema autónomo no lineal de tiempo continuo y una técnica recomendada para medir dicho conjunto de exponentes (espectro, con la finalidad de detectar la existencia de ciclos límites o de caos en un circuito oscilador Colpitts implementado con un transistor BJT. A partir del modelo de Ebers-Möll del transistor BJT se derivaron las ecuaciones de estado que rigen al circuito, luego se adoptó un caso numérico de estudio, y mediante el uso de un programa de simulación matemática se aplicó la metodología propuesta para determinar el espectro de Lyapunov del oscilador. Los resultados obtenidos evidencian la existencia de caos para algunos conjuntos de valores de los parámetros del circuito.

A variational approach to Lyapunov type inequalities from ODEs to PDEs

CERN Document Server

Cañada, Antonio

2015-01-01

This book highlights the current state of Lyapunov-type inequalities through a detailed analysis. Aimed toward researchers and students working in differential equations and those interested in the applications of stability theory and resonant systems, the book begins with an overview Lyapunov’s original results and moves forward to include prevalent results obtained in the past ten years. Detailed proofs and an emphasis on basic ideas are provided for different boundary conditions for ordinary differential equations, including Neumann, Dirichlet, periodic, and antiperiodic conditions. Novel results of higher eigenvalues, systems of equations, partial differential equations as well as variational approaches are presented. To this respect, a new and unified variational point of view  is introduced for the treatment of such problems and a systematic discussion of different types of boundary conditions is featured. Various problems make the study of Lyapunov-type inequalities of interest to those in pure and ...

Using the centre of percussion to design a steering controller for an autonomous race car

Science.gov (United States)

Kritayakirana, Krisada; Gerdes, J. Christian

2012-01-01

Understanding how a race car driver controls a vehicle at its friction limits can provide insights into the development of vehicle safety systems. In this paper, a race car driver's behaviour inspires the design of an autonomous racing controller. The resulting controller uses the vehicle's centre of percussion (COP) to design feedforward and feedback steering. At the COP, the effects of rotation and translation from the rear tire force cancel each other out; consequently, the feedforward steering command is robust to the disturbances from the rear tire force. Using the COP also simplifies the equations of motion, as the vehicle's lateral motion is decoupled from the vehicle's yaw motion and highlights the challenge of controlling a vehicle when the rear tires are highly saturated. The resulting dynamics can be controlled with a linear state feedback based on a lane-keeping system with additional yaw damping. Utilising Lyapunov theory, the closed-loop system is shown to remain stable even when the rear tires are highly saturated. The experimental results demonstrate that an autonomous vehicle can operate at its limits while maintaining a minimal lateral error.

Global stability analysis of epidemiological models based on Volterra–Lyapunov stable matrices

International Nuclear Information System (INIS)

Liao Shu; Wang Jin

2012-01-01

Highlights: ► Global dynamics of high dimensional dynamical systems. ► A systematic approach for global stability analysis. ► Epidemiological models of environment-dependent diseases. - Abstract: In this paper, we study the global dynamics of a class of mathematical epidemiological models formulated by systems of differential equations. These models involve both human population and environmental component(s) and constitute high-dimensional nonlinear autonomous systems, for which the global asymptotic stability of the endemic equilibria has been a major challenge in analyzing the dynamics. By incorporating the theory of Volterra–Lyapunov stable matrices into the classical method of Lyapunov functions, we present an approach for global stability analysis and obtain new results on some three- and four-dimensional model systems. In addition, we conduct numerical simulation to verify the analytical results.

Synthesis of state observer and nonlinear output feedback controller design of AC machines

International Nuclear Information System (INIS)

Al-Tahir, Ali Abdul Razzaq

2016-01-01

The research work developed in this thesis has been mainly devoted to the observation and sensor-less control problems of electrical systems. Three major contributions have been carried out using the high - gain concept and output feedback adaptive nonlinear control for online UPS. In this thesis, we dealt with synthesis of sampled high - gain observers for nonlinear systems application to PMSMs and DFIGs. We particularly focus on two constraints: sampling effect and tracking unmeasured mechanical and magnetic state variables. The first contribution consists in a high gain observer design that performs a relatively accurate estimation of both mechanical and magnetic state variable using the available measurements on stator currents and voltages of PMSM. We propose a global exponential observer having state predictor for a class of nonlinear globally Lipschitz system. In second contribution, we proposed a novel non - standard HGO design for non-injective feedback relation application to variable speed DFIG based WPGS. Meanwhile, a reduced system model is analyzed, provided by observability test to check is it possible synthesis state observer for sensor-less control. In last contribution, an adaptive observer for states and parameters estimation are designed for a class of state - affine systems application to output feedback adaptive nonlinear control of three-phase AC/DC boost power converter for online UPS systems. Basically, the problem focused on cascade nonlinear adaptive controller that is developed making use Lyapunov theory. The parameters uncertainties are processed by the practical control laws under back-stepping design techniques with capacity of adaptation. (author)

Design, implementation and analysis of fully digital 1-D controllable multiscroll chaos

KAUST Repository

Mansingka, Abhinav S.; Radwan, Ahmed G.; Salama, Khaled N.

2011-01-01

This paper introduces the fully digital implementation of a 1-D multiscroll chaos generator based on a staircase nonlinearity in the 3rd-order jerk system using the Euler approximation. For the first time, digital design is exploited to provide real-time controllability of (i) number of scrolls, (ii) position in 1-D space, (iii) Euler step size and (iv) system parameter. The effect of variations in these fields on the maximum Lyapunov exponent (MLE) is analyzed. The system is implemented using Verilog HDL and synthesized on an Xilinx Virtex 4 FPGA, exhibiting area utilization less than 3.5% and high performance with experimentally verified throughput up to 3.33 Gbits/s. This fully digital system enables applications in modulation schemes and chaos-based cryptosystems without analog to digital conversion. © 2011 IEEE.

Design, implementation and analysis of fully digital 1-D controllable multiscroll chaos

KAUST Repository

Mansingka, Abhinav S.

2011-12-01

This paper introduces the fully digital implementation of a 1-D multiscroll chaos generator based on a staircase nonlinearity in the 3rd-order jerk system using the Euler approximation. For the first time, digital design is exploited to provide real-time controllability of (i) number of scrolls, (ii) position in 1-D space, (iii) Euler step size and (iv) system parameter. The effect of variations in these fields on the maximum Lyapunov exponent (MLE) is analyzed. The system is implemented using Verilog HDL and synthesized on an Xilinx Virtex 4 FPGA, exhibiting area utilization less than 3.5% and high performance with experimentally verified throughput up to 3.33 Gbits/s. This fully digital system enables applications in modulation schemes and chaos-based cryptosystems without analog to digital conversion. © 2011 IEEE.

An adaptive robust controller for time delay maglev transportation systems

Science.gov (United States)

Milani, Reza Hamidi; Zarabadipour, Hassan; Shahnazi, Reza

2012-12-01

For engineering systems, uncertainties and time delays are two important issues that must be considered in control design. Uncertainties are often encountered in various dynamical systems due to modeling errors, measurement noises, linearization and approximations. Time delays have always been among the most difficult problems encountered in process control. In practical applications of feedback control, time delay arises frequently and can severely degrade closed-loop system performance and in some cases, drives the system to instability. Therefore, stability analysis and controller synthesis for uncertain nonlinear time-delay systems are important both in theory and in practice and many analytical techniques have been developed using delay-dependent Lyapunov function. In the past decade the magnetic and levitation (maglev) transportation system as a new system with high functionality has been the focus of numerous studies. However, maglev transportation systems are highly nonlinear and thus designing controller for those are challenging. The main topic of this paper is to design an adaptive robust controller for maglev transportation systems with time-delay, parametric uncertainties and external disturbances. In this paper, an adaptive robust control (ARC) is designed for this purpose. It should be noted that the adaptive gain is derived from Lyapunov-Krasovskii synthesis method, therefore asymptotic stability is guaranteed.

Robust Switching Control and Subspace Identification for Flutter of Flexible Wing

Directory of Open Access Journals (Sweden)

Yizhe Wang

2018-01-01

Full Text Available Active flutter suppression and subspace identification for a flexible wing model using micro fiber composite actuator were experimentally studied in a low speed wind tunnel. NACA0006 thin airfoil model was used for the experimental object to verify the performance of identification algorithm and designed controller. The equation of the fluid, vibration, and piezoelectric coupled motion was theoretically analyzed and experimentally identified under the open-loop and closed-loop condition by subspace method for controller design. A robust pole placement algorithm in terms of linear matrix inequality that accommodates the model uncertainty caused by identification deviation and flow speed variation was utilized to stabilize the divergent aeroelastic system. For further enlarging the flutter envelope, additional controllers were designed subject to the models beyond the flutter speed. Wind speed was measured online as the decision parameter of switching between the controllers. To ensure the stability of arbitrary switching, Common Lyapunov function method was applied to design the robust pole placement controllers for different models to ensure that the closed-loop system shared a common Lyapunov function. Wind tunnel result showed that the designed controllers could stabilize the time varying aeroelastic system over a wide range under arbitrary switching.

Lyapunov exponents for infinite dimensional dynamical systems

Science.gov (United States)

Mhuiris, Nessan Mac Giolla

1987-01-01

Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.

Synchronization Between Two Different Switched Chaotic Systems By Switching Control

Directory of Open Access Journals (Sweden)

Du Li Ming

2016-01-01

Full Text Available This paper is concerned with the synchronization problem of two different switched chaotic systems, considering the general case that the master-slave switched chaotic systems have uncertainties. Two basic problems are considered: one is projective synchronization of switched chaotic systems under arbitrary switching; the other is projective synchronization of switched chaotic systems by design of switching when synchronization cannot achieved by using any subsystems alone. For the two problems, common Lyapunov function method and multiple Lyapunov function method are used respectively, an adaptive control scheme has been presented, some sufficient synchronization conditions are attainted, and the switching signal is designed. Finally, the numerical simulation is provide to show the effectiveness of our method.

Self-optimizing robust nonlinear model predictive control

NARCIS (Netherlands)

Lazar, M.; Heemels, W.P.M.H.; Jokic, A.; Thoma, M.; Allgöwer, F.; Morari, M.

2009-01-01

This paper presents a novel method for designing robust MPC schemes that are self-optimizing in terms of disturbance attenuation. The method employs convex control Lyapunov functions and disturbance bounds to optimize robustness of the closed-loop system on-line, at each sampling instant - a unique

H∞ Control of Polynomial Fuzzy Systems: A Sum of Squares Approach

OpenAIRE

Bomo W. Sanjaya; Bambang Riyanto Trilaksono; Arief Syaichu-Rohman

2014-01-01

This paper proposes the control design ofa nonlinear polynomial fuzzy system with H∞ performance objective using a sum of squares (SOS) approach. Fuzzy model and controller are represented by a polynomial fuzzy model and controller. The design condition is obtained by using polynomial Lyapunov functions that not only guarantee stability but also satisfy the H∞ performance objective. The design condition is represented in terms of an SOS that can be numerically solved via the SOSTOOLS. A simul...

A Lyapunov Function Based Remedial Action Screening Tool Using Real-Time Data

Energy Technology Data Exchange (ETDEWEB)

Mitra, Joydeep [Michigan State Univ., East Lansing, MI (United States); Ben-Idris, Mohammed [Univ. of Nevada, Reno, NV (United States); Faruque, Omar [Florida State Univ., Tallahassee, FL (United States); Backhaus, Scott [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Deb, Sidart [LCG Consulting, Los Altos, CA (United States)

2016-03-30

This report summarizes the outcome of a research project that comprised the development of a Lyapunov function based remedial action screening tool using real-time data (L-RAS). The L-RAS is an advanced computational tool that is intended to assist system operators in making real-time redispatch decisions to preserve power grid stability. The tool relies on screening contingencies using a homotopy method based on Lyapunov functions to avoid, to the extent possible, the use of time domain simulations. This enables transient stability evaluation at real-time speed without the use of massively parallel computational resources. The project combined the following components. 1. Development of a methodology for contingency screening using a homotopy method based on Lyapunov functions and real-time data. 2. Development of a methodology for recommending remedial actions based on the screening results. 3. Development of a visualization and operator interaction interface. 4. Testing of screening tool, validation of control actions, and demonstration of project outcomes on a representative real system simulated on a Real-Time Digital Simulator (RTDS) cluster. The project was led by Michigan State University (MSU), where the theoretical models including homotopy-based screening, trajectory correction using real-time data, and remedial action were developed and implemented in the form of research-grade software. Los Alamos National Laboratory (LANL) contributed to the development of energy margin sensitivity dynamics, which constituted a part of the remedial action portfolio. Florida State University (FSU) and Southern California Edison (SCE) developed a model of the SCE system that was implemented on FSU's RTDS cluster to simulate real-time data that was streamed over the internet to MSU where the L-RAS tool was executed and remedial actions were communicated back to FSU to execute stabilizing controls on the simulated system. LCG Consulting developed the visualization

Dynamic Analysis and Adaptive Sliding Mode Controller for a Chaotic Fractional Incommensurate Order Financial System

Science.gov (United States)

Hajipour, Ahmad; Tavakoli, Hamidreza

2017-12-01

In this study, the dynamic behavior and chaos control of a chaotic fractional incommensurate-order financial system are investigated. Using well-known tools of nonlinear theory, i.e. Lyapunov exponents, phase diagrams and bifurcation diagrams, we observe some interesting phenomena, e.g. antimonotonicity, crisis phenomena and route to chaos through a period doubling sequence. Adopting largest Lyapunov exponent criteria, we find that the system yields chaos at the lowest order of 2.15. Next, in order to globally stabilize the chaotic fractional incommensurate order financial system with uncertain dynamics, an adaptive fractional sliding mode controller is designed. Numerical simulations are used to demonstrate the effectiveness of the proposed control method.

Lyapunov vectors and assimilation in the unstable subspace: theory and applications

International Nuclear Information System (INIS)

Palatella, Luigi; Carrassi, Alberto; Trevisan, Anna

2013-01-01

Based on a limited number of noisy observations, estimation algorithms provide a complete description of the state of a system at current time. Estimation algorithms that go under the name of assimilation in the unstable subspace (AUS) exploit the nonlinear stability properties of the forecasting model in their formulation. Errors that grow due to sensitivity to initial conditions are efficiently removed by confining the analysis solution in the unstable and neutral subspace of the system, the subspace spanned by Lyapunov vectors with positive and zero exponents, while the observational noise does not disturb the system along the stable directions. The formulation of the AUS approach in the context of four-dimensional variational assimilation (4DVar-AUS) and the extended Kalman filter (EKF-AUS) and its application to chaotic models is reviewed. In both instances, the AUS algorithms are at least as efficient but simpler to implement and computationally less demanding than their original counterparts. As predicted by the theory when error dynamics is linear, the optimal subspace dimension for 4DVar-AUS is given by the number of positive and null Lyapunov exponents, while the EKF-AUS algorithm, using the same unstable and neutral subspace, recovers the solution of the full EKF algorithm, but dealing with error covariance matrices of a much smaller dimension and significantly reducing the computational burden. Examples of the application to a simplified model of the atmospheric circulation and to the optimal velocity model for traffic dynamics are given. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)

Feedback control and adaptive control of the energy resource chaotic system

International Nuclear Information System (INIS)

Sun Mei; Tian Lixin; Jiang Shumin; Xu Jun

2007-01-01

In this paper, the problem of control for the energy resource chaotic system is considered. Two different method of control, feedback control (include linear feedback control, non-autonomous feedback control) and adaptive control methods are used to suppress chaos to unstable equilibrium or unstable periodic orbits. The Routh-Hurwitz criteria and Lyapunov direct method are used to study the conditions of the asymptotic stability of the steady states of the controlled system. The designed adaptive controller is robust with respect to certain class of disturbances in the energy resource chaotic system. Numerical simulations are presented to show these results

Design of adaptive sliding mode control for synchronization Genesio–Tesi chaotic system

International Nuclear Information System (INIS)

Ghamati, Mina; Balochian, Saeed

2015-01-01

In this paper two adaptive sliding mode controls for synchronizing the state trajectories of the Genesio–Tesi system with unknown parameters and external disturbance are proposed. A switching surface is introduced and based on this switching surface, two adaptive sliding mode control schemes are presented to guarantee the occurrence of the sliding motion. The stability and robustness of the two proposed schemes are proved using Lyapunov stability theory. The effectiveness of our introduced schemes is provided by numerical simulations

Performance enhanced design of chaos controller for the mechanical centrifugal flywheel governor system via adaptive dynamic surface control

Directory of Open Access Journals (Sweden)

Shaohua Luo

2016-09-01

Full Text Available This paper addresses chaos suppression of the mechanical centrifugal flywheel governor system with output constraint and fully unknown parameters via adaptive dynamic surface control. To have a certain understanding of chaotic nature of the mechanical centrifugal flywheel governor system and subsequently design its controller, the useful tools like the phase diagrams and corresponding time histories are employed. By using tangent barrier Lyapunov function, a dynamic surface control scheme with neural network and tracking differentiator is developed to transform chaos oscillation into regular motion and the output constraint rule is not broken in whole process. Plugging second-order tracking differentiator into chaos controller tackles the “explosion of complexity” of backstepping and improves the accuracy in contrast with the first-order filter. Meanwhile, Chebyshev neural network with adaptive law whose input only depends on a subset of Chebyshev polynomials is derived to learn the behavior of unknown dynamics. The boundedness of all signals of the closed-loop system is verified in stability analysis. Finally, the results of numerical simulations illustrate effectiveness and exhibit the superior performance of the proposed scheme by comparing with the existing ADSC method.

Chaos synchronization of a chaotic system via nonlinear control

International Nuclear Information System (INIS)

Park, Ju H.

2005-01-01

In this letter, the problem of chaos synchronization of a chaotic system which is proposed by Lue et al. [Int J Bifurcat Chaos 2004;14:1507] is considered. A novel nonlinear controller is designed based on the Lyapunov stability theory. The proposed controller ensures that the states of the controlled chaotic slave system asymptotically synchronizes the states of the master system. A numerical example is given to illuminate the design procedure and advantage of the result derived

Generalized direct Lyapunov method for the analysis of stability and attraction in general time systems

International Nuclear Information System (INIS)

Druzhinina, O V; Shestakov, A A

2002-01-01

A generalized direct Lyapunov method is put forward for the study of stability and attraction in general time systems of the following types: the classical dynamical system in the sense of Birkhoff, the general system in the sense of Zubov, the general system in the sense of Seibert, the general system with delay, and the general 'input-output' system. For such systems, with the help of generalized Lyapunov functions with respect to two filters, two quasifilters, or two filter bases, necessary and sufficient conditions for stability and attraction are obtained under minimal assumptions about the mathematical structure of the general system

Design of stability-guaranteed neurofuzzy logic controller for nuclear steam generators

International Nuclear Information System (INIS)

Cho, B.H.; No, H.C.

1996-01-01

A neurofuzzy logic controller (NFLC), which is implemented by using a multilayer neural network with special types of fuzzifier, inference engine and defuzzifier, is applied to the water level control of a nuclear steam generator (SG). This type of NFLC has the structural advantage that arbitrary two-input, single-output linear controllers can be adequately mapped into a set of specific control rules of the NFLC. In order to design a stability-guaranteed NFLC, the stable sector of the given linear gain is obtained from Lyapunov's stability criteria. Then this sector is mapped into two linear rule tables that are used as the limits of NFLC control rules. The automatic generation of NFLC rule tables is accomplished by using the back-error-propagation (BEP) algorithm. There are two separate paths for the error back propagation in the SG. One considers the level dynamics depending on the tank capacity and the other takes into account the reverse dynamics of the SG. The amounts of error back propagated through these paths show opposite effects in the BEP algorithm from each other for the swell-shrink phenomenon. Through computer simulation it is found that the BEP algorithm adequately generates NFLC rule tables according to given learning parameters. (orig.)

Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System.

Science.gov (United States)

Rozenbaum, Efim B; Ganeshan, Sriram; Galitski, Victor

2017-02-24

It was proposed recently that the out-of-time-ordered four-point correlator (OTOC) may serve as a useful characteristic of quantum-chaotic behavior, because, in the semiclassical limit ℏ→0, its rate of exponential growth resembles the classical Lyapunov exponent. Here, we calculate the four-point correlator C(t) for the classical and quantum kicked rotor-a textbook driven chaotic system-and compare its growth rate at initial times with the standard definition of the classical Lyapunov exponent. Using both quantum and classical arguments, we show that the OTOC's growth rate and the Lyapunov exponent are, in general, distinct quantities, corresponding to the logarithm of the phase-space averaged divergence rate of classical trajectories and to the phase-space average of the logarithm, respectively. The difference appears to be more pronounced in the regime of low kicking strength K, where no classical chaos exists globally. In this case, the Lyapunov exponent quickly decreases as K→0, while the OTOC's growth rate may decrease much slower, showing a higher sensitivity to small chaotic islands in the phase space. We also show that the quantum correlator as a function of time exhibits a clear singularity at the Ehrenfest time t_{E}: transitioning from a time-independent value of t^{-1}lnC(t) at ttime at t>t_{E}. We note that the underlying physics here is the same as in the theory of weak (dynamical) localization [Aleiner and Larkin, Phys. Rev. B 54, 14423 (1996)PRBMDO0163-182910.1103/PhysRevB.54.14423; Tian, Kamenev, and Larkin, Phys. Rev. Lett. 93, 124101 (2004)PRLTAO0031-900710.1103/PhysRevLett.93.124101] and is due to a delay in the onset of quantum interference effects, which occur sharply at a time of the order of the Ehrenfest time.

Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models

Science.gov (United States)

De Cruz, Lesley; Schubert, Sebastian; Demaeyer, Jonathan; Lucarini, Valerio; Vannitsem, Stéphane

2018-05-01

The stability properties of intermediate-order climate models are investigated by computing their Lyapunov exponents (LEs). The two models considered are PUMA (Portable University Model of the Atmosphere), a primitive-equation simple general circulation model, and MAOOAM (Modular class="text">Arbitrary-Order Ocean-Atmosphere Model), a quasi-geostrophic coupled ocean-class="text">atmosphere model on a β-plane. We wish to investigate the effect of the different levels of filtering on the instabilities and dynamics of the atmospheric flows. Moreover, we assess the impact of the oceanic coupling, the dissipation scheme, and the resolution on the spectra of LEs. The PUMA Lyapunov spectrum is computed for two different values of the meridional temperature gradient defining the Newtonian forcing to the temperature field. The increase in the gradient gives rise to a higher baroclinicity and stronger instabilities, corresponding to a larger dimension of the unstable manifold and a larger first LE. The Kaplan-Yorke dimension of the attractor increases as well. The convergence rate of the rate function for the large deviation law of the finite-time Lyapunov exponents (FTLEs) is fast for all exponents, which can be interpreted as resulting from the absence of a clear-cut atmospheric timescale separation in such a model. The MAOOAM spectra show that the dominant atmospheric instability is correctly represented even at low resolutions. However, the dynamics of the central manifold, which is mostly associated with the ocean dynamics, is not fully resolved because of its associated long timescales, even at intermediate orders. As expected, increasing the mechanical atmosphere-ocean coupling coefficient or introducing a turbulent diffusion parametrisation reduces the Kaplan-Yorke dimension and Kolmogorov-Sinai entropy. In all considered configurations, we are not yet in the regime in which one can robustly define large deviation laws describing the statistics of the FTLEs. This

Switching Fuzzy Guaranteed Cost Control for Nonlinear Networked Control Systems

Directory of Open Access Journals (Sweden)

Linqin Cai

2014-01-01

Full Text Available This paper deals with the problem of guaranteed cost control for a class of nonlinear networked control systems (NCSs with time-varying delay. A guaranteed cost controller design method is proposed to achieve the desired control performance based on the switched T-S fuzzy model. The switching mechanism is introduced to handle the uncertainties of NCSs. Based on Lyapunov functional approach, some sufficient conditions for the existence of state feedback robust guaranteed cost controller are presented. Simulation results show that the proposed method is effective to guarantee system’s global asymptotic stability and quality of service (QoS.

Application of the Lyapunov exponent to detect noise-induced chaos in oscillating microbial cultures

International Nuclear Information System (INIS)

Patnaik, P.R.

2005-01-01

Oscillating microbial processes can, under certain conditions, gravitate into chaotic behavior induced by external noise. Detection and control of chaos are important for the survival of the microorganisms and to operate a process usefully. In this study the largest Lyapunov exponent is recommended as a convenient and reliable index of chaos in continuous oscillating cultures. For the growth of Saccharomyces cerevisiae as a model system, the exponents increase with the oxygen mass transfer coefficient and decrease as the dilution rate increases. By comparing with the corresponding time-domain oscillations determined earlier, it is inferred that weakly oscillating cultures are less likely to be driven to chaotic behavior. The main carbon source, glucose, is quite robust to chaotic destabilization, thus enhancing its suitability as a manipulated variable for bioreactor control

Controlling uncertain neutral dynamic systems with delay in control input

International Nuclear Information System (INIS)

Park, Ju H.; Kwon, O.

2005-01-01

This article gives a novel criterion for the asymptotic stabilization of the zero solutions of a class of neutral systems with delays in control input. By constructing Lyapunov functionals, we have obtained the criterion which is expressed in terms of matrix inequalities. The solutions of the inequalities can be easily solved by efficient convex optimization algorithms. A numerical example is included to illustrate the design procedure of the proposed method

Reliability of Lyapunov characteristic exponents computed by the two-particle method

Science.gov (United States)

Mei, Lijie; Huang, Li

2018-03-01

For highly complex problems, such as the post-Newtonian formulation of compact binaries, the two-particle method may be a better, or even the only, choice to compute the Lyapunov characteristic exponent (LCE). This method avoids the complex calculations of variational equations compared with the variational method. However, the two-particle method sometimes provides spurious estimates to LCEs. In this paper, we first analyze the equivalence in the definition of LCE between the variational and two-particle methods for Hamiltonian systems. Then, we develop a criterion to determine the reliability of LCEs computed by the two-particle method by considering the magnitude of the initial tangent (or separation) vector ξ0 (or δ0), renormalization time interval τ, machine precision ε, and global truncation error ɛT. The reliable Lyapunov characteristic indicators estimated by the two-particle method form a V-shaped region, which is restricted by d0, ε, and ɛT. Finally, the numerical experiments with the Hénon-Heiles system, the spinning compact binaries, and the post-Newtonian circular restricted three-body problem strongly support the theoretical results.

Algoritmos paralelos y distribuidos para resolver ecuaciones matriciales de Lyapunov en problemas de reducción de modelos.

OpenAIRE

CLAVER IBORRA, JOSE MANUEL

2011-01-01

La reducción de modelos para problemas de control de gran tamaño es actualmente uno de los temas fundamentales en teoría de sistemas y control. Entre diversas técnicas existentes, los métodos de truncamiento de estados son los que permiten una mayor precisión en la representación del sistema reducido. Muchos de estos métodos necesitan resolver una o más ecuaciones de Lyapunov (habitualmente acopladas), requiriéndose en ocasiones el factor de Cholesky de su solución. En esta tesis se pesentan ...

A method for determining the non-existence of a common quadratic Lyapunov function for switched linear systems based on particle swarm optimisation

Czech Academy of Sciences Publication Activity Database

Duarte-Mermoud, M.A.; Ordonez-Hurtado, R.H.; Zagalak, Petr

2012-01-01

Roč. 43, č. 11 (2012), s. 2015-2029 ISSN 0020-7721 R&D Projects: GA ČR(CZ) GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Switched linear systems * Lyapunov function * particle swarm optimization Subject RIV: BC - Control Systems Theory Impact factor: 1.305, year: 2012 http://library.utia.cas.cz/separaty/2012/AS/zagalak-0382169.pdf

Construction of the Lyapunov Spectrum in a Chaotic System Displaying Phase Synchronization

Energy Technology Data Exchange (ETDEWEB)

Carlo, Leonardo De, E-mail: neoleodeo@gmail.com [Gran Sasso Science Institute (GSSI) (Italy); Gentile, Guido, E-mail: gentile@mat.uniroma3.it; Giuliani, Alessandro, E-mail: giuliani@mat.uniroma3.it [Università degli Studi Roma Tre, Dipartimento di Matematica e Fisica (Italy)

2016-06-15

We consider a three-dimensional chaotic system consisting of the suspension of Arnold’s cat map coupled with a clock via a weak dissipative interaction. We show that the coupled system displays a synchronization phenomenon, in the sense that the relative phase between the suspension flow and the clock locks to a special value, thus making the motion fall onto a lower dimensional attractor. More specifically, we construct the attractive invariant manifold, of dimension smaller than three, using a convergent perturbative expansion. Moreover, we compute via convergent series the Lyapunov exponents, including notably the central one. The result generalizes a previous construction of the attractive invariant manifold in a similar but simpler model. The main novelty of the current construction relies in the computation of the Lyapunov spectrum, which consists of non-trivial analytic exponents. Some conjectures about a possible smoothening transition of the attractor as the coupling is increased are also discussed.

Riemannian theory of Hamiltonian chaos and Lyapunov exponents

Science.gov (United States)

Casetti, Lapo; Clementi, Cecilia; Pettini, Marco

1996-12-01

A nonvanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system; however, no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ɛ=E/N, the energy per degree of freedom. The functional dependence λ1(ɛ) is of great interest because, among other reasons, it detects the existence of weakly and strongly chaotic regimes. This aim, the analytic computation of λ1(ɛ), is successfully reached within a theoretical framework that makes use of a geometrization of Newtonian dynamics in the language of Riemannian differential geometry. An alternative point of view about the origin of chaos in these systems is obtained independently of the standard explanation based on homoclinic intersections. Dynamical instability (chaos) is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of the Jacobi-Levi-Civita equation (JLCE) for geodesic spread. In this paper it is shown how to derive from the JLCE an effective stability equation. Under general conditions, this effective equation formally describes a stochastic oscillator; an analytic formula for the instability growth rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam β model and to a chain of coupled rotators. Excellent agreement is found between the theoretical prediction and numeric values of λ1(ɛ) for both models.

Periodic orbits of solar sail equipped with reflectance control device in Earth-Moon system

Science.gov (United States)

Yuan, Jianping; Gao, Chen; Zhang, Junhua

2018-02-01

In this paper, families of Lyapunov and halo orbits are presented with a solar sail equipped with a reflectance control device in the Earth-Moon system. System dynamical model is established considering solar sail acceleration, and four solar sail steering laws and two initial Sun-sail configurations are introduced. The initial natural periodic orbits with suitable periods are firstly identified. Subsequently, families of solar sail Lyapunov and halo orbits around the L1 and L2 points are designed with fixed solar sail characteristic acceleration and varying reflectivity rate and pitching angle by the combination of the modified differential correction method and continuation approach. The linear stabilities of solar sail periodic orbits are investigated, and a nonlinear sliding model controller is designed for station keeping. In addition, orbit transfer between the same family of solar sail orbits is investigated preliminarily to showcase reflectance control device solar sail maneuver capability.

Comment on 'Exact analytical solution for the generalized Lyapunov exponent of the two-dimensional Anderson localization'

International Nuclear Information System (INIS)

Markos, P; Schweitzer, L; Weyrauch, M

2004-01-01

In a recent publication, Kuzovkov et al (2002 J. Phys.: Condens. Matter. 14 13777) announced an analytical solution of the two-dimensional Anderson localization problem via the calculation of a generalized Lyapunov exponent using signal theory. Surprisingly, for certain energies and small disorder strength they observed delocalized states. We study the transmission properties of the same model using well-known transfer matrix methods. Our results disagree with the findings obtained using signal theory. We point to the possible origin of this discrepancy and comment on the general strategy of using a generalized Lyapunov exponent for studying Anderson localization. (comment)

Abstraction of continuous dynamical systems utilizing lyapunov functions

DEFF Research Database (Denmark)

Sloth, Christoffer; Wisniewski, Rafael

2010-01-01

This paper considers the development of a method for abstracting continuous dynamical systems by timed automata. The method is based on partitioning the state space of dynamical systems with invariant sets, which form cells representing locations of the timed automata. To enable verification...... of the dynamical system based on the abstraction, conditions for obtaining sound, complete, and refinable abstractions are set up. It is proposed to partition the state space utilizing sub-level sets of Lyapunov functions, since they are positive invariant sets. The existence of sound abstractions for Morse......-Smale systems and complete and refinable abstractions for linear systems are shown....

Less Conservative ℋ∞ Fuzzy Control for Discrete-Time Takagi-Sugeno Systems

Directory of Open Access Journals (Sweden)

Leonardo Amaral Mozelli

2011-01-01

Full Text Available New analysis and control design conditions of discrete-time fuzzy systems are proposed. Using fuzzy Lyapunov's functions and introducing slack variables, less conservative conditions are obtained. The controller guarantees system stabilization and ℋ∞ performance. Numerical tests and a practical experiment in Chua's circuit are presented to show the effectiveness.

Scaled Bilateral Teleoperation Using Discrete-Time Sliding-Mode Controller

NARCIS (Netherlands)

Khan, S.; Sabanovic, A.; Nergiz, A.O.

2009-01-01

In this paper, the design of a discrete-time sliding-mode controller based on Lyapunov theory is presented along with a robust disturbance observer and is applied to a piezostage for high-precision motion. A linear model of a piezostage was used with nominal parameters to compensate the disturbance

A modular design of incremental Lyapunov functions for microgrid control with power sharing

NARCIS (Netherlands)

Persis, Claudio De; Monshizadeh, Nima

2015-01-01

In this paper we contribute a theoretical framework that sheds a new light on the problem of microgrid analysis and control. The starting point is an energy function comprising the kinetic energy associated with the elements that emulate the rotating machinery and terms taking into account the

Adiabatic invariants and asymptotic behavior of Lyapunov exponents of the Schrodinger equation

International Nuclear Information System (INIS)

Delyon, F.; Foulon, P.

1986-01-01

We give an upper bound for the high-energy behavior of the Lyapunov exponent of the one-dimensional Schrodinger equation. We relate this behavior to the diffrentiability properties of the potential. As an application, this result provides an upper bound for the asymptotic length of the gaps of the Schrodinger equation

Stabilization of Parametric Roll Resonance with Active U-Tanks via Lyapunov Control Design

DEFF Research Database (Denmark)

Holden, Christian; Galeazzi, Roberto; Fossen, Thor Inge

2009-01-01

Parametric ship roll resonance is a phenomenon where a ship can rapidly develop high roll motion while sailing in longitudinal waves. This effect can be described mathematically by periodic changes of the parameters of the equations of motion, which lead to a bifurcation. In this paper, the control...

Two-Degrees of Freedom and Variable Structure Controllers for Induction Motor Drives

Directory of Open Access Journals (Sweden)

ZAKY, M.

2018-02-01

Full Text Available This paper presents a two-degrees-of-Freedom (2DOF and variable structure control (VSC schemes for induction motor (IM drives. The designed VSC incorporates independent feedback and feedforward terms as 2DOF control principle. This structure improves the response of the proposed VSC under speed reference tracking and load disturbance changes. Stability of VSC using Lyapunov theory is discussed. Due to the variable nature of the switching function of VSC, two conditions to ensure Lyapunov stability candidate are derived based on the error signal. A design criterion for the parameters of VSC are introduced to guarantee the stability. The complete IM drive system with the proposed VSC controller is built using MATLAB/Simulink. A laboratory prototype is executed experimentally using DSP-DS1104 control board. All controllers are implemented practically. Simulation and experimental results are provided under different working conditions. Performance evaluation of classic control schemes and the proposed VSC approach is presented. The proposed VSC approach gives superior behavior under speed reference variations and torque disturbances. The disturbances using the proposed controller are strongly suppressed compared to classic 2DOF control scheme.

Lyapunov exponent and topological entropy plateaus in piecewise linear maps

International Nuclear Information System (INIS)

Botella-Soler, V; Oteo, J A; Ros, J; Glendinning, P

2013-01-01

We consider a two-parameter family of piecewise linear maps in which the moduli of the two slopes take different values. We provide numerical evidence of the existence of some parameter regions in which the Lyapunov exponent and the topological entropy remain constant. Analytical proof of this phenomenon is also given for certain cases. Surprisingly however, the systems with that property are not conjugate as we prove by using kneading theory. (paper)

Control Strategies for Guided Collective Motion

Science.gov (United States)

2015-02-27

J.K. Parrish , “Oscillator models and collective motion,” IEEE Control Systems Magzine, Vol. 27, 2007, pp. 89-105. [18] S. H. Strogatz , “From Kuramoto...Automatic Control, 54(2), 2009, pp. 353-357. [21] H. Hong and S. H. Strogatz , “Kuramoto Model of Coupled Oscillators with Positive and Negative...2013) provided similar results by utilizing a modified Kuramoto model ( Strogatz (2000)). Paley (2008) proposed a Lyapunov-based design methodology to

Lyapunov stability and its application to systems of ordinary differential equations

Science.gov (United States)

Kennedy, E. W.

1979-01-01

An outline and a brief introduction to some of the concepts and implications of Lyapunov stability theory are presented. Various aspects of the theory are illustrated by the inclusion of eight examples, including the Cartesian coordinate equations of the two-body problem, linear and nonlinear (Van der Pol's equation) oscillatory systems, and the linearized Kustaanheimo-Stiefel element equations for the unperturbed two-body problem.

H∞ Control of Polynomial Fuzzy Systems: A Sum of Squares Approach

Directory of Open Access Journals (Sweden)

Bomo W. Sanjaya

2014-07-01

Full Text Available This paper proposes the control design ofa nonlinear polynomial fuzzy system with H∞ performance objective using a sum of squares (SOS approach. Fuzzy model and controller are represented by a polynomial fuzzy model and controller. The design condition is obtained by using polynomial Lyapunov functions that not only guarantee stability but also satisfy the H∞ performance objective. The design condition is represented in terms of an SOS that can be numerically solved via the SOSTOOLS. A simulation study is presented to show the effectiveness of the SOS-based H∞ control designfor nonlinear polynomial fuzzy systems.

Safety factor profile control in a tokamak

CERN Document Server

Bribiesca Argomedo, Federico; Prieur, Christophe

2014-01-01

Control of the Safety Factor Profile in a Tokamak uses Lyapunov techniques to address a challenging problem for which even the simplest physically relevant models are represented by nonlinear, time-dependent, partial differential equations (PDEs). This is because of the  spatiotemporal dynamics of transport phenomena (magnetic flux, heat, densities, etc.) in the anisotropic plasma medium. Robustness considerations are ubiquitous in the analysis and control design since direct measurements on the magnetic flux are impossible (its estimation relies on virtual sensors) and large uncertainties remain in the coupling between the plasma particles and the radio-frequency waves (distributed inputs). The Brief begins with a presentation of the reference dynamical model and continues by developing a Lyapunov function for the discretized system (in a polytopic linear-parameter-varying formulation). The limitations of this finite-dimensional approach motivate new developments in the infinite-dimensional framework. The t...

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.

Using largest Lyapunov exponent to confirm the intrinsic stability of boiling water reactors

International Nuclear Information System (INIS)

Gavilian-Moreno, Carlos; Espinosa-Paredes, Gilberto

2016-01-01

The aim of this paper is the study of instability state of boiling water reactors with a method based in largest Lyapunov exponents (LLEs). Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the LLE. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. This method was applied to a set of signals from several nuclear power plant (NPP) reactors under commercial operating conditions that experienced instabilities events, apparently each of a different nature. Laguna Verde and Forsmark NPPs with in-phase instabilities, and Cofrentes NPP with out-of-phases instability. This study presents the results of intrinsic instability in the boiling water reactors of three NPPs. In the analyzed cases the limit cycle was not reached, which implies that the point of equilibrium exerts influence and attraction on system evolution

Using largest Lyapunov exponent to confirm the intrinsic stability of boiling water reactors

Energy Technology Data Exchange (ETDEWEB)

Gavilian-Moreno, Carlos [Iberdrola Generacion, S.A., Cofrentes Nuclear Power Plant, Project Engineering Department, Paraje le Plano S/N, Valencia (Spain); Espinosa-Paredes, Gilberto [Area de ingeniera en Recursos Energeticos, Universidad Autonoma Metropolitana-Iztapalapa, Mexico city (Mexico)

2016-04-15

The aim of this paper is the study of instability state of boiling water reactors with a method based in largest Lyapunov exponents (LLEs). Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the LLE. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. This method was applied to a set of signals from several nuclear power plant (NPP) reactors under commercial operating conditions that experienced instabilities events, apparently each of a different nature. Laguna Verde and Forsmark NPPs with in-phase instabilities, and Cofrentes NPP with out-of-phases instability. This study presents the results of intrinsic instability in the boiling water reactors of three NPPs. In the analyzed cases the limit cycle was not reached, which implies that the point of equilibrium exerts influence and attraction on system evolution.

Using Largest Lyapunov Exponent to Confirm the Intrinsic Stability of Boiling Water Reactors

Directory of Open Access Journals (Sweden)

Carlos J. Gavilán-Moreno

2016-04-01

Full Text Available The aim of this paper is the study of instability state of boiling water reactors with a method based in largest Lyapunov exponents (LLEs. Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the LLE. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. This method was applied to a set of signals from several nuclear power plant (NPP reactors under commercial operating conditions that experienced instabilities events, apparently each of a different nature. Laguna Verde and Forsmark NPPs with in-phase instabilities, and Cofrentes NPP with out-of-phases instability. This study presents the results of intrinsic instability in the boiling water reactors of three NPPs. In the analyzed cases the limit cycle was not reached, which implies that the point of equilibrium exerts influence and attraction on system evolution.

Adaptive Backstepping Controller Design for Leveling Control of an Underwater Platform Based on Joint Space

Directory of Open Access Journals (Sweden)

Zhi-Lin Zeng

2014-01-01

Full Text Available This paper focuses on high precision leveling control of an underwater heavy load platform, which is viewed as an underwater parallel robot on the basis of its work pattern. The kinematic of platform with deformation is analyzed and the dynamics model of joint space is established. An adaptive backstepping controller according to Lyapunov's function is proposed for leveling control of platform based on joint space. Furthermore, the “lowest point fixed angle error” leveling scheme called “chase” is chosen for leveling control of platform. The digital simulation and practical experiment of single joint space actuator are carried out, and the results show high precision servo control of joint space. On the basis of this, the platform leveling control simulation relies on the hardware-in-loop system. The results indicate that the proposed controller can effectively restrain the influence from system parameter uncertainties and external disturbance to realize high precision leveling control of the underwater platform.

Adaptive controller design for modified projective synchronization of Genesio-Tesi chaotic system with uncertain parameters

International Nuclear Information System (INIS)

Park, Ju H.

2007-01-01

The paper addresses control problem for the modified projective synchronization of the Genesio-Tesi chaotic systems with three uncertain parameters. An adaptive control law is derived to make the states of two identical Genesio-Tesi systems asymptotically synchronized up to specific ratios. The stability analysis in the paper is proved using a well-known Lyapunov stability theory. A numerical simulation is presented to show the effectiveness of the proposed chaos synchronization scheme

Discrete-time inverse optimal control for nonlinear systems

CERN Document Server

Sanchez, Edgar N

2013-01-01

Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th

Design of a new adaptive fuzzy controller and its application to vibration control of a vehicle seat installed with an MR damper

International Nuclear Information System (INIS)

Phu, Do Xuan; Shin, Do Kyun; Choi, Seung-Bok

2015-01-01

This paper presents a new adaptive fuzzy controller featuring a combination of two different control methodologies: H infinity control technique and sliding mode control. It is known that both controllers are powerful in terms of high performance and robust stability. However, both control methods require an accurate dynamic model to design a state variable based controller in order to maintain their advantages. Thus, in this work a fuzzy control method which does not require an accurate dynamic model is adopted and two control methodologies are integrated to maintain the advantages even in an uncertain environment of the dynamic system. After a brief explanation of the interval type 2 fuzzy logic, a new adaptive fuzzy controller associated with the H infinity control and sliding mode control is formulated on the basis of Lyapunov stability theory. Subsequently, the formulated controller is applied to vibration control of a vehicle seat equipped with magnetorheological fluid damper (MR damper in short). An experimental setup for realization of the proposed controller is established and vibration control performances such as acceleration at the driver’s seat are evaluated. In addition, in order to demonstrate the effectiveness of the proposed controller, a comparative work with two existing controllers is undertaken. It is shown through simulation and experiment that the proposed controller can provide much better vibration control performance than the two existing controllers. (paper)

Fuzzy control with random delays using invariant cones and its application to control of energy processes in microelectromechanical motion devices

Energy Technology Data Exchange (ETDEWEB)

Sinha, A.S.C. [Purdue Univ., Indianapolis, IN (United States). Dept. of Electrical Engineering; Lyshevski, S. [Rochester Inst. of Technology, NY (United States)

2005-05-01

In this paper, a class of microelectromechanical systems described by nonlinear differential equations with random delays is examined. Robust fuzzy controllers are designed to control the energy conversion processes with the ultimate objective to guarantee optimal achievable performance. The fuzzy rule base used consists of a collection of r fuzzy IF-THEN rules defined as a function of the conditional variable. The method of the theory of cones and Lyapunov functionals is used to design a class of local fuzzy control laws. A verifiably sufficient condition for stochastic stability of fuzzy stochastic microelectromechanical systems is given. As an example, we have considered the design of a fuzzy control law for an electrostatic micromotor. (author)

Fuzzy control with random delays using invariant cones and its application to control of energy processes in microelectromechanical motion devices

International Nuclear Information System (INIS)

Sinha, A.S.C.; Lyshevski, S.

2005-01-01

In this paper, a class of microelectromechanical systems described by nonlinear differential equations with random delays is examined. Robust fuzzy controllers are designed to control the energy conversion processes with the ultimate objective to guarantee optimal achievable performance. The fuzzy rule base used consists of a collection of r fuzzy IF-THEN rules defined as a function of the conditional variable. The method of the theory of cones and Lyapunov functionals is used to design a class of local fuzzy control laws. A verifiably sufficient condition for stochastic stability of fuzzy stochastic microelectromechanical systems is given. As an example, we have considered the design of a fuzzy control law for an electrostatic micromotor

Conditional Lyapunov exponents and transfer entropy in coupled bursting neurons under excitation and coupling mismatch

Science.gov (United States)

Soriano, Diogo C.; Santos, Odair V. dos; Suyama, Ricardo; Fazanaro, Filipe I.; Attux, Romis

2018-03-01

This work has a twofold aim: (a) to analyze an alternative approach for computing the conditional Lyapunov exponent (λcmax) aiming to evaluate the synchronization stability between nonlinear oscillators without solving the classical variational equations for the synchronization error dynamical system. In this first framework, an analytic reference value for λcmax is also provided in the context of Duffing master-slave scenario and precisely evaluated by the proposed numerical approach; (b) to apply this technique to the study of synchronization stability in chaotic Hindmarsh-Rose (HR) neuronal models under uni- and bi-directional resistive coupling and different excitation bias, which also considered the root mean square synchronization error, information theoretic measures and asymmetric transfer entropy in order to offer a better insight of the synchronization phenomenon. In particular, statistical and information theoretical measures were able to capture similarity increase between the neuronal oscillators just after a critical coupling value in accordance to the largest conditional Lyapunov exponent behavior. On the other hand, transfer entropy was able to detect neuronal emitter influence even in a weak coupling condition, i.e. under the increase of conditional Lyapunov exponent and apparently desynchronization tendency. In the performed set of numerical simulations, the synchronization measures were also evaluated for a two-dimensional parameter space defined by the neuronal coupling (emitter to a receiver neuron) and the (receiver) excitation current. Such analysis is repeated for different feedback couplings as well for different (emitter) excitation currents, revealing interesting characteristics of the attained synchronization region and conditions that facilitate the emergence of the synchronous behavior. These results provide a more detailed numerical insight of the underlying behavior of a HR in the excitation and coupling space, being in accordance

Nonlinear control of voltage source converters in AC-DC power system.

Science.gov (United States)

Dash, P K; Nayak, N

2014-07-01

This paper presents the design of a robust nonlinear controller for a parallel AC-DC power system using a Lyapunov function-based sliding mode control (LYPSMC) strategy. The inputs for the proposed control scheme are the DC voltage and reactive power errors at the converter station and the active and reactive power errors at the inverter station of the voltage-source converter-based high voltage direct current transmission (VSC-HVDC) link. The stability and robust tracking of the system parameters are ensured by applying the Lyapunov direct method. Also the gains of the sliding mode control (SMC) are made adaptive using the stability conditions of the Lyapunov function. The proposed control strategy offers invariant stability to a class of systems having modeling uncertainties due to parameter changes and exogenous inputs. Comprehensive computer simulations are carried out to verify the proposed control scheme under several system disturbances like changes in short-circuit ratio, converter parametric changes, and faults on the converter and inverter buses for single generating system connected to the power grid in a single machine infinite-bus AC-DC network and also for a 3-machine two-area power system. Furthermore, a second order super twisting sliding mode control scheme has been presented in this paper that provides a higher degree of nonlinearity than the LYPSMC and damps faster the converter and inverter voltage and power oscillations. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Taxonomía de asteroides y cometas basada en los espectros de Lyapunov

Science.gov (United States)

Tancredi, G.; Motta, V.; Froeschlé, C.

Estudiaremos dos familias de objetos que sufren encuentros cercanos con planetas, a saber: la familia de cometas de Júpiter (JF) y los asteroides cercanos a la Tierra (NEAs). El movimiento de estos objetos es caótico en una escala de tiempo corta. Más aún, debido a los cambios erráticos en los elementos orbitales, la comparación de los valores actuales da poca información acerca de la posible vinculación dinámica entre los objetos de una misma familia. Calculamos una estimación finita de los Exponentes Característicos de Lyapunov (LCE), los llamamos Indicadores Característicos de Lyapunov (LCI) para ambas familias y analizamos las características del espacio de fase donde tiene lugar el movimiento de estos objetos. Integrando en un período suficientemente largo (e.g. 20000 años), encontramos que el LCI alcanza un valor cuasi-constante. La mayoría de los miembros de ambas familias muestran una concentración de los tiempos de Lyapunov (inverso del LCI) de alrededor de 50-100 años (Tancredi, 1995, Astron & Astrop., 299, 288). La concentración de los tiempos de Lyapunov es mayor para la familia de Júpiter que para los NEAs. Entre estos últimos, la menor dispersión se da para aquellos que cruzan la órbita de la Tierra. Se demostró que el espectro de los `indicadores locales' (Froeschlé et. al., 1990, Cel. Mec. 56, 307) o ``números de estiramiento'' (Voglis and Contopoulos, 1994, J. Phys. A 26, 4899) (relacionados con el LCI) son invariantes y nos dan una información más completa sobre el comportamiento caótico. Mediante la comparación de espectros discutimos la similitud entre los objetos de una misma familia y analizamos las diferentes posibles rutas al caos. Los espectros se clasifican mediante la comparación de los momentos de las distribuciones de los `números de estiramiento'. Aplicamos un método de agrupamiento jerárquico (Zappala et. al., 1990, Astron. J. 100, 2030) para identificar ``familias'' de espectros (grupos de espectros

Integral-based event triggering controller design for stochastic LTI systems via convex optimisation

Science.gov (United States)

Mousavi, S. H.; Marquez, H. J.

2016-07-01

The presence of measurement noise in the event-based systems can lower system efficiency both in terms of data exchange rate and performance. In this paper, an integral-based event triggering control system is proposed for LTI systems with stochastic measurement noise. We show that the new mechanism is robust against noise and effectively reduces the flow of communication between plant and controller, and also improves output performance. Using a Lyapunov approach, stability in the mean square sense is proved. A simulated example illustrates the properties of our approach.

A Hyperchaotic Attractor with Multiple Positive Lyapunov Exponents

International Nuclear Information System (INIS)

Guo-Si, Hu

2009-01-01

There are many hyperchaotic systems, but few systems can generate hyperchaotic attractors with more than three PLEs (positive Lyapunov exponents). A new hyperchaotic system, constructed by adding an approximate time-delay state feedback to a five-dimensional hyperchaotic system, is presented. With the increasing number of phase-shift units used in this system, the number of PLEs also steadily increases. Hyperchaotic attractors with 25 PLEs can be generated by this system with 32 phase-shift units. The sum of the PLEs will reach the maximum value when 23 phase-shift units are used. A simple electronic circuit, consisting of 16 operational amplifiers and two analogy multipliers, is presented for confirming hyperchaos of order 5, i.e., with 5 PLEs

Lyapunov Orbits in the Jupiter System Using Electrodynamic Tethers

Science.gov (United States)

Bokelmann, Kevin; Russell, Ryan P.; Lantoine, Gregory

2013-01-01

Various researchers have proposed the use of electrodynamic tethers for power generation and capture from interplanetary transfers. The effect of tether forces on periodic orbits in Jupiter-satellite systems are investigated. A perturbation force is added to the restricted three-body problem model and a series of simplifications allows development of a conservative system that retains the Jacobi integral. Expressions are developed to find modified locations of equilibrium positions. Modified families of Lyapunov orbits are generated as functions of tether size and Jacobi integral. Zero velocity curves and stability analyses are used to evaluate the dynamical properties of tether-modified orbits.

Adaptive fuzzy PID control for a quadrotor stabilisation

Science.gov (United States)

Cherrat, N.; Boubertakh, H.; Arioui, H.

2018-02-01

This paper deals with the design of an adaptive fuzzy PID control law for attitude and altitude stabilization of a quadrotor despite the system model uncertainties and disturbances. To this end, a PID control with adaptive gains is used in order to approximate a virtual ideal control previously designed to achieve the predefined objective. Specifically, the control gains are estimated and adjusted by mean of a fuzzy system whose parameters are adjusted online via a gradient descent-based adaptation law. The analysis of the closed-loop system is given by the Lyapunov approach. The simulation results are presented to illustrate the efficiency of the proposed approach.

Guaranteed cost control of time-delay chaotic systems

International Nuclear Information System (INIS)

Park, Ju H.; Kwon, O.M.

2006-01-01

This article studies a guaranteed cost control problem for a class of time-delay chaotic systems. Attention is focused on the design of memory state feedback controllers such that the resulting closed-loop system is asymptotically stable and an adequate level of performance is also guaranteed. Using the Lyapunov method and LMI (linear matrix inequality) framework, two criteria for the existence of the controller are derived in terms of LMIs. A numerical example is given to illustrate the proposed method

Synchronizing two coupled chaotic neurons in external electrical stimulation using backstepping control

International Nuclear Information System (INIS)

Deng Bin; Wang Jiang; Fei Xiangyang

2006-01-01

Backstepping design is a recursive procedure that combines the choice of a Lyapunov function with the design of a controller. In this paper, the backstepping control is used to synchronize two coupled chaotic neurons in external electrical stimulation. The coupled model is based on the nonlinear cable model and only one state variable can be controlled in practice. The backstepping design needs only one controller to synchronize two chaotic systems and it can be applied to a variety of chaotic systems whether they contain external excitation or not, so the two coupled chaotic neurons in external electrical stimulation can be synchronized perfectly by backstepping control. Numerical simulations demonstrate the effectiveness of this design

Determination of the Lyapunov exponents and the information dimension in some dynamical systems

International Nuclear Information System (INIS)

Ziar, A.

1992-01-01

Classical phase space for some dynamical systems relevant in nuclear physics are studied. The nuclei is described by convex billiards or in the mean field theory. In both cases, besides the Poincare surface of sections which gives a qualitative description, each trajectory is characterized by its maximum Lyapunov exponent. The analytic monodromy matrix for a free particle in convex billiards rotating around an axis perpendicular to the plan of billiards, is determined, generalizing a previous result obtained for static billiards. In the frame of the mean field theory, it is shown an interesting alternative to the Lyapunov exponent, which is the dimension of the manifold in the phase space associated to the trajectory, leading to the evaluation of the relative chaotic volume in phase space as a function of the different parameters. The dimension appears as a character which could be determined easily for the rotating mean field, where the dimension of the manifold on which the trajectory is lying could be equal to 5 or 4 for chaotic trajectories, and less or equal to 3 for regular ones

Analysis of Multiple Structural Changes in Financial Contagion Based on the Largest Lyapunov Exponents

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Rui Wang

2014-01-01

Full Text Available A modified multiple structural changes model is built to test structural breaks of the financial system based on calculating the largest Lyapunov exponents of the financial time series. Afterwards, the Lorenz system is used as a simulation example to inspect the new model. As the Lorenz system has strong nonlinearity, the verification results show that the new model has good capability in both finding the breakpoint and revealing the changes in nonlinear characteristics of the time series. The empirical study based on the model used daily data from the S&P 500 stock index during the global financial crisis from 2005 to 2012. The results provide four breakpoints of the period, which divide the contagion into four stages: stationary, local outbreak, global outbreak, and recovery period. An additional significant result is the obvious chaos characteristic difference in the largest Lyapunov exponents and the standard deviation at various stages, particularly at the local outbreak stage.

Chattering-Free Adaptive Sliding Mode Control for Attitude Tracking of Spacecraft with External Disturbance

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Xuxi Zhang

2014-01-01

Full Text Available The attitude tracking problem of spacecraft in the presence of unknown disturbance is investigated. By using the adaptive control technique and the Lyapunov stability theory, a chattering-free adaptive sliding mode control law is proposed for the attitude tracking problem of spacecraft with unknown disturbance. Simulation results are employed to demonstrate the effectiveness of the proposed control design technique in this paper.

Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system

OpenAIRE

Kuznetsov, N. V.; Leonov, G. A.; Mokaev, T. N.; Prasad, A.; Shrimali, M. D.

2015-01-01

The Rabinovich system, describing the process of interaction between waves in plasma, is considered. It is shown that the Rabinovich system can exhibit a hidden attractor in the case of multistability as well as a classical self-excited attractor. The hidden attractor in this system can be localized by analytical/numerical methods based on the continuation and perpetual points. The concept of finite-time Lyapunov dimension is developed for numerical study of the dimension of attractors. A con...

Asymptotic analysis and optimal control of an integro-differential system modelling healthy and cancer cells exposed to chemotherapy

KAUST Repository

Pouchol, Camille; Clairambault, Jean; Lorz, Alexander; Tré lat, Emmanuel

2017-01-01

to the treatment. We analyse the asymptotic behaviour of the model under constant infusion of drugs. By designing an appropriate Lyapunov function, we prove that both cell densities converge to Dirac masses. We then define an optimal control problem, by considering

Lyapunov, singular and bred vectors in a multi-scale system: an empirical exploration of vectors related to instabilities

International Nuclear Information System (INIS)

Norwood, Adrienne; Kalnay, Eugenia; Ide, Kayo; Yang, Shu-Chih; Wolfe, Christopher

2013-01-01

We compute and compare the three types of vectors frequently used to explore the instability properties of dynamical models, namely Lyapunov vectors (LVs), singular vectors (SVs) and bred vectors (BVs) in two systems, using the Wolfe–Samelson (2007 Tellus A 59 355–66) algorithm to compute all of the Lyapunov vectors. The first system is the Lorenz (1963 J. Atmos. Sci. 20 130–41) three-variable model. Although the leading Lyapunov vector, LV1, grows fastest globally, the second Lyapunov vector, LV2, which has zero growth globally, often grows faster than LV1 locally. Whenever this happens, BVs grow closer to LV2, suggesting that in larger atmospheric or oceanic models where several instabilities can grow in different areas of the world, BVs will grow toward the fastest growing local unstable mode. A comparison of their growth rates at different times shows that all three types of dynamical vectors have the ability to predict regime changes and the duration of the new regime based on their growth rates in the last orbit of the old regime, as shown for BVs by Evans et al (2004 Bull. Am. Meteorol. Soc. 520–4). LV1 and BVs have similar predictive skill, LV2 has a tendency to produce false alarms, and even LV3 shows that maximum decay is also associated with regime change. Initial and final SVs grow much faster and are the most accurate predictors of regime change, although the characteristics of the initial SVs are strongly dependent on the length of the optimization window. The second system is the toy ‘ocean-atmosphere’ model developed by Peña and Kalnay (2004 Nonlinear Process. Geophys. 11 319–27) coupling three Lorenz (1963 J. Atmos. Sci. 20 130–41) systems with different time scales, in order to test the effects of fast and slow modes of growth on the dynamical vectors. A fast ‘extratropical atmosphere’ is weakly coupled to a fast ‘tropical atmosphere’ which is, in turn, strongly coupled to a slow ‘ocean’ system, the latter coupling

Anti-Synchronization of Chaotic Systems via Adaptive Sliding Mode Control

International Nuclear Information System (INIS)

Jawaada, Wafaa; Noorani, M. S. M.; Al-Sawalha, M. Mossa

2012-01-01

An anti-synchronization scheme is proposed to achieve the anti-synchronization behavior between chaotic systems with fully unknown parameters. A sliding surface and an adaptive sliding mode controller are designed to gain the anti-synchronization. The stability of the error dynamics is proven theoretically using the Lyapunov stability theory. Finally numerical results are presented to justify the theoretical analysis

Decentralized adaptive neural control for high-order interconnected stochastic nonlinear time-delay systems with unknown system dynamics.

Science.gov (United States)

Si, Wenjie; Dong, Xunde; Yang, Feifei

2018-03-01

This paper is concerned with the problem of decentralized adaptive backstepping state-feedback control for uncertain high-order large-scale stochastic nonlinear time-delay systems. For the control design of high-order large-scale nonlinear systems, only one adaptive parameter is constructed to overcome the over-parameterization, and neural networks are employed to cope with the difficulties raised by completely unknown system dynamics and stochastic disturbances. And then, the appropriate Lyapunov-Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions of high-order large-scale systems for the first time. At last, on the basis of Lyapunov stability theory, the decentralized adaptive neural controller was developed, and it decreases the number of learning parameters. The actual controller can be designed so as to ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges in the small neighborhood of zero. The simulation example is used to further show the validity of the design method. Copyright © 2018 Elsevier Ltd. All rights reserved.

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.

Distributed predictive control of spiral wave in cardiac excitable media

International Nuclear Information System (INIS)

Zheng-Ning, Gan; Xin-Ming, Cheng

2010-01-01

In this paper, we propose the distributed predictive control strategies of spiral wave in cardiac excitable media. The modified FitzHugh–Nagumo model was used to express the cardiac excitable media approximately. Based on the control-Lyapunov theory, we obtained the distributed control equation, which consists of a positive control-Lyapunov function and a positive cost function. Using the equation, we investigate two kinds of robust control strategies: the time-dependent distributed control strategy and the space-time dependent distributed control strategy. The feasibility of the strategies was demonstrated via an illustrative example, in which the spiral wave was prevented to occur, and the possibility for inducing ventricular fibrillation was eliminated. The strategies are helpful in designing various cardiac devices. Since the second strategy is more efficient and robust than the first one, and the response time in the second strategy is far less than that in the first one, the former is suitable for the quick-response control systems. In addition, our spatiotemporal control strategies, especially the second strategy, can be applied to other cardiac models, even to other reaction-diffusion systems. (general)

Lag Synchronization Between Two Coupled Networks via Open-Plus-Closed-Loop and Adaptive Controls

International Nuclear Information System (INIS)

Tong-Chun Hu; Yong-Qing Wu; Shi-Xing Li

2016-01-01

In this paper, we study lag synchronization between two coupled networks and apply two types of control schemes, including the open-plus-closed-loop (OPCL) and adaptive controls. We then design the corresponding control algorithms according to the OPCL and adaptive feedback schemes. With the designed controllers, we obtain two theorems on the lag synchronization based on Lyapunov stability theory and Barbalat's lemma. Finally we provide numerical examples to show the effectiveness of the obtained controllers and see that the adaptive control is stronger than the OPCL control when realizing the lag synchronization between two coupled networks with different coupling structures. (paper)

Perturbation theory for Lyapunov exponents of an Anderson model on a strip

CERN Document Server

Schulz-Baldes, H

2003-01-01

It is proven that the localization length of an Anderson model on a strip of width $L$ is bounded above by $L/\\lambda^2$ for small values of the coupling constant $\\lambda$ of the disordered potential. For this purpose, a new formalism is developed in order to calculate the bottom Lyapunov exponent associated with random products of large symplectic matrices perturbatively in the coupling constant of the randomness.

Fuzzy Backstepping Sliding Mode Control for Mismatched Uncertain System

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H. Q. Hou

2014-06-01

Full Text Available Sliding mode controllers have succeeded in many control problems that the conventional control theories have difficulties to deal with; however it is practically impossible to achieve high-speed switching control. Therefore, in this paper an adaptive fuzzy backstepping sliding mode control scheme is derived for mismatched uncertain systems. Firstly fuzzy sliding mode controller is designed using backstepping method based on the Lyapunov function approach, which is capable of handling mismatched problem. Then fuzzy sliding mode controller is designed using T-S fuzzy model method, it can improve the performance of the control systems and their robustness. Finally this method of control is applied to nonlinear system as a case study; simulation results are also provided the performance of the proposed controller.

Intercept Algorithm for Maneuvering Targets Based on Differential Geometry and Lyapunov Theory

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Yunes Sh. ALQUDSI

2018-03-01

Full Text Available Nowadays, the homing guidance is utilized in the existed and under development air defense systems (ADS to effectively intercept the targets. The targets became smarter and capable to fly and maneuver professionally and the tendency to design missile with a small warhead became greater, then there is a pressure to produce a more precise and accurate missile guidance system based on intelligent algorithms to ensure effective interception of highly maneuverable targets. The aim of this paper is to present an intelligent guidance algorithm that effectively and precisely intercept the maneuverable and smart targets by virtue of the differential geometry (DG concepts. The intercept geometry and engagement kinematics, in addition to the direct intercept condition are developed and expressed in DG terms. The guidance algorithm is then developed by virtue of DG and Lyapunov theory. The study terminates with 2D engagement simulation with illustrative examples, to demonstrate that, the derived DG guidance algorithm is a generalized guidance approach and the well-known proportional navigation (PN guidance law is a subset of this approach.

A new interpretation of zero Lyapunov exponents in BKL time for Mixmaster cosmology

International Nuclear Information System (INIS)

Wu Xin

2010-01-01

A global relationship between cosmological time and Belinskii-Khalatnikov-Lifshitz (BKL) time during the entire evolution of the Mixmaster Bianchi IX universe is used to explain why all the Lyapunov exponents are zero at the BKL time. The actual reason is that the domain of the cosmological time is finite as the BKL time runs from minus infinity to infinity.

Nonfragile Robust Model Predictive Control for Uncertain Constrained Systems with Time-Delay Compensation

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Wei Jiang

2016-01-01

Full Text Available This study investigates the problem of asymptotic stabilization for a class of discrete-time linear uncertain time-delayed systems with input constraints. Parametric uncertainty is assumed to be structured, and delay is assumed to be known. In Lyapunov stability theory framework, two synthesis schemes of designing nonfragile robust model predictive control (RMPC with time-delay compensation are put forward, where the additive and the multiplicative gain perturbations are, respectively, considered. First, by designing appropriate Lyapunov-Krasovskii (L-K functions, the robust performance index is defined as optimization problems that minimize upper bounds of infinite horizon cost function. Then, to guarantee closed-loop stability, the sufficient conditions for the existence of desired nonfragile RMPC are obtained in terms of linear matrix inequalities (LMIs. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approaches.

Lyapunov spectrum of the separated flow around the NACA 0012 airfoil and its dependence on numerical discretization

International Nuclear Information System (INIS)

Fernandez, P.; Wang, Q.

2017-01-01

We investigate the impact of numerical discretization on the Lyapunov spectrum of separated flow simulations. The two-dimensional chaotic flow around the NACA 0012 airfoil at a low Reynolds number and large angle of attack is considered to that end. Time, space and accuracy-order refinement studies are performed to examine each of these effects separately. Numerical results show that the time discretization has a small impact on the dynamics of the system, whereas the spatial discretization can dramatically change them. Also, the finite-time Lyapunov exponents associated to unstable modes are shown to be positively skewed, and quasi-homoclinic tangencies are observed in the attractor of the system. The implications of these results on flow physics and sensitivity analysis of chaotic flows are discussed.

Lyapunov spectrum of the separated flow around the NACA 0012 airfoil and its dependence on numerical discretization

Science.gov (United States)

Fernandez, P.; Wang, Q.

2017-12-01

We investigate the impact of numerical discretization on the Lyapunov spectrum of separated flow simulations. The two-dimensional chaotic flow around the NACA 0012 airfoil at a low Reynolds number and large angle of attack is considered to that end. Time, space and accuracy-order refinement studies are performed to examine each of these effects separately. Numerical results show that the time discretization has a small impact on the dynamics of the system, whereas the spatial discretization can dramatically change them. Also, the finite-time Lyapunov exponents associated to unstable modes are shown to be positively skewed, and quasi-homoclinic tangencies are observed in the attractor of the system. The implications of these results on flow physics and sensitivity analysis of chaotic flows are discussed.

Temperature Control of Gas Chromatograph Based on Switched Delayed System Techniques

Directory of Open Access Journals (Sweden)

Xiao-Liang Wang

2014-01-01

Full Text Available We address the temperature control problem of the gas chromatograph. We model the temperature control system of the gas chromatograph into a switched delayed system and analyze the stability by common Lyapunov functional technique. The PI controller parameters can be given based on the proposed linear matrix inequalities (LMIs condition and the designed controller can make the temperature of gas chromatograph track the reference signal asymptotically. An experiment is given to illustrate the effectiveness of the stability criterion.

Event-Driven Control for Networked Control Systems With Quantization and Markov Packet Losses.

Science.gov (United States)

Yang, Hongjiu; Xu, Yang; Zhang, Jinhui

2016-05-23

In this paper, event-driven is used in a networked control system (NCS) which is subjected to the effect of quantization and packet losses. A discrete event-detector is used to monitor specific events in the NCS. Both an arbitrary region quantizer and Markov jump packet losses are also considered for the NCS. Based on zoom strategy and Lyapunov theory, a complete proof is given to guarantee mean square stability of the closed-loop system. Stabilization of the NCS is ensured by designing a feedback controller. Lastly, an inverted pendulum model is given to show the advantages and effectiveness of the proposed results.

Spacecraft attitude control using neuro-fuzzy approximation of the optimal controllers

Science.gov (United States)

Kim, Sung-Woo; Park, Sang-Young; Park, Chandeok

2016-01-01

In this study, a neuro-fuzzy controller (NFC) was developed for spacecraft attitude control to mitigate large computational load of the state-dependent Riccati equation (SDRE) controller. The NFC was developed by training a neuro-fuzzy network to approximate the SDRE controller. The stability of the NFC was numerically verified using a Lyapunov-based method, and the performance of the controller was analyzed in terms of approximation ability, steady-state error, cost, and execution time. The simulations and test results indicate that the developed NFC efficiently approximates the SDRE controller, with asymptotic stability in a bounded region of angular velocity encompassing the operational range of rapid-attitude maneuvers. In addition, it was shown that an approximated optimal feedback controller can be designed successfully through neuro-fuzzy approximation of the optimal open-loop controller.

Continuation of probability density functions using a generalized Lyapunov approach

Energy Technology Data Exchange (ETDEWEB)

Baars, S., E-mail: s.baars@rug.nl [Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK Groningen (Netherlands); Viebahn, J.P., E-mail: viebahn@cwi.nl [Centrum Wiskunde & Informatica (CWI), P.O. Box 94079, 1090 GB, Amsterdam (Netherlands); Mulder, T.E., E-mail: t.e.mulder@uu.nl [Institute for Marine and Atmospheric research Utrecht, Department of Physics and Astronomy, Utrecht University, Princetonplein 5, 3584 CC Utrecht (Netherlands); Kuehn, C., E-mail: ckuehn@ma.tum.de [Technical University of Munich, Faculty of Mathematics, Boltzmannstr. 3, 85748 Garching bei München (Germany); Wubs, F.W., E-mail: f.w.wubs@rug.nl [Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK Groningen (Netherlands); Dijkstra, H.A., E-mail: h.a.dijkstra@uu.nl [Institute for Marine and Atmospheric research Utrecht, Department of Physics and Astronomy, Utrecht University, Princetonplein 5, 3584 CC Utrecht (Netherlands); School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY (United States)

2017-05-01

Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability density functions of systems of stochastic partial differential equations near fixed points, under a small noise approximation. Key innovation is the efficient solution of a generalized Lyapunov equation using an iterative method involving low-rank approximations. We apply and illustrate the capabilities of the method using a problem in physical oceanography, i.e. the occurrence of multiple steady states of the Atlantic Ocean circulation.

A Lyapunov method for stability analysis of piecewise-affine systems over non-invariant domains

Science.gov (United States)

Rubagotti, Matteo; Zaccarian, Luca; Bemporad, Alberto

2016-05-01

This paper analyses stability of discrete-time piecewise-affine systems, defined on possibly non-invariant domains, taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system. An algorithm based on linear programming is proposed, in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction. The results are based on the definition of a piecewise-affine Lyapunov function, which is in general discontinuous on the boundaries of the regions. The proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach. Two numerical examples are shown, among which a case where the proposed method is applied to a closed-loop system, to which model predictive control was applied without a-priori guarantee of stability.

Uniform persistence and upper Lyapunov exponents for monotone skew-product semiflows

International Nuclear Information System (INIS)

Novo, Sylvia; Obaya, Rafael; Sanz, Ana M

2013-01-01

Several results of uniform persistence above and below a minimal set of an abstract monotone skew-product semiflow are obtained. When the minimal set has a continuous separation the results are given in terms of the principal spectrum. In the case that the semiflow is generated by the solutions of a family of non-autonomous differential equations of ordinary, delay or parabolic type, the former results are strongly improved. A method of calculus of the upper Lyapunov exponent of the minimal set is also determined. (paper)

Effect of parameter calculation in direct estimation of the Lyapunov exponent in short time series

Directory of Open Access Journals (Sweden)

A. M. López Jiménez

2002-01-01

Full Text Available The literature about non-linear dynamics offers a few recommendations, which sometimes are divergent, about the criteria to be used in order to select the optimal calculus parameters in the estimation of Lyapunov exponents by direct methods. These few recommendations are circumscribed to the analysis of chaotic systems. We have found no recommendation for the estimation of λ starting from the time series of classic systems. The reason for this is the interest in distinguishing variability due to a chaotic behavior of determinist dynamic systems of variability caused by white noise or linear stochastic processes, and less in the identification of non-linear terms from the analysis of time series. In this study we have centered in the dependence of the Lyapunov exponent, obtained by means of direct estimation, of the initial distance and the time evolution. We have used generated series of chaotic systems and generated series of classic systems with varying complexity. To generate the series we have used the logistic map.

Control and estimation of piecewise affine systems

CERN Document Server

Xu, Jun

2014-01-01

As a powerful tool to study nonlinear systems and hybrid systems, piecewise affine (PWA) systems have been widely applied to mechanical systems. Control and Estimation of Piecewise Affine Systems presents several research findings relating to the control and estimation of PWA systems in one unified view. Chapters in this title discuss stability results of PWA systems, using piecewise quadratic Lyapunov functions and piecewise homogeneous polynomial Lyapunov functions. Explicit necessary and sufficient conditions for the controllability and reachability of a class of PWA systems are

Geodesic stability, Lyapunov exponents, and quasinormal modes

International Nuclear Information System (INIS)

Cardoso, Vitor; Miranda, Alex S.; Berti, Emanuele; Witek, Helvi; Zanchin, Vilson T.

2009-01-01

Geodesic motion determines important features of spacetimes. Null unstable geodesics are closely related to the appearance of compact objects to external observers and have been associated with the characteristic modes of black holes. By computing the Lyapunov exponent, which is the inverse of the instability time scale associated with this geodesic motion, we show that, in the eikonal limit, quasinormal modes of black holes in any dimensions are determined by the parameters of the circular null geodesics. This result is independent of the field equations and only assumes a stationary, spherically symmetric and asymptotically flat line element, but it does not seem to be easily extendable to anti-de Sitter spacetimes. We further show that (i) in spacetime dimensions greater than four, equatorial circular timelike geodesics in a Myers-Perry black-hole background are unstable, and (ii) the instability time scale of equatorial null geodesics in Myers-Perry spacetimes has a local minimum for spacetimes of dimension d≥6.

On robust control of uncertain chaotic systems: a sliding-mode synthesis via chaotic optimization

International Nuclear Information System (INIS)

Lu Zhao; Shieh Leangsan; Chen GuanRong

2003-01-01

This paper presents a novel Lyapunov-based control approach which utilizes a Lyapunov function of the nominal plant for robust tracking control of general multi-input uncertain nonlinear systems. The difficulty of constructing a control Lyapunov function is alleviated by means of predefining an optimal sliding mode. The conventional schemes for constructing sliding modes of nonlinear systems stipulate that the system of interest is canonical-transformable or feedback-linearizable. An innovative approach that exploits a chaotic optimizing algorithm is developed thereby obtaining the optimal sliding manifold for the control purpose. Simulations on the uncertain chaotic Chen's system illustrate the effectiveness of the proposed approach

Dynamic Analysis and Circuit Design of a Novel Hyperchaotic System with Fractional-Order Terms

Directory of Open Access Journals (Sweden)

Abir Lassoued

2017-01-01

Full Text Available A novel hyperchaotic system with fractional-order (FO terms is designed. Its highly complex dynamics are investigated in terms of equilibrium points, Lyapunov spectrum, and attractor forms. It will be shown that the proposed system exhibits larger Lyapunov exponents than related hyperchaotic systems. Finally, to enhance its potential application, a related circuit is designed by using the MultiSIM Software. Simulation results verify the effectiveness of the suggested circuit.

New fuzzy approximate model for indirect adaptive control of distributed solar collectors

KAUST Repository

Elmetennani, Shahrazed

2014-06-01

This paper studies the problem of controlling a parabolic solar collectors, which consists of forcing the outlet oil temperature to track a set reference despite possible environmental disturbances. An approximate model is proposed to simplify the controller design. The presented controller is an indirect adaptive law designed on the fuzzy model with soft-sensing of the solar irradiance intensity. The proposed approximate model allows the achievement of a simple low dimensional set of nonlinear ordinary differential equations that reproduces the dynamical behavior of the system taking into account its infinite dimension. Stability of the closed loop system is ensured by resorting to Lyapunov Control functions for an indirect adaptive controller.

New fuzzy approximate model for indirect adaptive control of distributed solar collectors

KAUST Repository

Elmetennani, Shahrazed; Laleg-Kirati, Taous-Meriem

2014-01-01

This paper studies the problem of controlling a parabolic solar collectors, which consists of forcing the outlet oil temperature to track a set reference despite possible environmental disturbances. An approximate model is proposed to simplify the controller design. The presented controller is an indirect adaptive law designed on the fuzzy model with soft-sensing of the solar irradiance intensity. The proposed approximate model allows the achievement of a simple low dimensional set of nonlinear ordinary differential equations that reproduces the dynamical behavior of the system taking into account its infinite dimension. Stability of the closed loop system is ensured by resorting to Lyapunov Control functions for an indirect adaptive controller.

A Switching Anti-windup Design Using Multiple Lyapunov Functions

NARCIS (Netherlands)

Lu, L.; Lin, Z.; Chen, J.

2009-01-01

This paper proposes a switching anti-windup design, which aims to enlarge the domain of attraction of the closed-loop system. Multiple anti-windup gains along with an index function that orchestrates the switching among these anti-windup gains are designed based on the min function of multiple

Phase space reconstruction and estimation of the largest Lyapunov exponent for gait kinematic data

Energy Technology Data Exchange (ETDEWEB)

Josiński, Henryk [Silesian University of Technology, Akademicka 16, 44-100 Gliwice (Poland); Świtoński, Adam [Polish-Japanese Institute of Information Technology, Aleja Legionów 2, 41-902 Bytom (Poland); Silesian University of Technology, Akademicka 16, 44-100 Gliwice (Poland); Michalczuk, Agnieszka; Wojciechowski, Konrad [Polish-Japanese Institute of Information Technology, Aleja Legionów 2, 41-902 Bytom (Poland)

2015-03-10

The authors describe an example of application of nonlinear time series analysis directed at identifying the presence of deterministic chaos in human motion data by means of the largest Lyapunov exponent. The method was previously verified on the basis of a time series constructed from the numerical solutions of both the Lorenz and the Rössler nonlinear dynamical systems.

Non Lyapunov stability of a constant spatially developing 2-D gas flow

Science.gov (United States)

Balint, Agneta M.; Balint, Stefan; Tanasie, Loredana

2017-01-01

Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 2-D gas flow are analyzed in a particular phase space of continuously differentiable functions, endowed with the usual algebraic operations and the topology generated by the uniform convergence on the plane. For this purpose the Euler equations linearized at the constant flow are used. The Lyapunov stability analysis was presented in [1] and this paper is a continuation of [1].

An Event-Triggered Online Energy Management Algorithm of Smart Home: Lyapunov Optimization Approach

Directory of Open Access Journals (Sweden)

Wei Fan

2016-05-01

Full Text Available As an important component of the smart grid on the user side, a home energy management system is the core of optimal operation for a smart home. In this paper, the energy scheduling problem for a household equipped with photovoltaic devices was investigated. An online energy management algorithm based on event triggering was proposed. The Lyapunov optimization method was adopted to schedule controllable load in the household. Without forecasting related variables, real-time decisions were made based only on the current information. Energy could be rapidly regulated under the fluctuation of distributed generation, electricity demand and market price. The event-triggering mechanism was adopted to trigger the execution of the online algorithm, so as to cut down the execution frequency and unnecessary calculation. A comprehensive result obtained from simulation shows that the proposed algorithm could effectively decrease the electricity bills of users. Moreover, the required computational resource is small, which contributes to the low-cost energy management of a smart home.

Regularized semiclassical limits: Linear flows with infinite Lyapunov exponents

KAUST Repository

Athanassoulis, Agissilaos; Katsaounis, Theodoros; Kyza, Irene

2016-01-01

Semiclassical asymptotics for Schrödinger equations with non-smooth potentials give rise to ill-posed formal semiclassical limits. These problems have attracted a lot of attention in the last few years, as a proxy for the treatment of eigenvalue crossings, i.e. general systems. It has recently been shown that the semiclassical limit for conical singularities is in fact well-posed, as long as the Wigner measure (WM) stays away from singular saddle points. In this work we develop a family of refined semiclassical estimates, and use them to derive regularized transport equations for saddle points with infinite Lyapunov exponents, extending the aforementioned recent results. In the process we answer a related question posed by P.L. Lions and T. Paul in 1993. If we consider more singular potentials, our rigorous estimates break down. To investigate whether conical saddle points, such as -|x|, admit a regularized transport asymptotic approximation, we employ a numerical solver based on posteriori error control. Thus rigorous upper bounds for the asymptotic error in concrete problems are generated. In particular, specific phenomena which render invalid any regularized transport for -|x| are identified and quantified. In that sense our rigorous results are sharp. Finally, we use our findings to formulate a precise conjecture for the condition under which conical saddle points admit a regularized transport solution for the WM. © 2016 International Press.

Regularized semiclassical limits: Linear flows with infinite Lyapunov exponents

KAUST Repository

Athanassoulis, Agissilaos

2016-08-30

Semiclassical asymptotics for Schrödinger equations with non-smooth potentials give rise to ill-posed formal semiclassical limits. These problems have attracted a lot of attention in the last few years, as a proxy for the treatment of eigenvalue crossings, i.e. general systems. It has recently been shown that the semiclassical limit for conical singularities is in fact well-posed, as long as the Wigner measure (WM) stays away from singular saddle points. In this work we develop a family of refined semiclassical estimates, and use them to derive regularized transport equations for saddle points with infinite Lyapunov exponents, extending the aforementioned recent results. In the process we answer a related question posed by P.L. Lions and T. Paul in 1993. If we consider more singular potentials, our rigorous estimates break down. To investigate whether conical saddle points, such as -|x|, admit a regularized transport asymptotic approximation, we employ a numerical solver based on posteriori error control. Thus rigorous upper bounds for the asymptotic error in concrete problems are generated. In particular, specific phenomena which render invalid any regularized transport for -|x| are identified and quantified. In that sense our rigorous results are sharp. Finally, we use our findings to formulate a precise conjecture for the condition under which conical saddle points admit a regularized transport solution for the WM. © 2016 International Press.

Flatness-based adaptive fuzzy control of chaotic finance dynamics

Science.gov (United States)

Rigatos, G.; Siano, P.; Loia, V.; Tommasetti, A.; Troisi, O.

2017-11-01

A flatness-based adaptive fuzzy control is applied to the problem of stabilization of the dynamics of a chaotic finance system, describing interaction between the interest rate, the investment demand and the price exponent. By proving that the system is differentially flat and by applying differential flatness diffeomorphisms, its transformation to the linear canonical (Brunovsky) is performed. For the latter description of the system, the design of a stabilizing state feedback controller becomes possible. A first problem in the design of such a controller is that the dynamic model of the finance system is unknown and thus it has to be identified with the use neurofuzzy approximators. The estimated dynamics provided by the approximators is used in the computation of the control input, thus establishing an indirect adaptive control scheme. The learning rate of the approximators is chosen from the requirement the system's Lyapunov function to have always a negative first-order derivative. Another problem that has to be dealt with is that the control loop is implemented only with the use of output feedback. To estimate the non-measurable state vector elements of the finance system, a state observer is implemented in the control loop. The computation of the feedback control signal requires the solution of two algebraic Riccati equations at each iteration of the control algorithm. Lyapunov stability analysis demonstrates first that an H-infinity tracking performance criterion is satisfied. This signifies elevated robustness against modelling errors and external perturbations. Moreover, the global asymptotic stability is proven for the control loop.

Final Technical Report: Distributed Controls for High Penetrations of Renewables

Energy Technology Data Exchange (ETDEWEB)

Byrne, Raymond H. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Neely, Jason C. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Rashkin, Lee J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Trudnowski, Daniel J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Wilson, David G. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2015-12-01

The goal of this effort was to apply four potential control analysis/design approaches to the design of distributed grid control systems to address the impact of latency and communications uncertainty with high penetrations of photovoltaic (PV) generation. The four techniques considered were: optimal fixed structure control; Nyquist stability criterion; vector Lyapunov analysis; and Hamiltonian design methods. A reduced order model of the Western Electricity Coordinating Council (WECC) developed for the Matlab Power Systems Toolbox (PST) was employed for the study, as well as representative smaller systems (e.g., a two-area, three-area, and four-area power system). Excellent results were obtained with the optimal fixed structure approach, and the methodology we developed was published in a journal article. This approach is promising because it offers a method for designing optimal control systems with the feedback signals available from Phasor Measurement Unit (PMU) data as opposed to full state feedback or the design of an observer. The Nyquist approach inherently handles time delay and incorporates performance guarantees (e.g., gain and phase margin). We developed a technique that works for moderate sized systems, but the approach does not scale well to extremely large system because of computational complexity. The vector Lyapunov approach was applied to a two area model to demonstrate the utility for modeling communications uncertainty. Application to large power systems requires a method to automatically expand/contract the state space and partition the system so that communications uncertainty can be considered. The Hamiltonian Surface Shaping and Power Flow Control (HSSPFC) design methodology was selected to investigate grid systems for energy storage requirements to support high penetration of variable or stochastic generation (such as wind and PV) and loads. This method was applied to several small system models.

Two (multi point nonlinear Lyapunov systems associated with an n th order nonlinear system of differential equations – existence and uniqueness

Directory of Open Access Journals (Sweden)

Murty K. N.

2000-01-01

Full Text Available This paper presents a criterion for the existence and uniqueness of solutions to two and multipoint boundary value problems associated with an n th order nonlinear Lyapunov system. A variation of parameters formula is developed and used as a tool to obtain existence and uniqueness. We discuss solution of the second order problem by the ADI method and develop a fixed point method to find the general solution of the n th order Lyapunov system. The results of Barnett (SIAM J. Appl. Anal. 24(1, 1973 are a particular case.

Guaranteed Cost Fault-Tolerant Control for Networked Control Systems with Sensor Faults

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Qixin Zhu

2015-01-01

Full Text Available For the large scale and complicated structure of networked control systems, time-varying sensor faults could inevitably occur when the system works in a poor environment. Guaranteed cost fault-tolerant controller for the new networked control systems with time-varying sensor faults is designed in this paper. Based on time delay of the network transmission environment, the networked control systems with sensor faults are modeled as a discrete-time system with uncertain parameters. And the model of networked control systems is related to the boundary values of the sensor faults. Moreover, using Lyapunov stability theory and linear matrix inequalities (LMI approach, the guaranteed cost fault-tolerant controller is verified to render such networked control systems asymptotically stable. Finally, simulations are included to demonstrate the theoretical results.

Robust fractional order sliding mode control of doubly-fed induction generator (DFIG)-based wind turbines.

Science.gov (United States)

Ebrahimkhani, Sadegh

2016-07-01

Wind power plants have nonlinear dynamics and contain many uncertainties such as unknown nonlinear disturbances and parameter uncertainties. Thus, it is a difficult task to design a robust reliable controller for this system. This paper proposes a novel robust fractional-order sliding mode (FOSM) controller for maximum power point tracking (MPPT) control of doubly fed induction generator (DFIG)-based wind energy conversion system. In order to enhance the robustness of the control system, uncertainties and disturbances are estimated using a fractional order uncertainty estimator. In the proposed method a continuous control strategy is developed to achieve the chattering free fractional order sliding-mode control, and also no knowledge of the uncertainties and disturbances or their bound is assumed. The boundedness and convergence properties of the closed-loop signals are proven using Lyapunov׳s stability theory. Simulation results in the presence of various uncertainties were carried out to evaluate the effectiveness and robustness of the proposed control scheme. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Adaptive Superheat Control of a Refrigeration Plant using Backstepping

DEFF Research Database (Denmark)

Rasmussen, Henrik

2008-01-01

This paper proposes a novel method for superheat and capacity control of refrigeration systems. The new idea is to control the superheat by the compressor speed and capacity by the refrigerant flow. This gives a highly nonlinear transfer operator from compressor speed input to the superheat output....... A new low order nonlinear model of the evaporator is developed and used in a backstepping design of an adaptive nonlinear controller.  The stability of the proposed method is validated theoretically by Lyapunov analysis and experimental results shows the performance of the system for a wide range...

Chaotic operation and chaos control of travelling wave ultrasonic motor.

Science.gov (United States)

Shi, Jingzhuo; Zhao, Fujie; Shen, Xiaoxi; Wang, Xiaojie

2013-08-01

The travelling wave ultrasonic motor, which is a nonlinear dynamic system, has complex chaotic phenomenon with some certain choices of system parameters and external inputs, and its chaotic characteristics have not been studied until now. In this paper, the preliminary study of the chaos phenomenon in ultrasonic motor driving system has been done. The experiment of speed closed-loop control is designed to obtain several groups of time sampling data sequence of the amplitude of driving voltage, and phase-space reconstruction is used to analyze the chaos characteristics of these time sequences. The largest Lyapunov index is calculated and the result is positive, which shows that the travelling wave ultrasonic motor has chaotic characteristics in a certain working condition Then, the nonlinear characteristics of travelling wave ultrasonic motor are analyzed which includes Lyapunov exponent map, the bifurcation diagram and the locus of voltage relative to speed based on the nonlinear chaos model of a travelling wave ultrasonic motor. After that, two kinds of adaptive delay feedback controllers are designed in this paper to control and suppress chaos in USM speed control system. Simulation results show that the method can control unstable periodic orbits, suppress chaos in USM control system. Proportion-delayed feedback controller was designed following and arithmetic of fuzzy logic was used to adaptively adjust the delay time online. Simulation results show that this method could fast and effectively change the chaos movement into periodic or fixed-point movement and make the system enter into stable state from chaos state. Finally the chaos behavior was controlled. Copyright © 2013 Elsevier B.V. All rights reserved.

Adaptive Neural-Sliding Mode Control of Active Suspension System for Camera Stabilization

Directory of Open Access Journals (Sweden)

Feng Zhao

2015-01-01

Full Text Available The camera always suffers from image instability on the moving vehicle due to the unintentional vibrations caused by road roughness. This paper presents a novel adaptive neural network based on sliding mode control strategy to stabilize the image captured area of the camera. The purpose is to suppress vertical displacement of sprung mass with the application of active suspension system. Since the active suspension system has nonlinear and time varying characteristics, adaptive neural network (ANN is proposed to make the controller robustness against systematic uncertainties, which release the model-based requirement of the sliding model control, and the weighting matrix is adjusted online according to Lyapunov function. The control system consists of two loops. The outer loop is a position controller designed with sliding mode strategy, while the PID controller in the inner loop is to track the desired force. The closed loop stability and asymptotic convergence performance can be guaranteed on the basis of the Lyapunov stability theory. Finally, the simulation results show that the employed controller effectively suppresses the vibration of the camera and enhances the stabilization of the entire camera, where different excitations are considered to validate the system performance.

Position Control of Switched Reluctance Motor Using Super Twisting Algorithm

Directory of Open Access Journals (Sweden)

Muhammad Rafiq Mufti

2016-01-01

Full Text Available The inherent problem of chattering in traditional sliding mode control is harmful for practical application of control system. This paper pays a considerable attention to a chattering-free control method, that is, higher-order sliding mode (super twisting algorithm. The design of a position controller for switched reluctance motor is presented and its stability is assured using Lyapunov stability theorem. In order to highlight the advantages of higher-order sliding mode controller (HOSMC, a classical first-order sliding mode controller (FOSMC is also applied to the same system and compared. The simulation results reflect the effectiveness of the proposed technique.

Development of fault tolerant adaptive control laws for aerospace systems

Science.gov (United States)

Perez Rocha, Andres E.

The main topic of this dissertation is the design, development and implementation of intelligent adaptive control techniques designed to maintain healthy performance of aerospace systems subjected to malfunctions, external parameter changes and/or unmodeled dynamics. The dissertation is focused on the development of novel adaptive control configurations that rely on non-linear functions that appear in the immune system of living organisms as main source of adaptation. One of the main goals of this dissertation is to demonstrate that these novel adaptive control architectures are able to improve overall performance and protect the system while reducing control effort and maintaining adequate operation outside bounds of nominal design. This research effort explores several phases, ranging from theoretical stability analysis, simulation and hardware implementation on different types of aerospace systems including spacecraft, aircraft and quadrotor vehicles. The results presented in this dissertation are focused on two main adaptivity approaches, the first one is intended for aerospace systems that do not attain large angles and use exact feedback linearization of Euler angle kinematics. A proof of stability is presented by means of the circle Criterion and Lyapunov's direct method. The second approach is intended for aerospace systems that can attain large attitude angles (e.g. space systems in gravity-less environments), the adaptation is incorporated on a baseline architecture that uses partial feedback linearization of quaternions kinematics. In this case, the closed loop stability was analyzed using Lyapunov's direct method and Barbalat's Lemma. It is expected that some results presented in this dissertation can contribute towards the validation and certification of direct adaptive controllers.

Chaos control and duration time of a class of uncertain chaotic systems

International Nuclear Information System (INIS)

Bowong, Samuel; Moukam Kakmeni, F.M.

2003-01-01

This Letter presents a robust control scheme for a class of uncertain chaotic systems in the canonical form, with unknown nonlinearities. To cope with the uncertainties, we combine Lyapunov methodology with observer design. The proposed strategy comprises an exponential linearizing feedback and an uncertainty estimator. The developed control scheme allows chaos suppression. The advantage of this method over the existing results is that the control time is explicitly computed. Simulations studies are conducted to verify the effectiveness of the scheme

Aeroassisted orbital maneuvering using Lyapunov optimal feedback control

Science.gov (United States)

Grantham, Walter J.; Lee, Byoung-Soo

1987-01-01

A Liapunov optimal feedback controller incorporating a preferred direction of motion at each state of the system which is opposite to the gradient of a specified descent function is developed for aeroassisted orbital transfer from high-earth orbit to LEO. The performances of the Liapunov controller and a calculus-of-variations open-loop minimum-fuel controller, both of which are based on the 1962 U.S. Standard Atmosphere, are simulated using both the 1962 U.S. Standard Atmosphere and an atmosphere corresponding to the STS-6 Space Shuttle flight. In the STS-6 atmosphere, the calculus-of-variations open-loop controller fails to exit the atmosphere, while the Liapunov controller achieves the optimal minimum-fuel conditions, despite the + or - 40 percent fluctuations in the STS-6 atmosphere.

Reinforcement learning design-based adaptive tracking control with less learning parameters for nonlinear discrete-time MIMO systems.

Science.gov (United States)

Liu, Yan-Jun; Tang, Li; Tong, Shaocheng; Chen, C L Philip; Li, Dong-Juan

2015-01-01

Based on the neural network (NN) approximator, an online reinforcement learning algorithm is proposed for a class of affine multiple input and multiple output (MIMO) nonlinear discrete-time systems with unknown functions and disturbances. In the design procedure, two networks are provided where one is an action network to generate an optimal control signal and the other is a critic network to approximate the cost function. An optimal control signal and adaptation laws can be generated based on two NNs. In the previous approaches, the weights of critic and action networks are updated based on the gradient descent rule and the estimations of optimal weight vectors are directly adjusted in the design. Consequently, compared with the existing results, the main contributions of this paper are: 1) only two parameters are needed to be adjusted, and thus the number of the adaptation laws is smaller than the previous results and 2) the updating parameters do not depend on the number of the subsystems for MIMO systems and the tuning rules are replaced by adjusting the norms on optimal weight vectors in both action and critic networks. It is proven that the tracking errors, the adaptation laws, and the control inputs are uniformly bounded using Lyapunov analysis method. The simulation examples are employed to illustrate the effectiveness of the proposed algorithm.

Evaluating Noise Sensitivity on the Time Series Determination of Lyapunov Exponents Applied to the Nonlinear Pendulum

Directory of Open Access Journals (Sweden)

L.F.P. Franca

2003-01-01

Full Text Available This contribution presents an investigation on noise sensitivity of some of the most disseminated techniques employed to estimate Lyapunov exponents from time series. Since noise contamination is unavoidable in cases of data acquisition, it is important to recognize techniques that could be employed for a correct identification of chaos. State space reconstruction and the determination of Lyapunov exponents are carried out to investigate the response of a nonlinear pendulum. Signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the signal. Basically, the analyses of periodic and chaotic motions are carried out. Results obtained from mathematical model are compared with the one obtained from time series analysis, evaluating noise sensitivity. This procedure allows the identification of the best techniques to be employed in the analysis of experimental data.

The use of Lyapunov differential inequalities for estimating the transients of mechanical systems

Science.gov (United States)

Alyshev, A. S.; Dudarenko, N. A.; Melnikov, V. G.; Melnikov, G. I.

2018-05-01

In this paper we consider an autonomous mechanical system in a finite neighborhood of the zero of the phase space of states. The system is given as a matrix differential equation in the Cauchy form with the right-hand side of the polynomial structure. We propose a method for constructing a sequence of linear inhomogeneous differential inequalities for Lyapunov functions. As a result, we obtain estimates of transient processes in the form of functional inequalities.

Polyhedral Lyapunov functions structurally ensure global asymptotic stability of dynamical networks iff the Jacobian is non-singular

NARCIS (Netherlands)

Blanchini, Franco; Giordano, G.

2017-01-01

For a vast class of dynamical networks, including chemical reaction networks (CRNs) with monotonic reaction rates, the existence of a polyhedral Lyapunov function (PLF) implies structural (i.e., parameter-free) local stability. Global structural stability is ensured under the additional

Controlling chaos in the permanent magnet synchronous motor

International Nuclear Information System (INIS)

Zribi, Mohamed; Oteafy, Ahmed; Smaoui, Nejib

2009-01-01

The Permanent Magnet Synchronous Motor (PMSM) is known to exhibit chaotic behavior under certain conditions. This paper proposes to use an instantaneous Lyapunov exponent control algorithm to control the PMSM. One of the objectives of the control approach is to bring order to the PMSM and to drive it to any user-defined desired state. Simulation results under different operating conditions indicate that the proposed control scheme works well. Moreover, the proposed Lyapunov exponent control scheme is able to induce chaos on the permanent magnet synchronous motor. Simulation results show the effectiveness of the proposed control scheme in chaotifing the response of the motor.

Moment Lyapunov Exponent and Stochastic Stability of Binary Airfoil under Combined Harmonic and Non-Gaussian Colored Noise Excitations

Science.gov (United States)

Hu, D. L.; Liu, X. B.

Both periodic loading and random forces commonly co-exist in real engineering applications. However, the dynamic behavior, especially dynamic stability of systems under parametric periodic and random excitations has been reported little in the literature. In this study, the moment Lyapunov exponent and stochastic stability of binary airfoil under combined harmonic and non-Gaussian colored noise excitations are investigated. The noise is simplified to an Ornstein-Uhlenbeck process by applying the path-integral method. Via the singular perturbation method, the second-order expansions of the moment Lyapunov exponent are obtained, which agree well with the results obtained by the Monte Carlo simulation. Finally, the effects of the noise and parametric resonance (such as subharmonic resonance and combination additive resonance) on the stochastic stability of the binary airfoil system are discussed.

Distributed Cooperative Control of Multiple Nonlinear Systems with Nonholonomic Constraints and Uncertainty

Science.gov (United States)

2015-04-04

this testbed, there are four P3-AT mobile robots. Each robot is equipped with a camera and a laser sensor. Between robots, there is wireless...shows the formation tracking of the 4 followers, the blue spots represent each follower robot, the black spot represent the trajectory of centroid of...P. Jiang, “Lyapunov design of global state and output trackers for nonholonomic control systems,” Int. J. of Control, pp. 744–761, 2000. [97] Y. P

Advanced Interval Type-2 Fuzzy Sliding Mode Control for Robot Manipulator

Directory of Open Access Journals (Sweden)

Ji-Hwan Hwang

2017-01-01

Full Text Available In this paper, advanced interval type-2 fuzzy sliding mode control (AIT2FSMC for robot manipulator is proposed. The proposed AIT2FSMC is a combination of interval type-2 fuzzy system and sliding mode control. For resembling a feedback linearization (FL control law, interval type-2 fuzzy system is designed. For compensating the approximation error between the FL control law and interval type-2 fuzzy system, sliding mode controller is designed, respectively. The tuning algorithms are derived in the sense of Lyapunov stability theorem. Two-link rigid robot manipulator with nonlinearity is used to test and the simulation results are presented to show the effectiveness of the proposed method that can control unknown system well.

Dissipativity-Based Reliable Control for Fuzzy Markov Jump Systems With Actuator Faults.

Science.gov (United States)

Tao, Jie; Lu, Renquan; Shi, Peng; Su, Hongye; Wu, Zheng-Guang

2017-09-01

This paper is concerned with the problem of reliable dissipative control for Takagi-Sugeno fuzzy systems with Markov jumping parameters. Considering the influence of actuator faults, a sufficient condition is developed to ensure that the resultant closed-loop system is stochastically stable and strictly ( Q, S,R )-dissipative based on a relaxed approach in which mode-dependent and fuzzy-basis-dependent Lyapunov functions are employed. Then a reliable dissipative control for fuzzy Markov jump systems is designed, with sufficient condition proposed for the existence of guaranteed stability and dissipativity controller. The effectiveness and potential of the obtained design method is verified by two simulation examples.

Complete synchronization of uncertain chaotic systems via a single proportional adaptive controller: A comparative study

Energy Technology Data Exchange (ETDEWEB)

Ahmad, Israr, E-mail: iak-2000plus@yahoo.com; Saaban, Azizan Bin, E-mail: azizan.s@uum.edu.my; Ibrahim, Adyda Binti, E-mail: adyda@uum.edu.my [School of Quantitative Sciences, College of Arts & Sciences, UUM (Malaysia); Shahzad, Mohammad, E-mail: dmsinfinite@gmail.com [College of Applied Sciences Nizwa, Ministry of Higher Education, Sultanate of Oman (Oman)

2015-12-11

This paper addresses a comparative computational study on the synchronization quality, cost and converging speed for two pairs of identical chaotic and hyperchaotic systems with unknown time-varying parameters. It is assumed that the unknown time-varying parameters are bounded. Based on the Lyapunov stability theory and using the adaptive control method, a single proportional controller is proposed to achieve the goal of complete synchronizations. Accordingly, appropriate adaptive laws are designed to identify the unknown time-varying parameters. The designed control strategy is easy to implement in practice. Numerical simulations results are provided to verify the effectiveness of the proposed synchronization scheme.

Parameter-dependent PWQ Lyapunov function stability criteria for uncertain piecewise linear systems

Directory of Open Access Journals (Sweden)

Morten Hovd

2018-01-01

Full Text Available The calculation of piecewise quadratic (PWQ Lyapunov functions is addressed in view of stability analysis of uncertain piecewise linear dynamics. As main contribution, the linear matrix inequality (LMI approach proposed in (Johansson and Rantzer, 1998 for the stability analysis of PWL and PWA dynamics is extended to account for parametric uncertainty based on a improved relaxation technique. The results are applied for the analysis of a Phase Locked Loop (PLL benchmark and the ability to guarantee a stability region in the parameter space well beyond the state of the art is demonstrated.

Dynamical Analysis, Synchronization, Circuit Design, and Secure Communication of a Novel Hyperchaotic System

Directory of Open Access Journals (Sweden)

Li Xiong

2017-01-01

Full Text Available This paper is devoted to introduce a novel fourth-order hyperchaotic system. The hyperchaotic system is constructed by adding a linear feedback control level based on a modified Lorenz-like chaotic circuit with reduced number of amplifiers. The local dynamical entities, such as the basic dynamical behavior, the divergence, the eigenvalue, and the Lyapunov exponents of the new hyperchaotic system, are all investigated analytically and numerically. Then, an active control method is derived to achieve global chaotic synchronization of the novel hyperchaotic system through making the synchronization error system asymptotically stable at the origin based on Lyapunov stability theory. Next, the proposed novel hyperchaotic system is applied to construct another new hyperchaotic system with circuit deformation and design a new hyperchaotic secure communication circuit. Furthermore, the implementation of two novel electronic circuits of the proposed hyperchaotic systems is presented, examined, and realized using physical components. A good qualitative agreement is shown between the simulations and the experimental results around 500 kHz and below 1 MHz.

Chaos synchronizations of chaotic systems via active nonlinear control

International Nuclear Information System (INIS)

Huang, J; Xiao, T J

2008-01-01

This paper not only investigates the chaos synchronization between two LCC chaotic systems, but also discusses the chaos synchronization between LCC system and Genesio system. Some novel active nonlinear controllers are designed to achieve synchronizations between drive and response systems effectively. Moreover, the sufficient conditions of synchronizations are derived by using Lyapunov stability theorem. Numerical simulations are presented to verify the theoretical analysis, which shows that the synchronization schemes are global effective

Speed Sensorless Field Oriented Control of an Induction Motor at zero speed with identification of inverter parameters

DEFF Research Database (Denmark)

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

2002-01-01

Using adaptive Lyapunov design a new approach for the design of an observer for speed sensorless control is developed. The resulting scheme leads to a nonlinear full order observer for the motor states and for the motor and inverter parameters including the rotor speed. Assuming motor parameters ...... known the design achieves stability with guaranteed region of attraction. Experiments demonstrate high dynamic performance even at zero rotor speed based only on the slip frequency caused by the load torque....

Boundary control of nonlinear coupled heat systems using backstepping

KAUST Repository

Bendevis, Paul

2016-10-20

A state feedback boundary controller is designed for a 2D coupled PDE system modelling heat transfer in a membrane distillation system for water desalination. Fluid is separated into two compartments with nonlinear coupling at a membrane boundary. The controller sets the temperature on one boundary in order to track a temperature difference across the membrane boundary. The control objective is achieved by an extension of backstepping methods to these coupled equations. Stability of the target system via Lyapunov like methods, and the invertibility of the integral transformation are used to show the stability of the tracking error.

Robust Control for the Segway with Unknown Control Coefficient and Model Uncertainties

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Byung Woo Kim

2016-06-01

Full Text Available The Segway, which is a popular vehicle nowadays, is an uncertain nonlinear system and has an unknown time-varying control coefficient. Thus, we should consider the unknown time-varying control coefficient and model uncertainties to design the controller. Motivated by this observation, we propose a robust control for the Segway with unknown control coefficient and model uncertainties. To deal with the time-varying unknown control coefficient, we employ the Nussbaum gain technique. We introduce an auxiliary variable to solve the underactuated problem. Due to the prescribed performance control technique, the proposed controller does not require the adaptive technique, neural network, and fuzzy logic to compensate the uncertainties. Therefore, it can be simple. From the Lyapunov stability theory, we prove that all signals in the closed-loop system are bounded. Finally, we provide the simulation results to demonstrate the effectiveness of the proposed control scheme.

Dynamic stability of running: The effects of speed and leg amputations on the maximal Lyapunov exponent

International Nuclear Information System (INIS)

Look, Nicole; Arellano, Christopher J.; Grabowski, Alena M.; Kram, Rodger; McDermott, William J.; Bradley, Elizabeth

2013-01-01

In this paper, we study dynamic stability during running, focusing on the effects of speed, and the use of a leg prosthesis. We compute and compare the maximal Lyapunov exponents of kinematic time-series data from subjects with and without unilateral transtibial amputations running at a wide range of speeds. We find that the dynamics of the affected leg with the running-specific prosthesis are less stable than the dynamics of the unaffected leg and also less stable than the biological legs of the non-amputee runners. Surprisingly, we find that the center-of-mass dynamics of runners with two intact biological legs are slightly less stable than those of runners with amputations. Our results suggest that while leg asymmetries may be associated with instability, runners may compensate for this effect by increased control of their center-of-mass dynamics

Wavelet neural network load frequency controller

International Nuclear Information System (INIS)

Hemeida, Ashraf Mohamed

2005-01-01

This paper presents the feasibility of applying a wavelet neural network (WNN) approach for the load frequency controller (LFC) to damp the frequency oscillations of two area power systems due to load disturbances. The present intelligent control system trained the wavelet neural network (WNN) controller on line with adaptive learning rates, which are derived in the sense of a discrete type Lyapunov stability theorem. The present WNN controller is designed individually for each area. The proposed technique is applied successfully for a wide range of operating conditions. The time simulation results indicate its superiority and effectiveness over the conventional approach. The effects of consideration of the governor dead zone on the system performance are studied using the proposed controller and the conventional one

Design of a nonlinear backstepping control strategy of grid interconnected wind power system based PMSG

Science.gov (United States)

Errami, Y.; Obbadi, A.; Sahnoun, S.; Benhmida, M.; Ouassaid, M.; Maaroufi, M.

2016-07-01

This paper presents nonlinear backstepping control for Wind Power Generation System (WPGS) based Permanent Magnet Synchronous Generator (PMSG) and connected to utility grid. The block diagram of the WPGS with PMSG and the grid side back-to-back converter is established with the dq frame of axes. This control scheme emphasises the regulation of the dc-link voltage and the control of the power factor at changing wind speed. Besides, in the proposed control strategy of WPGS, Maximum Power Point Tracking (MPPT) technique and pitch control are provided. The stability of the regulators is assured by employing Lyapunov analysis. The proposed control strategy for the system has been validated by MATLAB simulations under varying wind velocity and the grid fault condition. In addition, a comparison of simulation results based on the proposed Backstepping strategy and conventional Vector Control is provided.

Global Tracking Control of Quadrotor VTOL Aircraft in Three-Dimensional Space

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Duc Khac Do

2014-07-01

Full Text Available This paper presents a method to design controllers that force a quadrotor vertical take-off and landing (VTOL aircraft to globally asymptotically track a reference trajectory in three-dimensional space. Motivated by the vehicle's steering practice, the roll and pitch angles are considered as immediate controls plus the total thrust force  provided by the aircraft's four rotors to control the position and yaw angle of the aircraft. The control design is based on the newly introduced one-step ahead backstepping, the standard backstepping and Lyapunov's direct methods. A combination of Euler angles and unit-quaternion for the attitude representation of the aircraft is used to obtain global tracking control results. The paper also includes a design of observers that exponentially estimate the aircraft's linear velocity vector and disturbances. Simulations illustrate the results.

Interaction of Lyapunov vectors in the formulation of the nonlinear extension of the Kalman filter.

Science.gov (United States)

Palatella, Luigi; Trevisan, Anna

2015-04-01

When applied to strongly nonlinear chaotic dynamics the extended Kalman filter (EKF) is prone to divergence due to the difficulty of correctly forecasting the forecast error probability density function. In operational forecasting applications ensemble Kalman filters circumvent this problem with empirical procedures such as covariance inflation. This paper presents an extension of the EKF that includes nonlinear terms in the evolution of the forecast error estimate. This is achieved starting from a particular square-root implementation of the EKF with assimilation confined in the unstable subspace (EKF-AUS), that is, the span of the Lyapunov vectors with non-negative exponents. When the error evolution is nonlinear, the space where it is confined is no more restricted to the unstable and neutral subspace causing filter divergence. The algorithm presented here, denominated EKF-AUS-NL, includes the nonlinear terms in the error dynamics: These result from the nonlinear interaction among the leading Lyapunov vectors and account for all directions where the error growth may take place. Numerical results show that with the nonlinear terms included, filter divergence can be avoided. We test the algorithm on the Lorenz96 model, showing very promising results.

Subgeometric Ergodicity Analysis of Continuous-Time Markov Chains under Random-Time State-Dependent Lyapunov Drift Conditions

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Mokaedi V. Lekgari

2014-01-01

Full Text Available We investigate random-time state-dependent Foster-Lyapunov analysis on subgeometric rate ergodicity of continuous-time Markov chains (CTMCs. We are mainly concerned with making use of the available results on deterministic state-dependent drift conditions for CTMCs and on random-time state-dependent drift conditions for discrete-time Markov chains and transferring them to CTMCs.

Robust Adaptive Sliding Mode Control for Generalized Function Projective Synchronization of Different Chaotic Systems with Unknown Parameters

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Xiuchun Li

2013-01-01

Full Text Available When the parameters of both drive and response systems are all unknown, an adaptive sliding mode controller, strongly robust to exotic perturbations, is designed for realizing generalized function projective synchronization. Sliding mode surface is given and the controlled system is asymptotically stable on this surface with the passage of time. Based on the adaptation laws and Lyapunov stability theory, an adaptive sliding controller is designed to ensure the occurrence of the sliding motion. Finally, numerical simulations are presented to verify the effectiveness and robustness of the proposed method even when both drive and response systems are perturbed with external disturbances.

Boundary control of fluid flow through porous media

DEFF Research Database (Denmark)

Hasan, Agus; Foss, Bjarne; Sagatun, Svein Ivar

2010-01-01

The flow of fluids through porous media can be described by the Boussinesq’s equation with mixed boundary conditions; a Neumann’s boundary condition and a nonlinear boundary condition. The nonlinear boundary condition provides a means to control the fluid flow through porous media. In this paper,......, some stabilizing controllers are constructed for various cases using Lyapunov design.......The flow of fluids through porous media can be described by the Boussinesq’s equation with mixed boundary conditions; a Neumann’s boundary condition and a nonlinear boundary condition. The nonlinear boundary condition provides a means to control the fluid flow through porous media. In this paper...

Robust control for constant thrust rendezvous under thrust failure

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Qi Yongqiang

2015-04-01

Full Text Available A robust constant thrust rendezvous approach under thrust failure is proposed based on the relative motion dynamic model. Firstly, the design problem is cast into a convex optimization problem by introducing a Lyapunov function subject to linear matrix inequalities. Secondly, the robust controllers satisfying the requirements can be designed by solving this optimization problem. Then, a new algorithm of constant thrust fitting is proposed through the impulse compensation and the fuel consumption under the theoretical continuous thrust and the actual constant thrust is calculated and compared by using the method proposed in this paper. Finally, the proposed method having the advantage of saving fuel is proved and the actual constant thrust switch control laws are obtained through the isochronous interpolation method, meanwhile, an illustrative example is provided to show the effectiveness of the proposed control design method.

Stability and Control of Large-Scale Dynamical Systems A Vector Dissipative Systems Approach

CERN Document Server

Haddad, Wassim M

2011-01-01

Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures. Large-scale dynami

Robust adaptive controller design for a class of uncertain nonlinear systems using online T-S fuzzy-neural modeling approach.

Science.gov (United States)

Chien, Yi-Hsing; Wang, Wei-Yen; Leu, Yih-Guang; Lee, Tsu-Tian

2011-04-01

This paper proposes a novel method of online modeling and control via the Takagi-Sugeno (T-S) fuzzy-neural model for a class of uncertain nonlinear systems with some kinds of outputs. Although studies about adaptive T-S fuzzy-neural controllers have been made on some nonaffine nonlinear systems, little is known about the more complicated uncertain nonlinear systems. Because the nonlinear functions of the systems are uncertain, traditional T-S fuzzy control methods can model and control them only with great difficulty, if at all. Instead of modeling these uncertain functions directly, we propose that a T-S fuzzy-neural model approximates a so-called virtual linearized system (VLS) of the system, which includes modeling errors and external disturbances. We also propose an online identification algorithm for the VLS and put significant emphasis on robust tracking controller design using an adaptive scheme for the uncertain systems. Moreover, the stability of the closed-loop systems is proven by using strictly positive real Lyapunov theory. The proposed overall scheme guarantees that the outputs of the closed-loop systems asymptotically track the desired output trajectories. To illustrate the effectiveness and applicability of the proposed method, simulation results are given in this paper.

Models and synchronization of time-delayed complex dynamical networks with multi-links based on adaptive control

International Nuclear Information System (INIS)

Peng Haipeng; Wei Nan; Li Lixiang; Xie Weisheng; Yang Yixian

2010-01-01

In this Letter, time-delay has been introduced in to split the networks, upon which a model of complex dynamical networks with multi-links has been constructed. Moreover, based on Lyapunov stability theory and some hypotheses, we achieve synchronization between two complex networks with different structures by designing effective controllers. The validity of the results was proved through numerical simulations of this Letter.

Synchronization and Control of Linearly Coupled Singular Systems

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Fang Qingxiang

2013-01-01

Full Text Available The synchronization and control problem of linearly coupled singular systems is investigated. The uncoupled dynamical behavior at each node is general and can be chaotic or, otherwise the coupling matrix is not assumed to be symmetrical. Some sufficient conditions for globally exponential synchronization are derived based on Lyapunov stability theory. These criteria, which are in terms of linear matrix inequality (LMI, indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold. The controllers are designed for state feedback control and pinning control, respectively. Finally, a numerical example is provided to illustrate the effectiveness of the proposed conditions.

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.

Command Filtered Adaptive Fuzzy Neural Network Backstepping Control for Marine Power System

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Xin Zhang

2014-01-01

Full Text Available In order to retrain chaotic oscillation of marine power system which is excited by periodic electromagnetism perturbation, a novel command-filtered adaptive fuzzy neural network backstepping control method is designed. First, the mathematical model of marine power system is established based on the two parallel nonlinear model. Then, main results of command-filtered adaptive fuzzy neural network backstepping control law are given. And the Lyapunov stability theory is applied to prove that the system can remain closed-loop asymptotically stable with this controller. Finally, simulation results indicate that the designed controller can suppress chaotic oscillation with fast convergence speed that makes the system return to the equilibrium point quickly; meanwhile, the parameter which induces chaotic oscillation can also be discriminated.

The Dynamics and Sliding Mode Control of Multiple Cooperative Welding Robot Manipulators

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Bin Zi

2012-08-01

Full Text Available This paper deals with the design, dynamic modelling and sliding mode control of multiple cooperative welding robot manipulators (MWRMs. The MWRMs can handle complex tasks that are difficult or even impossible for a single manipulator. The kinematics and dynamics of the MWRMs are studied on the basis of the Denavit-Hartenberg and Lagrange method. Following that, considering the MWRM system with nonlinear and unknown disturbances, a non-singular terminal sliding mode control strategy is designed. By means of the Lyapunov function, the stability of the controller is proved. Simulation results indicate that the good control performance of the MWRMs is achieved by the non-singular terminal sliding mode controller, which also illustrates the correctness of the dynamic modelling and effectiveness of the proposed control strategy.

Control system design guide

Energy Technology Data Exchange (ETDEWEB)

Sellers, David; Friedman, Hannah; Haasl, Tudi; Bourassa, Norman; Piette, Mary Ann

2003-05-01

The ''Control System Design Guide'' (Design Guide) provides methods and recommendations for the control system design process and control point selection and installation. Control systems are often the most problematic system in a building. A good design process that takes into account maintenance, operation, and commissioning can lead to a smoothly operating and efficient building. To this end, the Design Guide provides a toolbox of templates for improving control system design and specification. HVAC designers are the primary audience for the Design Guide. The control design process it presents will help produce well-designed control systems that achieve efficient and robust operation. The spreadsheet examples for control valve schedules, damper schedules, and points lists can streamline the use of the control system design concepts set forth in the Design Guide by providing convenient starting points from which designers can build. Although each reader brings their own unique questions to the text, the Design Guide contains information that designers, commissioning providers, operators, and owners will find useful.

Mixed H2/Hinfinity output-feedback control of second-order neutral systems with time-varying state and input delays.

Science.gov (United States)

Karimi, Hamid Reza; Gao, Huijun

2008-07-01

A mixed H2/Hinfinity output-feedback control design methodology is presented in this paper for second-order neutral linear systems with time-varying state and input delays. Delay-dependent sufficient conditions for the design of a desired control are given in terms of linear matrix inequalities (LMIs). A controller, which guarantees asymptotic stability and a mixed H2/Hinfinity performance for the closed-loop system of the second-order neutral linear system, is then developed directly instead of coupling the model to a first-order neutral system. A Lyapunov-Krasovskii method underlies the LMI-based mixed H2/Hinfinity output-feedback control design using some free weighting matrices. The simulation results illustrate the effectiveness of the proposed methodology.

High-Order Sliding Mode-Based Synchronous Control of a Novel Stair-Climbing Wheelchair Robot

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Juanxiu Liu

2015-01-01

Full Text Available For the attitude control of a novel stair-climbing wheelchair with inertial uncertainties and external disturbance torques, a new synchronous control method is proposed via combing high-order sliding mode control techniques with cross-coupling techniques. For this purpose, a proper controller is designed, which can improve the performance of the system under conditions of uncertainties and torque perturbations and also can guarantee the synchronization of the system. Firstly, a robust high-order sliding mode control law is designed to track the desired position trajectories effectively. Secondly, considering the coordination of the multiple joints, a high-order sliding mode synchronization controller is designed to reduce the synchronization errors and tracking errors based on the controller designed previously. Stability of the closed-loop system is proved by Lyapunov theory. The simulation is performed by MATLAB to verify the effectiveness of the proposed controller. By comparing the simulation results of two controllers, it is obvious that the proposed scheme has better performance and stronger robustness.

Reliable gain-scheduled control of discrete-time systems and its application to CSTR model

Science.gov (United States)

Sakthivel, R.; Selvi, S.; Mathiyalagan, K.; Shi, Y.

2016-10-01

This paper is focused on reliable gain-scheduled controller design for a class of discrete-time systems with randomly occurring nonlinearities and actuator fault. Further, the nonlinearity in the system model is assumed to occur randomly according to a Bernoulli distribution with measurable time-varying probability in real time. The main purpose of this paper is to design a gain-scheduled controller by implementing a probability-dependent Lyapunov function and linear matrix inequality (LMI) approach such that the closed-loop discrete-time system is stochastically stable for all admissible randomly occurring nonlinearities. The existence conditions for the reliable controller is formulated in terms of LMI constraints. Finally, the proposed reliable gain-scheduled control scheme is applied on continuously stirred tank reactor model to demonstrate the effectiveness and applicability of the proposed design technique.

Sensor fault detection and recovery in satellite attitude control

Science.gov (United States)

Nasrolahi, Seiied Saeed; Abdollahi, Farzaneh

2018-04-01

This paper proposes an integrated sensor fault detection and recovery for the satellite attitude control system. By introducing a nonlinear observer, the healthy sensor measurements are provided. Considering attitude dynamics and kinematic, a novel observer is developed to detect the fault in angular rate as well as attitude sensors individually or simultaneously. There is no limit on type and configuration of attitude sensors. By designing a state feedback based control signal and Lyapunov stability criterion, the uniformly ultimately boundedness of tracking errors in the presence of sensor faults is guaranteed. Finally, simulation results are presented to illustrate the performance of the integrated scheme.

Optimal and robust control of a class of nonlinear systems using dynamically re-optimised single network adaptive critic design

Science.gov (United States)

Tiwari, Shivendra N.; Padhi, Radhakant

2018-01-01

Following the philosophy of adaptive optimal control, a neural network-based state feedback optimal control synthesis approach is presented in this paper. First, accounting for a nominal system model, a single network adaptive critic (SNAC) based multi-layered neural network (called as NN1) is synthesised offline. However, another linear-in-weight neural network (called as NN2) is trained online and augmented to NN1 in such a manner that their combined output represent the desired optimal costate for the actual plant. To do this, the nominal model needs to be updated online to adapt to the actual plant, which is done by synthesising yet another linear-in-weight neural network (called as NN3) online. Training of NN3 is done by utilising the error information between the nominal and actual states and carrying out the necessary Lyapunov stability analysis using a Sobolev norm based Lyapunov function. This helps in training NN2 successfully to capture the required optimal relationship. The overall architecture is named as 'Dynamically Re-optimised single network adaptive critic (DR-SNAC)'. Numerical results for two motivating illustrative problems are presented, including comparison studies with closed form solution for one problem, which clearly demonstrate the effectiveness and benefit of the proposed approach.

Outer synchronization of complex networks with internal delay and coupling delay via aperiodically intermittent pinning control

Science.gov (United States)

Zhang, Chuan; Wang, Xingyuan; Wang, Chunpeng; Xia, Zhiqiu

This paper concerns the outer synchronization problem between two complex delayed networks via the method of aperiodically intermittent pinning control. Apart from previous works, internal delay and coupling delay are both involved in this model, and the designed intermittent controllers can be aperiodic. The main work in this paper can be summarized as follows: First, two cases of aperiodically intermittent control with constant gain and adaptive gain are implemented, respectively. The intermittent control and pinning control are combined to reduce consumptions further. Then, based on the Lyapunov stability theory, synchronization protocols are given by strict derivation. Especially, the designed controllers are indeed simple and valid in application of theory to practice. Finally, numerical examples put the proposed control methods to the test.

Design of Optimal Hybrid Position/Force Controller for a Robot Manipulator Using Neural Networks

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Vikas Panwar

2007-01-01

Full Text Available The application of quadratic optimization and sliding-mode approach is considered for hybrid position and force control of a robot manipulator. The dynamic model of the manipulator is transformed into a state-space model to contain two sets of state variables, where one describes the constrained motion and the other describes the unconstrained motion. The optimal feedback control law is derived solving matrix differential Riccati equation, which is obtained using Hamilton Jacobi Bellman optimization. The optimal feedback control law is shown to be globally exponentially stable using Lyapunov function approach. The dynamic model uncertainties are compensated with a feedforward neural network. The neural network requires no preliminary offline training and is trained with online weight tuning algorithms that guarantee small errors and bounded control signals. The application of the derived control law is demonstrated through simulation with a 4-DOF robot manipulator to track an elliptical planar constrained surface while applying the desired force on the surface.

Adaptive fuzzy sliding-mode control for multi-input multi-output chaotic systems

International Nuclear Information System (INIS)

Poursamad, Amir; Markazi, Amir H.D.

2009-01-01

This paper describes an adaptive fuzzy sliding-mode control algorithm for controlling unknown or uncertain, multi-input multi-output (MIMO), possibly chaotic, dynamical systems. The control approach encompasses a fuzzy system and a robust controller. The fuzzy system is designed to mimic an ideal sliding-mode controller, and the robust controller compensates the difference between the fuzzy controller and the ideal one. The parameters of the fuzzy system, as well as the uncertainty bound of the robust controller, are tuned adaptively. The adaptive laws are derived in the Lyapunov sense to guarantee the asymptotic stability and tracking of the controlled system. The effectiveness of the proposed method is shown by applying it to some well-known chaotic systems.

Analysis, Adaptive Control and Anti-Synchronization of a Six-Term Novel Jerk Chaotic System with two Exponential Nonlinearities and its Circuit Simulation

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S. Vaidyanathan

2014-11-01

Full Text Available This research work proposes a six-term novel 3-D jerk chaotic system with two exponential nonlinearities. This work also analyses system’s fundamental properties such as dissipativity, equilibria, Lyapunov exponents and Kaplan-Yorke dimension. The phase portraits of the jerk chaotic system simulated using MATLAB, depict the strange chaotic attractor of the system. For the parameter values and initial conditions chosen in this work, the Lyapunov exponents of the novel jerk chaotic system are obtained as L1 = 0.24519, L2 = 0 and L3 = −0.84571. Also, the Kaplan-Yorke dimension of the novel jerk chaotic system is obtained as DKY = 2.2899. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system having two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve global chaos anti-synchronization of two identical novel jerk chaotic systems with two unknown system parameters. Finally, an electronic circuit realization of the novel jerk chaotic system is presented using SPICE to confirm the feasibility of the theoretical model.

Synthetic jet flow control of two-dimensional NACA 65(1)-412 airfoil flow with finite-time lyapunov exponent analysis of Lagrangian coherent structures

Science.gov (United States)

Jeong, Peter Inuk

Synthetic jet (SJ) control of a low-Reynolds number, unsteady, compressible, viscous flow over a NACA 65-(1)412 airfoil, typical for unmanned air vehicles and gas turbines, has been investigated computationally. A particular focus was placed in the development and control of Lagrangian Coherent Structures (LCS) and the associated Finite-Time Lyapunov Exponent (FTLE) fields. The FTLE fields quantitatively measure of the repulsion rate in forward-time and the attraction rate in backward-time, and provide a unique perspective on effective flow control. A Discontinuous-Galerkin (DG) methods, high-fidelity Navier-Stokes solver performs direct numerical simulation (DNS) of the airfoil flow. Three SJ control strategies have been investigated: immediately downstream of flow separation, normal to the separated shear layer; near the leading edge, normal to the airfoil suction side; near the trailing edge, normal to the airfoil pressure side. A finite difference algorithm computes the FTLE from DNS velocity data. A baseline flow without SJ control is compared to SJ actuated flows. The baseline flow forms a regular, time-periodic, asymmetric von Karman vortex street in the wake. The SJ downstream of flow separation increases recirculation region vorticity and reduces the effective angle of attack. This decreases the time-averaged lift by 2:98% and increases the time-averaged drag by 5:21%. The leading edge SJ produces small vortices that deflect the shear layer downwards, and decreases the effective angle of attack. This reduces the time-averaged lift by 1:80%, and the time-averaged drag by 1:84%. The trailing edge SJ produces perturbations that add to pressure side vortices without affecting global flow characteristics. The time-averaged lift decreases by 0:47%, and the time-averaged drag increases by 0:20%. For all SJ cases, the aerodynamic performance is much more dependent on changes to the pressure distribution than changes to the skin friction distribution. No proposed

A Novel Secondary Control for Microgrid Based on Synergetic Control of Multi-Agent System

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Zhiwen Yu

2016-03-01

Full Text Available In power systems, the secondary control is a very useful way to restore the system frequency and voltage to the rated value. This paper tries to propose a secondary frequency and voltage control of islanded microgrids based on the distributed synergetic control of multi-agent systems. In the proposed control, since each distributed generation only requires its own information and that of the neighbors, the secondary control is fully distributed. The system is more reliable because the central controller and complex communication network are reduced in the distributed structure. Based on multi-agent systems, the dynamic model is established, and distributed synergetic control algorithms are given to design the secondary control of the islanded microgrid. Meanwhile, the system has globally asymptotic stability under the proposed control, which is proved by the direct Lyapunov method. Simulation results about a test microgrid are given to verify the effectiveness of the proposed control.

Chaos synchronization of a new chaotic system via nonlinear control

International Nuclear Information System (INIS)

Zhang Qunjiao; Lu Junan

2008-01-01

This paper investigates chaos synchronization of a new chaotic system [Lue J, Chen G, Cheng D. A new chaotic system and beyond: the generalized Lorenz-like system. Int J Bifurcat Chaos 2004;14:1507-37]. Two kinds of novel nonlinear controllers are designed based on the Lyapunov stability theory. It can be viewed as an improvement to the existing results of reference [Park JH. Chaos synchronization of a chaotic system via nonlinear control. Chaos, Solitons and Fractals 2005;25:579-84] because we use less controllers but realize a global and exponential asymptotical synchronization. Numerical simulations are provided to show the effectiveness and advantage of this method

Neural network-based optimal adaptive output feedback control of a helicopter UAV.

Science.gov (United States)

Nodland, David; Zargarzadeh, Hassan; Jagannathan, Sarangapani

2013-07-01

Helicopter unmanned aerial vehicles (UAVs) are widely used for both military and civilian operations. Because the helicopter UAVs are underactuated nonlinear mechanical systems, high-performance controller design for them presents a challenge. This paper introduces an optimal controller design via an output feedback for trajectory tracking of a helicopter UAV, using a neural network (NN). The output-feedback control system utilizes the backstepping methodology, employing kinematic and dynamic controllers and an NN observer. The online approximator-based dynamic controller learns the infinite-horizon Hamilton-Jacobi-Bellman equation in continuous time and calculates the corresponding optimal control input by minimizing a cost function, forward-in-time, without using the value and policy iterations. Optimal tracking is accomplished by using a single NN utilized for the cost function approximation. The overall closed-loop system stability is demonstrated using Lyapunov analysis. Finally, simulation results are provided to demonstrate the effectiveness of the proposed control design for trajectory tracking.

Adaptive Sliding Control for a Class of Fractional Commensurate Order Chaotic Systems

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Jian Yuan

2015-01-01

Full Text Available This paper proposes adaptive sliding mode control design for a class of fractional commensurate order chaotic systems. We firstly introduce a fractional integral sliding manifold for the nominal systems. Secondly we prove the stability of the corresponding fractional sliding dynamics. Then, by introducing a Lyapunov candidate function and using the Mittag-Leffler stability theory we derive the desired sliding control law. Furthermore, we prove that the proposed sliding manifold is also adapted for the fractional systems in the presence of uncertainties and external disturbances. At last, we design a fractional adaptation law for the perturbed fractional systems. To verify the viability and efficiency of the proposed fractional controllers, numerical simulations of fractional Lorenz’s system and Chen’s system are presented.

Recursive Backstepping Stabilization of a Wheeled Mobile Robot

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Faical Mnif

2004-12-01

Full Text Available This research is aimed to the development of a dynamic control to enhance the performance of the existing dynamic controllers for mobile robots. System dynamics of the car-like robot with nonholonomic constraints were employed. A Backstepping approach for the design of discontinuous state feedback controller is used for the design of the controller. It is shown that the origin of the closed loop system can be made stable in the sense of Lyapunov. The control design is made on the basis of a suitable Lyapunov function candidate. The effectiveness of the proposed approach is tested through simulation on a car-like vehicle mobile robot.

Observer Based Sliding Mode Attitude Control: Theoretical and Experimental Results

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U. Jørgensen

2011-07-01

Full Text Available In this paper we present the design of a sliding mode controller for attitude control of spacecraft actuated by three orthogonal reaction wheels. The equilibrium of the closed loop system is proved to be asymptotically stable in the sense of Lyapunov. Due to cases where spacecraft do not have angular velocity measurements, an estimator for the generalized velocity is derived and asymptotic stability is proven for the observer. The approach is tested on an experimental platform with a sphere shaped Autonomous Underwater Vehicle SATellite: AUVSAT, developed at the Norwegian University of Science and Technology.

Adaptive Fractional Fuzzy Sliding Mode Control for Multivariable Nonlinear Systems

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Junhai Luo

2014-01-01

Full Text Available This paper presents a robust adaptive fuzzy sliding mode control method for a class of uncertain nonlinear systems. The fractional order calculus is employed in the parameter updating stage. The underlying stability analysis as well as parameter update law design is carried out by Lyapunov based technique. In the simulation, two examples including a comparison with the traditional integer order counterpart are given to show the effectiveness of the proposed method. The main contribution of this paper consists in the control performance is better for the fractional order updating law than that of traditional integer order.

Fractional order sliding-mode control based on parameters auto-tuning for velocity control of permanent magnet synchronous motor.

Science.gov (United States)

Zhang, BiTao; Pi, YouGuo; Luo, Ying

2012-09-01

A fractional order sliding mode control (FROSMC) scheme based on parameters auto-tuning for the velocity control of permanent magnet synchronous motor (PMSM) is proposed in this paper. The control law of the proposed F(R)OSMC scheme is designed according to Lyapunov stability theorem. Based on the property of transferring energy with adjustable type in F(R)OSMC, this paper analyzes the chattering phenomenon in classic sliding mode control (SMC) is attenuated with F(R)OSMC system. A fuzzy logic inference scheme (FLIS) is utilized to obtain the gain of switching control. Simulations and experiments demonstrate that the proposed FROSMC not only achieve better control performance with smaller chatting than that with integer order sliding mode control, but also is robust to external load disturbance and parameter variations. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

Minimal-Learning-Parameter Technique Based Adaptive Neural Sliding Mode Control of MEMS Gyroscope

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Bin Xu

2017-01-01

Full Text Available This paper investigates an adaptive neural sliding mode controller for MEMS gyroscopes with minimal-learning-parameter technique. Considering the system uncertainty in dynamics, neural network is employed for approximation. Minimal-learning-parameter technique is constructed to decrease the number of update parameters, and in this way the computation burden is greatly reduced. Sliding mode control is designed to cancel the effect of time-varying disturbance. The closed-loop stability analysis is established via Lyapunov approach. Simulation results are presented to demonstrate the effectiveness of the method.

Multilateral Telecoordinated Control of Multiple Robots With Uncertain Kinematics.

Science.gov (United States)

Zhai, Di-Hua; Xia, Yuanqing

2017-06-06

This paper addresses the telecoordinated control of multiple robots in the simultaneous presence of asymmetric time-varying delays, nonpassive external forces, and uncertain kinematics/dynamics. To achieve the control objective, a neuroadaptive controller with utilizing prescribed performance control and switching control technique is developed, where the basic idea is to employ the concept of motion synchronization in each pair of master-slave robots and among all slave robots. By using the multiple Lyapunov-Krasovskii functionals method, the state-independent input-to-output practical stability of the closed-loop system is established. Compared with the previous approaches, the new design is straightforward and easier to implement and is applicable to a wider area. Simulation results on three pairs of three degrees-of-freedom robots confirm the theoretical findings.

Adaptive control of an exoskeleton robot with uncertainties on kinematics and dynamics.

Science.gov (United States)

Brahmi, Brahim; Saad, Maarouf; Ochoa-Luna, Cristobal; Rahman, Mohammad H

2017-07-01

In this paper, we propose a new adaptive control technique based on nonlinear sliding mode control (JSTDE) taking into account kinematics and dynamics uncertainties. This approach is applied to an exoskeleton robot with uncertain kinematics and dynamics. The adaptation design is based on Time Delay Estimation (TDE). The proposed strategy does not necessitate the well-defined dynamic and kinematic models of the system robot. The updated laws are designed using Lyapunov-function to solve the adaptation problem systematically, proving the close loop stability and ensuring the convergence asymptotically of the outputs tracking errors. Experiments results show the effectiveness and feasibility of JSTDE technique to deal with the variation of the unknown nonlinear dynamics and kinematics of the exoskeleton model.

A Hybrid Sensor Based Backstepping Control Approach with its Application to Fault-Tolerant Flight Control

NARCIS (Netherlands)

Sun, L.G.; De Visser, C.C.; Chu, Q.P.; Falkena, W.

2013-01-01

Recently, an incremental type sensor based backstepping (SBB) control approach, based on singular perturbation theory and Tikhonov’s theorem, has been proposed. This Lyapunov function based method uses measurements of control variables and less model knowledge, and it is not susceptible to the model

Control room design

International Nuclear Information System (INIS)

Zinke, H.

1980-01-01

To control a 1300 megawatt nuclear power plant, about 15000 plant parameters must be collected together to control and operate the plant. The control room design therefore is of particular importance. The main design criteria are: Required functions of the power plant process - Level of Automation - Ergonomics - Available Technology. Extensive analysis has resulted in a control room design method. This ensures that an objective solution will be reached. Resulting from this methodical approach are: 1. Scope, position and appearance of the instrumentation. 2. Scope, position and appearance of the operator controls. Process analysis dictates what instrumentation and operator controls are needed. The priority and importance of the control and instrumentation (this we define as the utilisation areas), dictates the rough layout of the control room. (orig./RW)

Fractional-order active fault-tolerant force-position controller design for the legged robots using saturated actuator with unknown bias and gain degradation

Science.gov (United States)

Farid, Yousef; Majd, Vahid Johari; Ehsani-Seresht, Abbas

2018-05-01

In this paper, a novel fault accommodation strategy is proposed for the legged robots subject to the actuator faults including actuation bias and effective gain degradation as well as the actuator saturation. First, the combined dynamics of two coupled subsystems consisting of the dynamics of the legs subsystem and the body subsystem are developed. Then, the interaction of the robot with the environment is formulated as the contact force optimization problem with equality and inequality constraints. The desired force is obtained by a dynamic model. A robust super twisting fault estimator is proposed to precisely estimate the defective torque amplitude of the faulty actuator in finite time. Defining a novel fractional sliding surface, a fractional nonsingular terminal sliding mode control law is developed. Moreover, by introducing a suitable auxiliary system and using its state vector in the designed controller, the proposed fault-tolerant control (FTC) scheme guarantees the finite-time stability of the closed-loop control system. The robustness and finite-time convergence of the proposed control law is established using the Lyapunov stability theory. Finally, numerical simulations are performed on a quadruped robot to demonstrate the stable walking of the robot with and without actuator faults, and actuator saturation constraints, and the results are compared to results with an integer order fault-tolerant controller.

Optimal Sliding Mode Controllers for Attitude Stabilization of Flexible Spacecraft

Directory of Open Access Journals (Sweden)

Chutiphon Pukdeboon

2011-01-01

Full Text Available The robust optimal attitude control problem for a flexible spacecraft is considered. Two optimal sliding mode control laws that ensure the exponential convergence of the attitude control system are developed. Integral sliding mode control (ISMC is applied to combine the first-order sliding mode with optimal control and is used to control quaternion-based spacecraft attitude manoeuvres with external disturbances and an uncertainty inertia matrix. For the optimal control part the state-dependent Riccati equation (SDRE and optimal Lyapunov techniques are employed to solve the infinite-time nonlinear optimal control problem. The second method of Lyapunov is used to guarantee the stability of the attitude control system under the action of the proposed control laws. An example of multiaxial attitude manoeuvres is presented and simulation results are included to verify the usefulness of the developed controllers.

Lane Changing Trajectory Planning and Tracking Controller Design for Intelligent Vehicle Running on Curved Road

Directory of Open Access Journals (Sweden)

Lie Guo

2014-01-01

Full Text Available To enhance the active safety and realize the autonomy of intelligent vehicle on highway curved road, a lane changing trajectory is planned and tracked for lane changing maneuver on curved road. The kinematics model of the intelligent vehicle with nonholonomic constraint feature and the tracking error model are established firstly. The longitudinal and lateral coupling and the difference of curvature radius between the outside and inside lane are taken into account, which is helpful to enhance the authenticity of desired lane changing trajectory on curved road. Then the trajectory tracking controller of closed-loop control structure is derived using integral backstepping method to construct a new virtual variable. The Lyapunov theory is applied to analyze the stability of the proposed tracking controller. Simulation results demonstrate that this controller can guarantee the convergences of both the relative position tracking errors and the position tracking synchronization.

Control synthesis of switched systems

CERN Document Server

Zhao, Xudong; Niu, Ben; Wu, Tingting

2017-01-01

This book offers its readers a detailed overview of the synthesis of switched systems, with a focus on switching stabilization and intelligent control. The problems investigated are not only previously unsolved theoretically but also of practical importance in many applications: voltage conversion, naval piloting and navigation and robotics, for example. The book considers general switched-system models and provides more efficient design methods to bring together theory and application more closely than was possible using classical methods. It also discusses several different classes of switched systems. For general switched linear systems and switched nonlinear systems comprising unstable subsystems, it introduces novel ideas such as invariant subspace theory and the time-scheduled Lyapunov function method of designing switching signals to stabilize the underlying systems. For some typical switched nonlinear systems affected by various complex dynamics, the book proposes novel design approaches based on inte...

Backstepping-based nonlinear adaptive control for coal-fired utility boiler-turbine units

International Nuclear Information System (INIS)

Fang, Fang; Wei, Le

2011-01-01

The control system of boiler-turbine unit plays an important role in improving efficiency and reducing emissions of power generation unit. The nonlinear, coupling and uncertainty of the unit caused by varying working conditions should be fully considered during the control system design. This paper presents an efficient control scheme based on backstepping theory for improving load adaptability of boiler-turbines in wide operation range. The design process of the scheme includes model preprocessing, control Lyapunov functions selection, interlaced computation of adaptive control laws, etc. For simplification and accuracy, differential of steam pipe inlet pressure and integral terms of target errors are adopted. Also, to enhance practicality, implementation steps of the scheme are proposed. A practical nonlinear model of a 500 MW coal-fired boiler-turbine unit is used to test the efficiency of the proposed scheme in different conditions.

Design of stability-guaranteed fuzzy logic controller for nuclear steam generators

International Nuclear Information System (INIS)

Cho, B.H.; No, H.C.

1996-01-01

A fuzzy logic controller (FLC) and a fuzzy logic filter (FLF), which have a special type of fuzzifier, inference engine, and defuzzifier, are applied to the water level control of a nuclear steam generator (S/G). It is shown that arbitrary two-input, single-output linear controllers can be adequately expressed by this FLC. A procedure to construct stability-guaranteed FLC rules is proposed. It contains the following steps: (1) the stable sector of linear feedback gains is obtained from the suboptimal concept based on LQR theory and the Lyapunov's stability criteria; (2) the stable sector of linear gains is mapped into two linear rule tables that are used as limits for the FLC rules; and (3) the construction of an FLC rule table is done by choosing certain rules that lie between these limits. This type of FLC guarantees asymptotic stability of the control system. The FLF generates a feedforward signal of S/G feedwater from the steam flow measurement using a fuzzy concept. Through computer simulation, it is found that the FLC with the FLF works better than a well-tuned PID controller with variable gains to reduce swell/shrink phenomena, especially for the water level deviation and abrupt steam flow disturbances that are typical in the existing power plants

Development of Analysis Tools for Certification of Flight Control Laws

Science.gov (United States)

2009-03-31

In Proc. Conf. on Decision and Control, pages 881-886, Bahamas, 2004. [7] G. Chesi, A. Garulli, A. Tesi , and A. Vicino. LMI-based computation of...Minneapolis, MN, 2006, pp. 117-122. [10] G. Chesi, A. Garulli, A. Tesi . and A. Vicino, "LMI-based computation of optimal quadratic Lyapunov functions...Convex Optimization. Cambridge Univ. Press. Chesi, G., A. Garulli, A. Tesi and A. Vicino (2005). LMI-based computation of optimal quadratic Lyapunov

Effective Power-Law Dependence of Lyapunov Exponents on the Central Mass in Galaxies

Science.gov (United States)

Delis, N.; Efthymiopoulos, C.; Kalapotharakos, C.

2015-01-01

Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L alpha m(sup p) between themean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p approximately equals 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local 'stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 - q with q approximately equaling 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x(sub 1) family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution of galaxies are discussed.

Synchronization and anti-synchronization coexist in Chen-Lee chaotic systems

International Nuclear Information System (INIS)

Chen, J.-H.; Chen, H.-K.; Lin, Y.-K.

2009-01-01

This study demonstrates that synchronization and anti-synchronization can coexist in Chen-Lee chaotic systems by direct linear coupling. Based on Lyapunov's direct method, a linear controller was designed to assure that two different types of synchronization can simultaneously be achieved. Further, the hybrid projective synchronization of Chen-Lee chaotic systems was studied using a nonlinear control scheme. The nonlinear controller was designed according to the Lyapunov stability theory to guarantee the hybrid projective synchronization, including synchronization, anti-synchronization, and projective synchronization. Finally, numerical examples are presented in order to illustrate the proposed synchronization approach.

Robust Tracking Control for a Piezoelectric Actuator

National Research Council Canada - National Science Library

Salah, M; McIntyre, M; Dawson, D; Wagner, J

2006-01-01

In this paper, a hysteresis model-based nonlinear robust controller is developed for a piezoelectric actuator, utilizing a Lyapunov-based stability analysis, which ensures that a desired displacement...

Cluster synchronization of community network with distributed time delays via impulsive control

International Nuclear Information System (INIS)

Leng Hui; Wu Zhao-Yan

2016-01-01

Cluster synchronization is an important dynamical behavior in community networks and deserves further investigations. A community network with distributed time delays is investigated in this paper. For achieving cluster synchronization, an impulsive control scheme is introduced to design proper controllers and an adaptive strategy is adopted to make the impulsive controllers unified for different networks. Through taking advantage of the linear matrix inequality technique and constructing Lyapunov functions, some synchronization criteria with respect to the impulsive gains, instants, and system parameters without adaptive strategy are obtained and generalized to the adaptive case. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results. (paper)

Non-fragile ?-? control for discrete-time stochastic nonlinear systems under event-triggered protocols

Science.gov (United States)

Sun, Ying; Ding, Derui; Zhang, Sunjie; Wei, Guoliang; Liu, Hongjian

2018-07-01

In this paper, the non-fragile ?-? control problem is investigated for a class of discrete-time stochastic nonlinear systems under event-triggered communication protocols, which determine whether the measurement output should be transmitted to the controller or not. The main purpose of the addressed problem is to design an event-based output feedback controller subject to gain variations guaranteeing the prescribed disturbance attenuation level described by the ?-? performance index. By utilizing the Lyapunov stability theory combined with S-procedure, a sufficient condition is established to guarantee both the exponential mean-square stability and the ?-? performance for the closed-loop system. In addition, with the help of the orthogonal decomposition, the desired controller parameter is obtained in terms of the solution to certain linear matrix inequalities. Finally, a simulation example is exploited to demonstrate the effectiveness of the proposed event-based controller design scheme.

Generalized Mutual Synchronization between Two Controlled Interdependent Networks

Directory of Open Access Journals (Sweden)

Quan Xu

2014-01-01

Full Text Available This paper mainly focuses on the generalized mutual synchronization between two controlled interdependent networks. First, we propose the general model of controlled interdependent networks A and B with time-varying internetwork delays coupling. Then, by constructing Lyapunov functions and utilizing adaptive control technique, some sufficient conditions are established to ensure that the mutual synchronization errors between the state variables of networks A and B can asymptotically converge to zero. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results and to explore potential application in future smart grid. The simulation results also show how interdependent topologies and internetwork coupling delays influence the mutual synchronizability, which help to design interdependent networks with optimal mutual synchronizability.

Estimate of the largest Lyapunov characteristic exponent of a high dimensional atmospheric global circulation model: a sensitivity analysis

International Nuclear Information System (INIS)

Guerrieri, A.

2009-01-01

In this report the largest Lyapunov characteristic exponent of a high dimensional atmospheric global circulation model of intermediate complexity has been estimated numerically. A sensitivity analysis has been carried out by varying the equator-to-pole temperature difference, the space resolution and the value of some parameters employed by the model. Chaotic and non-chaotic regimes of circulation have been found. [it

Robust intelligent sliding model control using recurrent cerebellar model articulation controller for uncertain nonlinear chaotic systems

International Nuclear Information System (INIS)

Peng Yafu

2009-01-01

In this paper, a robust intelligent sliding model control (RISMC) scheme using an adaptive recurrent cerebellar model articulation controller (RCMAC) is developed for a class of uncertain nonlinear chaotic systems. This RISMC system offers a design approach to drive the state trajectory to track a desired trajectory, and it is comprised of an adaptive RCMAC and a robust controller. The adaptive RCMAC is used to mimic an ideal sliding mode control (SMC) due to unknown system dynamics, and a robust controller is designed to recover the residual approximation error for guaranteeing the stable characteristic. Moreover, the Taylor linearization technique is employed to derive the linearized model of the RCMAC. The all adaptation laws of the RISMC system are derived based on the Lyapunov stability analysis and projection algorithm, so that the stability of the system can be guaranteed. Finally, the proposed RISMC system is applied to control a Van der Pol oscillator, a Genesio chaotic system and a Chua's chaotic circuit. The effectiveness of the proposed control scheme is verified by some simulation results with unknown system dynamics and existence of external disturbance. In addition, the advantages of the proposed RISMC are indicated in comparison with a SMC system

Core Power Control of the fast nuclear reactors with estimation of the delayed neutron precursor density using Sliding Mode method

International Nuclear Information System (INIS)

Ansarifar, G.R.; Nasrabadi, M.N.; Hassanvand, R.

2016-01-01

Highlights: • We present a S.M.C. system based on the S.M.O for control of a fast reactor power. • A S.M.O has been developed to estimate the density of delayed neutron precursor. • The stability analysis has been given by means Lyapunov approach. • The control system is guaranteed to be stable within a large range. • The comparison between S.M.C. and the conventional PID controller has been done. - Abstract: In this paper, a nonlinear controller using sliding mode method which is a robust nonlinear controller is designed to control a fast nuclear reactor. The reactor core is simulated based on the point kinetics equations and one delayed neutron group. Considering the limitations of the delayed neutron precursor density measurement, a sliding mode observer is designed to estimate it and finally a sliding mode control based on the sliding mode observer is presented. The stability analysis is given by means Lyapunov approach, thus the control system is guaranteed to be stable within a large range. Sliding Mode Control (SMC) is one of the robust and nonlinear methods which have several advantages such as robustness against matched external disturbances and parameter uncertainties. The employed method is easy to implement in practical applications and moreover, the sliding mode control exhibits the desired dynamic properties during the entire output-tracking process independent of perturbations. Simulation results are presented to demonstrate the effectiveness of the proposed controller in terms of performance, robustness and stability.

Nonlinear Control of Back-to-Back VSC-HVDC System via Command-Filter Backstepping

Directory of Open Access Journals (Sweden)

Jie Huang

2017-01-01

Full Text Available This paper proposed a command-filtered backstepping controller to improve the dynamic performance of back-to-back voltage-source-converter high voltage direct current (BTB VSC-HVDC. First, the principle and model of BTB VSC-HVDC in abc and d-q frame are described. Then, backstepping method is applied to design a controller to maintain the voltage balance and realize coordinated control of active and reactive power. Meanwhile, command filter is introduced to deal with the problem of input saturation and explosion of complexity in conventional backstepping, and a filter compensation signal is designed to diminish the adverse effects caused by the command filter. Next, the stability and convergence of the whole system are proved via the Lyapunov theorem of asymptotic stability. Finally, simulation results are given to demonstrate that proposed controller has a better dynamic performance and stronger robustness compared to the traditional PID algorithm, which also proves the effectiveness and possibility of the designed controller.

Robust high-precision attitude control for flexible spacecraft with improved mixed H2/H∞ control strategy under poles assignment constraint

Science.gov (United States)

Liu, Chuang; Ye, Dong; Shi, Keke; Sun, Zhaowei

2017-07-01

A novel improved mixed H2/H∞ control technique combined with poles assignment theory is presented to achieve attitude stabilization and vibration suppression simultaneously for flexible spacecraft in this paper. The flexible spacecraft dynamics system is described and transformed into corresponding state space form. Based on linear matrix inequalities (LMIs) scheme and poles assignment theory, the improved mixed H2/H∞ controller does not restrict the equivalence of the two Lyapunov variables involved in H2 and H∞ performance, which can reduce conservatives compared with traditional mixed H2/H∞ controller. Moreover, it can eliminate the coupling of Lyapunov matrix variables and system matrices by introducing slack variable that provides additional degree of freedom. Several simulations are performed to demonstrate the effectiveness and feasibility of the proposed method in this paper.

Path following of an Underactuated AUV Based on Fuzzy Backstepping Sliding Mode Control

Directory of Open Access Journals (Sweden)

Xiao Liang

2016-06-01

Full Text Available This paper addresses the path following problem of an underactuated autonomous underwater vehicle (AUV with the aim of dealing with parameter uncertainties and current disturbances. An adaptive robust control system was proposed by employing fuzzy logic, backstepping and sliding mode control theory. Fuzzy logic theory is adopted to approximate unknown system function, and the controller was designed by combining sliding mode control with backstepping thought. Firstly, the longitudinal speed was controlled, then the yaw angle was made as input of path following error to design the calm function and the change rate of path parameters. The controller stability was proved by Lyapunov stable theory. Simulation and outfield tests were conducted and the results showed that the controller is of excellent adaptability and robustness in the presence of parameter uncertainties and external disturbances. It is also shown to be able to avoid the chattering of AUV actuators.

Detection of the onset of numerical chaotic instabilities by lyapunov exponents

Directory of Open Access Journals (Sweden)

Alicia Serfaty De Markus

2001-01-01

Full Text Available It is commonly found in the fixed-step numerical integration of nonlinear differential equations that the size of the integration step is opposite related to the numerical stability of the scheme and to the speed of computation. We present a procedure that establishes a criterion to select the largest possible step size before the onset of chaotic numerical instabilities, based upon the observation that computational chaos does not occur in a smooth, continuous way, but rather abruptly, as detected by examining the largest Lyapunov exponent as a function of the step size. For completeness, examination of the bifurcation diagrams with the step reveals the complexity imposed by the algorithmic discretization, showing the robustness of a scheme to numerical instabilities, illustrated here for explicit and implicit Euler schemes. An example of numerical suppression of chaos is also provided.

Nonlinear Disturbance Observer Based Robust Tracking Control of Pneumatic Muscle

Directory of Open Access Journals (Sweden)

Youssif Mohamed Toum Elobaid

2014-01-01

Full Text Available Presently pneumatic muscles (PMs are used in various applications due to their simple construction, lightweight, and high force-to-weight ratio. However, pneumatic muscles are facing various problems due to their nonlinear characteristics and various uncertainties in real applications. To cope with the uncertainties and strong nonlinearity of a PM model, a nonlinear disturbance observer (NDO is designed to estimate the lumped disturbance. Based on the disturbance observer, the tracking control of PM is studied. Stability analysis based on Lyapunov method with respect to our proposed control law is discussed. The simulation results show the validity, effectiveness, and enhancing robustness of the proposed methods.

A new robust control for minirotorcraft unmanned aerial vehicles.

Science.gov (United States)

Mokhtari, M Rida; Cherki, Brahim

2015-05-01

This paper presents a new robust control based on finite-time Lyapunov stability controller and proved with backstepping method for the position and the attitude of a small rotorcraft unmanned aerial vehicle subjected to bounded uncertainties and disturbances. The dynamical motion equations are obtained by the Newton-Euler formalism. The proposed controller combines the advantage of the backstepping approach with finite-time convergence techniques to generate a control laws to guarantee the faster convergence of the state variables to their desired values in short time and compensate for the bounded disturbances. A formal proof of the closed-loop stability and finite-time convergence of tracking errors is derived using the Lyapunov function technique. Simulation results are presented to corroborate the effectiveness and the robustness of the proposed control method. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Distributed Adaptive Fuzzy Control for Nonlinear Multiagent Systems Via Sliding Mode Observers.

Science.gov (United States)

Shen, Qikun; Shi, Peng; Shi, Yan

2016-12-01

In this paper, the problem of distributed adaptive fuzzy control is investigated for high-order uncertain nonlinear multiagent systems on directed graph with a fixed topology. It is assumed that only the outputs of each follower and its neighbors are available in the design of its distributed controllers. Equivalent output injection sliding mode observers are proposed for each follower to estimate the states of itself and its neighbors, and an observer-based distributed adaptive controller is designed for each follower to guarantee that it asymptotically synchronizes to a leader with tracking errors being semi-globally uniform ultimate bounded, in which fuzzy logic systems are utilized to approximate unknown functions. Based on algebraic graph theory and Lyapunov function approach, using Filippov-framework, the closed-loop system stability analysis is conducted. Finally, numerical simulations are provided to illustrate the effectiveness and potential of the developed design techniques.

Distributed Secure Coordinated Control for Multiagent Systems Under Strategic Attacks.

Science.gov (United States)

Feng, Zhi; Wen, Guanghui; Hu, Guoqiang

2017-05-01

This paper studies a distributed secure consensus tracking control problem for multiagent systems subject to strategic cyber attacks modeled by a random Markov process. A hybrid stochastic secure control framework is established for designing a distributed secure control law such that mean-square exponential consensus tracking is achieved. A connectivity restoration mechanism is considered and the properties on attack frequency and attack length rate are investigated, respectively. Based on the solutions of an algebraic Riccati equation and an algebraic Riccati inequality, a procedure to select the control gains is provided and stability analysis is studied by using Lyapunov's method.. The effect of strategic attacks on discrete-time systems is also investigated. Finally, numerical examples are provided to illustrate the effectiveness of theoretical analysis.

Adaptive integral robust control and application to electromechanical servo systems.

Science.gov (United States)

Deng, Wenxiang; Yao, Jianyong

2017-03-01

This paper proposes a continuous adaptive integral robust control with robust integral of the sign of the error (RISE) feedback for a class of uncertain nonlinear systems, in which the RISE feedback gain is adapted online to ensure the robustness against disturbances without the prior bound knowledge of the additive disturbances. In addition, an adaptive compensation integrated with the proposed adaptive RISE feedback term is also constructed to further reduce design conservatism when the system also exists parametric uncertainties. Lyapunov analysis reveals the proposed controllers could guarantee the tracking errors are asymptotically converging to zero with continuous control efforts. To illustrate the high performance nature of the developed controllers, numerical simulations are provided. At the end, an application case of an actual electromechanical servo system driven by motor is also studied, with some specific design consideration, and comparative experimental results are obtained to verify the effectiveness of the proposed controllers. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Detecting unstable periodic orbits of nonlinear mappings by a novel quantum-behaved particle swarm optimization non-Lyapunov way

International Nuclear Information System (INIS)

Gao Fei; Gao Hongrui; Li Zhuoqiu; Tong Hengqing; Lee, Ju-Jang

2009-01-01

It is well known that set of unstable periodic orbits (UPOs) can be thought of as the skeleton for the dynamics. However, detecting UPOs of nonlinear map is one of the most challenging problems of nonlinear science in both numerical computations and experimental measures. In this paper, a new method is proposed to detect the UPOs in a non-Lyapunov way. Firstly three special techniques are added to quantum-behaved particle swarm optimization (QPSO), a novel mbest particle, contracting the searching space self-adaptively and boundaries restriction (NCB), then the new method NCB-QPSO is proposed. It can maintain an effective search mechanism with fine equilibrium between exploitation and exploration. Secondly, the problems of detecting the UPOs are converted into a non-negative functions' minimization through a proper translation in a non-Lyapunov way. Thirdly the simulations to 6 benchmark optimization problems and different high order UPOs of 5 classic nonlinear maps are done by the proposed method. And the results show that NCB-QPSO is a successful method in detecting the UPOs, and it has the advantages of fast convergence, high precision and robustness.

H∞ Control of Coronary Artery Input Time-Delay System via the Free-Matrix-Based Integral Inequality

Directory of Open Access Journals (Sweden)

Sha-sha Li

2018-01-01

Full Text Available The issue of H∞ control for the coronary artery input time-delay system with external disturbance is of concern. To further reduce conservation, we utilize the free-matrix-based integral inequality, Wirtinger-based integral inequality, and reciprocal convex combination approach to construct Lyapunov-Krasovskii function (LKF. Then a sufficient condition for controller design which can guarantee robust synchronization the coronary artery system is represented in terms of linear matrix inequality (LMI. Finally, a numerical example is exploited to show the effectiveness of the proposed methods.

Adaptive Synchronization for Two Different Stochastic Chaotic Systems with Unknown Parameters via a Sliding Mode Controller

Directory of Open Access Journals (Sweden)

Zengyun Wang

2013-01-01

Full Text Available This paper investigates the problem of synchronization for two different stochastic chaotic systems with unknown parameters and uncertain terms. The main work of this paper consists of the following aspects. Firstly, based on the Lyapunov theory in stochastic differential equations and the theory of sliding mode control, we propose a simple sliding surface and discuss the occurrence of the sliding motion. Secondly, we design an adaptive sliding mode controller to realize the asymptotical synchronization in mean squares. Thirdly, we design an adaptive sliding mode controller to realize the almost surely synchronization. Finally, the designed adaptive sliding mode controllers are used to achieve synchronization between two pairs of different stochastic chaos systems (Lorenz-Chen and Chen-Lu in the presence of the uncertainties and unknown parameters. Numerical simulations are given to demonstrate the robustness and efficiency of the proposed robust adaptive sliding mode controller.

Robust Optimal Adaptive Trajectory Tracking Control of Quadrotor Helicopter

Directory of Open Access Journals (Sweden)

M. Navabi

Full Text Available Abstract This paper focuses on robust optimal adaptive control strategy to deal with tracking problem of a quadrotor unmanned aerial vehicle (UAV in presence of parametric uncertainties, actuator amplitude constraints, and unknown time-varying external disturbances. First, Lyapunov-based indirect adaptive controller optimized by particle swarm optimization (PSO is developed for multi-input multi-output (MIMO nonlinear quadrotor to prevent input constraints violation, and then disturbance observer-based control (DOBC technique is aggregated with the control system to attenuate the effects of disturbance generated by an exogenous system. The performance of synthesis control method is evaluated by a new performance index function in time-domain, and the stability analysis is carried out using Lyapunov theory. Finally, illustrative numerical simulations are conducted to demonstrate the effectiveness of the presented approach in altitude and attitude tracking under several conditions, including large time-varying uncertainty, exogenous disturbance, and control input constraints.

Adaptive Event-Triggered Control Based on Heuristic Dynamic Programming for Nonlinear Discrete-Time Systems.

Science.gov (United States)

Dong, Lu; Zhong, Xiangnan; Sun, Changyin; He, Haibo

2017-07-01

This paper presents the design of a novel adaptive event-triggered control method based on the heuristic dynamic programming (HDP) technique for nonlinear discrete-time systems with unknown system dynamics. In the proposed method, the control law is only updated when the event-triggered condition is violated. Compared with the periodic updates in the traditional adaptive dynamic programming (ADP) control, the proposed method can reduce the computation and transmission cost. An actor-critic framework is used to learn the optimal event-triggered control law and the value function. Furthermore, a model network is designed to estimate the system state vector. The main contribution of this paper is to design a new trigger threshold for discrete-time systems. A detailed Lyapunov stability analysis shows that our proposed event-triggered controller can asymptotically stabilize the discrete-time systems. Finally, we test our method on two different discrete-time systems, and the simulation results are included.

An adaptive unscented Kalman filter-based adaptive tracking control for wheeled mobile robots with control constrains in the presence of wheel slipping

Directory of Open Access Journals (Sweden)

Mingyue Cui

2016-09-01

Full Text Available A novel control approach is proposed for trajectory tracking of a wheeled mobile robot with unknown wheels’ slipping. The longitudinal and lateral slipping are considered and processed as three time-varying parameters. The adaptive unscented Kalman filter is then designed to estimate the slipping parameters online, an adaptive adjustment of the noise covariances in the estimation process is implemented using a technique of covariance matching in the adaptive unscented Kalman filter context. Considering the practical physical constrains, a stable tracking control law for this robot system is proposed by the backstepping method. Asymptotic stability is guaranteed by Lyapunov stability theory. Control gains are determined online by applying pole placement method. Simulation and real experiment results show the effectiveness and robustness of the proposed control method.

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.

Master-slave synchronization of Lorenz systems using a single controller

International Nuclear Information System (INIS)

Oancea, Servilia; Grosu, Florin; Lazar, Anca; Grosu, Ioan

2009-01-01

A single controller for synchronization of two Lorenz systems is obtained by using Lyapunov function. Numerical results are given for the all three cases with one controller in each equation. Controller contains two or three variables of the master system.

Distributed Event-Triggered Control of Multiagent Systems with Time-Varying Topology

Directory of Open Access Journals (Sweden)

Jingwei Ma

2014-01-01

Full Text Available This paper studies the consensus of first-order discrete-time multiagent systems, where the interaction topology is time-varying. The event-triggered control is used to update the control input of each agent, and the event-triggering condition is designed based on the combination of the relative states of each agent to its neighbors. By applying the common Lyapunov function method, a sufficient condition for consensus, which is expressed as a group of linear matrix inequalities, is obtained and the feasibility of these linear matrix inequalities is further analyzed. Simulation examples are provided to explain the effectiveness of the theoretical results.

A Novel Approach to Sliding Mode Control of Time-Delay Systems

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Hongwei Xia

2013-01-01

Full Text Available This paper is concerned with the sliding mode control for a class of linear systems with time-varying delays. By utilizing a novel Lyapunov-Krasovskii functional and combining it with the delay fractioning approach as well as the free-weighting matrix technology, a sufficient condition is established such that the resulting sliding mode dynamics is asymptotically stable. Then, a sliding mode controller for reaching motion is synthesized to guarantee that the trajectories of the resulting closed-loop system can be driven onto a prescribed sliding surface and maintained there for all subsequent time. A numerical example is provided to illustrate the effectiveness of the proposed design approach.

Finite Time Control for Fractional Order Nonlinear Hydroturbine Governing System via Frequency Distributed Model

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Bin Wang

2016-01-01

Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.

Decentralized H∞ Control for Uncertain Interconnected Systems of Neutral Type via Dynamic Output Feedback

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Heli Hu

2014-01-01

Full Text Available The design of the dynamic output feedback H∞ control for uncertain interconnected systems of neutral type is investigated. In the framework of Lyapunov stability theory, a mathematical technique dealing with the nonlinearity on certain matrix variables is developed to obtain the solvability conditions for the anticipated controller. Based on the corresponding LMIs, the anticipated gains for dynamic output feedback can be achieved by solving some algebraic equations. Also, the norm of the transfer function from the disturbance input to the controlled output is less than the given index. A numerical example and the simulation results are given to show the effectiveness of the proposed method.

Receiver-exciter controller design

Science.gov (United States)

Jansma, P. A.

1982-01-01

A description of the general design of both the block 3 and block 4 receiver-exciter controllers for the Deep Space Network (DSN) Mark IV-A System is presented along with the design approach. The controllers are designed to enable the receiver-exciter subsystem (RCV) to be configured, calibrated, initialized and operated from a central location via high level instructions. The RECs are designed to be operated under the control of the DMC subsystem. The instructions are in the form of standard subsystem blocks (SSBs) received via the local area network (LAN). The centralized control provided by RECs and other DSCC controllers in Mark IV-A is intended to reduce DSN operations costs from the Mark III era.

Dynamic IQC-Based Control of Uncertain LFT Systems With Time-Varying State Delay.

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Yuan, Chengzhi; Wu, Fen

2016-12-01

This paper presents a new exact-memory delay control scheme for a class of uncertain systems with time-varying state delay under the integral quadratic constraint (IQC) framework. The uncertain system is described as a linear fractional transformation model including a state-delayed linear time-invariant (LTI) system and time-varying structured uncertainties. The proposed exact-memory delay controller consists of a linear state-feedback control law and an additional term that captures the delay behavior of the plant. We first explore the delay stability and the L 2 -gain performance using dynamic IQCs incorporated with quadratic Lyapunov functions. Then, the design of exact-memory controllers that guarantee desired L 2 -gain performance is examined. The resulting delay control synthesis conditions are formulated in terms of linear matrix inequalities, which are convex on all design variables including the scaling matrices associated with the IQC multipliers. The IQC-based exact-memory control scheme provides a novel approach for delay control designs via convex optimization, and advances existing control methods in two important ways: 1) better controlled performance and 2) simplified design procedure with less computational cost. The effectiveness and advantages of the proposed approach have been demonstrated through numerical studies.

Adaptive control method for core power control in TRIGA Mark II reactor

Science.gov (United States)

Sabri Minhat, Mohd; Selamat, Hazlina; Subha, Nurul Adilla Mohd

2018-01-01

The 1MWth Reactor TRIGA PUSPATI (RTP) Mark II type has undergone more than 35 years of operation. The existing core power control uses feedback control algorithm (FCA). It is challenging to keep the core power stable at the desired value within acceptable error bands to meet the safety demand of RTP due to the sensitivity of nuclear research reactor operation. Currently, the system is not satisfied with power tracking performance and can be improved. Therefore, a new design core power control is very important to improve the current performance in tracking and regulate reactor power by control the movement of control rods. In this paper, the adaptive controller and focus on Model Reference Adaptive Control (MRAC) and Self-Tuning Control (STC) were applied to the control of the core power. The model for core power control was based on mathematical models of the reactor core, adaptive controller model, and control rods selection programming. The mathematical models of the reactor core were based on point kinetics model, thermal hydraulic models, and reactivity models. The adaptive control model was presented using Lyapunov method to ensure stable close loop system and STC Generalised Minimum Variance (GMV) Controller was not necessary to know the exact plant transfer function in designing the core power control. The performance between proposed adaptive control and FCA will be compared via computer simulation and analysed the simulation results manifest the effectiveness and the good performance of the proposed control method for core power control.

A robust nonlinear stabilizer as a controller for improving transient stability in micro-grids.

Science.gov (United States)

Azimi, Seyed Mohammad; Afsharnia, Saeed

2017-01-01

This paper proposes a parametric-Lyapunov approach to the design of a stabilizer aimed at improving the transient stability of micro-grids (MGs). This strategy is applied to electronically-interfaced distributed resources (EI-DRs) operating with a unified control configuration applicable to all operational modes (i.e. grid-connected mode, islanded mode, and mode transitions). The proposed approach employs a simple structure compared with other nonlinear controllers, allowing ready implementation of the stabilizer. A new parametric-Lyapunov function is proposed rendering the proposed stabilizer more effective in damping system transition transients. The robustness of the proposed stabilizer is also verified based on both time-domain simulations and mathematical proofs, and an ultimate bound has been derived for the frequency transition transients. The proposed stabilizer operates by deploying solely local information and there are no needs for communication links. The deteriorating effects of the primary resource delays on the transient stability are also treated analytically. Finally, the effectiveness of the proposed stabilizer is evaluated through time-domain simulations and compared with the recently-developed stabilizers performed on a multi-resource MG. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Robust intelligent backstepping tracking control for uncertain non-linear chaotic systems using H∞ control technique

International Nuclear Information System (INIS)

Peng, Y.-F.

2009-01-01

The cerebellar model articulation controller (CMAC) is a non-linear adaptive system with built-in simple computation, good generalization capability and fast learning property. In this paper, a robust intelligent backstepping tracking control (RIBTC) system combined with adaptive CMAC and H ∞ control technique is proposed for a class of chaotic systems with unknown system dynamics and external disturbance. In the proposed control system, an adaptive backstepping cerebellar model articulation controller (ABCMAC) is used to mimic an ideal backstepping control (IBC), and a robust H ∞ controller is designed to attenuate the effect of the residual approximation errors and external disturbances with desired attenuation level. Moreover, the all adaptation laws of the RIBTC system are derived based on the Lyapunov stability analysis, the Taylor linearization technique and H ∞ control theory, so that the stability of the closed-loop system and H ∞ tracking performance can be guaranteed. Finally, three application examples, including a Duffing-Holmes chaotic system, a Genesio chaotic system and a Sprott circuit system, are used to demonstrate the effectiveness and performance of proposed robust control technique.

Analytic Quasi-Perodic Cocycles with Singularities and the Lyapunov Exponent of Extended Harper's Model

Science.gov (United States)

Jitomirskaya, S.; Marx, C. A.

2012-11-01

We show how to extend (and with what limitations) Avila's global theory of analytic SL(2,C) cocycles to families of cocycles with singularities. This allows us to develop a strategy to determine the Lyapunov exponent for the extended Harper's model, for all values of parameters and all irrational frequencies. In particular, this includes the self-dual regime for which even heuristic results did not previously exist in physics literature. The extension of Avila's global theory is also shown to imply continuous behavior of the LE on the space of analytic {M_2({C})}-cocycles. This includes rational approximation of the frequency, which so far has not been available.

Adaptive compensation control for attitude adjustment of quad-rotor unmanned aerial vehicle.

Science.gov (United States)

Song, Zhankui; Sun, Kaibiao

2017-07-01

A compensation control strategy based on adaptive back-stepping technique is presented to address the problem of attitude adjustment for a quad-rotor unmanned aerial vehicle (QR- UAV) with inertia parameter uncertainties, the limited airflow disturbance and the partial loss of rotation speed effectiveness. In the design process of control system, adaptive estimation technique is introduced into the closed loop system in order to compensate the lumped disturbance term. More specifically, the designed controller utilizes "prescribed performance bounds" method, and therefore guarantees the transient performance of tracking errors, even in the presence of the lumped disturbance. Adaptive compensation algorithms under the proposed closed loop system structure are derived in the sense of Lyapunov stability analysis such that the attitude tracking error converge to a small neighborhood of equilibrium point. Finally, the simulation results demonstrate the effectiveness of the proposed controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Dynamic analysis, controlling chaos and chaotification of a SMIB power system

International Nuclear Information System (INIS)

Chen, H.-K.; Lin, T.-N.; Chen, J.-H.

2005-01-01

The dynamic behaviors of a SMIB power system are studied in this paper. A single modal equation is used to analyze the qualitative behaviors of the system. The famous equation of motion is called 'swing equation'. The Lyapunov direct method is applied to obtain conditions of stability of the equilibrium points of the system. The bifurcation of the parameter dependent system is studied numerically. Besides, the phase portraits, the Poincare maps, and the Lyapunov exponents are presented to observe periodic and chaotic motions. Further, the addition of periodic force and the feedback control are used to control chaos effectively. Finally, the chaotification problem of the SMIB power system is also issued

Adaptive Droop Control for Microgrids Based on the Synergetic Control of Multi-Agent Systems

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Zhiwen Yu

2016-12-01

Full Text Available In this paper, a distributed synergetic control based on multi-agent systems is proposed to solve the problems of frequency and voltage errors, system stability and power sharing accuracy in the traditional droop control of microgrids. Starting with power flow equations, we build the secondary-order dynamic model of DG, which consists of three parts: (1 active power allocation; (2 active power-frequency; and (3 reactive power-voltage droop control. Considering time-delays in communication networks, a leaderless synergetic control algorithm is proposed to allocate the active power in inverse proportion to the droop coefficient, and the synergetic control with a virtual leader is proposed to control the system frequency and voltage to keep at the expected value. Besides, the direct Lyapunov method is introduced to verify the globally asymptotical stability. Moreover, the impacts of communication disturbance are also discussed from the aspects of control precision and system stability. Finally, based on a test microgrid, numerous cases are designed as illustration, and the simulation results validate the proposed method.

Nonlinear Output Feedback Control of Underwater Vehicle Propellers using Advance Speed Feedback

DEFF Research Database (Denmark)

Fossen, T.I.; Blanke, M.

1999-01-01

More accurate propeller shaft speed controllers can be designed by using nonlinear control theory. In this paper, an output feedback controller reconstructing the advance speed (speed of water going into the propeller) from vehicle speed measurements is derived. For this purpose a three-state model...... minimizes thruster losses due to variations in propeller axial inlet flow which 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. From the simulations it can be concluded...... of propeller shaft speed, forward (surge) speed of the vehicle and axial inlet flow of the propeller is applied. A nonlinear observer in combination with an output feedback integral controller are derived by applying Lyapunov stability theory and exponential stability is proven. The output feedback controller...

Persistent disturbance rejection via state feedback for networked control systems

Energy Technology Data Exchange (ETDEWEB)

Yue Dong [Institute of Information and Control Engineering Technology, Nanjing Normal University, 78 Bancang Street, Nanjing, Jiangsu 210042 (China)], E-mail: medongy@njnu.edu.cn; Lam, James [Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road (Hong Kong); Wang Zidong [Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex UB8 3PH (United Kingdom)], E-mail: Zidong.Wang@brunel.ac.uk

2009-04-15

The problem of persistent disturbance rejection via state feedback for networked control systems is concerned based on the Lyapunov function method. The effect of the network conditions, such as network-induced delay and data dropout, is considered in the modeling of the system. It is assumed that the state and the control signals are individually quantized by quantizers on the sensor side and the controller side. The feedback gain and the quantizer parameters that guarantee the internal stability and the disturbance rejection performance of the closed-loop system are obtained by solving some linear matrix inequalities. To illustrate the effectiveness of the proposed method, a numerical example is provided for the design of the feedback gain and the quantizer parameters.

Persistent disturbance rejection via state feedback for networked control systems

International Nuclear Information System (INIS)

Yue Dong; Lam, James; Wang Zidong

2009-01-01

The problem of persistent disturbance rejection via state feedback for networked control systems is concerned based on the Lyapunov function method. The effect of the network conditions, such as network-induced delay and data dropout, is considered in the modeling of the system. It is assumed that the state and the control signals are individually quantized by quantizers on the sensor side and the controller side. The feedback gain and the quantizer parameters that guarantee the internal stability and the disturbance rejection performance of the closed-loop system are obtained by solving some linear matrix inequalities. To illustrate the effectiveness of the proposed method, a numerical example is provided for the design of the feedback gain and the quantizer parameters.

Improved control for distributed parameter systems with time-dependent spatial domains utilizing mobile sensor–actuator networks

International Nuclear Information System (INIS)

Zhang Jian-Zhong; Cui Bao-Tong; Zhuang Bo

2017-01-01

A guidance policy for controller performance enhancement utilizing mobile sensor–actuator networks (MSANs) is proposed for a class of distributed parameter systems (DPSs), which are governed by diffusion partial differential equations (PDEs) with time-dependent spatial domains. Several sufficient conditions for controller performance enhancement are presented. First, the infinite dimensional operator theory is used to derive an abstract evolution equation of the systems under some rational assumptions on the operators, and a static output feedback controller is designed to control the spatial process. Then, based on Lyapunov stability arguments, guidance policies for collocated and non-collocated MSANs are provided to enhance the performance of the proposed controller, which show that the time-dependent characteristic of the spatial domains can significantly affect the design of the mobile scheme. Finally, a simulation example illustrates the effectiveness of the proposed policy. (paper)

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

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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

Delay-Range-Dependent H∞ Control for Automatic Mooring Positioning System with Time-Varying Input Delay

Directory of Open Access Journals (Sweden)

Xiaoyu Su

2014-01-01

Full Text Available Aiming at the economy and security of the positioning system in semi-submersible platform, the paper presents a new scheme based on the mooring line switching strategy. Considering the input delay in switching process, H∞ control with time-varying input delay is designed to calculate the control forces to resist disturbing forces. In order to reduce the conservativeness, the information of the lower bound of delay is taken into account, and a Lyapunov function which contains the range of delay is constructed. Besides, the input constraint is considered to avoid breakage of mooring lines. The sufficient conditions for delay-range-dependent stabilization are derived in terms of LMI, and the controller is also obtained. The effectiveness of the proposed approach is illustrated by a realistic design example.

Distributed robust adaptive control of high order nonlinear multi agent systems.

Science.gov (United States)

Hashemi, Mahnaz; Shahgholian, Ghazanfar

2018-03-01

In this paper, a robust adaptive neural network based controller is presented for multi agent high order nonlinear systems with unknown nonlinear functions, unknown control gains and unknown actuator failures. At first, Neural Network (NN) is used to approximate the nonlinear uncertainty terms derived from the controller design procedure for the followers. Then, a novel distributed robust adaptive controller is developed by combining the backstepping method and the Dynamic Surface Control (DSC) approach. The proposed controllers are distributed in the sense that the designed controller for each follower agent only requires relative state information between itself and its neighbors. By using the Young's inequality, only few parameters need to be tuned regardless of NN nodes number. Accordingly, the problems of dimensionality curse and explosion of complexity are counteracted, simultaneously. New adaptive laws are designed by choosing the appropriate Lyapunov-Krasovskii functionals. The proposed approach proves the boundedness of all the closed-loop signals in addition to the convergence of the distributed tracking errors to a small neighborhood of the origin. Simulation results indicate that the proposed controller is effective and robust. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Synchronization control of Hodgkin-Huxley neurons exposed to ELF electric field

International Nuclear Information System (INIS)

Che Yanqiu; Wang Jiang; Zhou Sisi; Deng Bin

2009-01-01

This paper presents an adaptive neural network H ∞ control for unidirectional synchronization of modified Hodgkin-Huxley (HH) neurons exposed to extremely low frequency (ELF) electric field. The proposed modified HH neurons exhibit periodic and chaotic dynamics in response to sinusoidal electric field stimulation. Based on the Lyapunov stability theory, we derive the updated laws of neural network for approximating the nonlinear uncertain functions of the error dynamical system. The H ∞ design technique makes the controller robust to unmodeled dynamics, disturbances and approximate errors. The proposed controller not only ensures closed-loop stability, but also guarantees an H ∞ performance for the synchronization error system. The states of the controlled slave system exponentially synchronize with that of the master one after control. The simulation results demonstrate the validity of the proposed method.

Adaptive Sliding Mode Control of MEMS Gyroscope Based on Neural Network Approximation

Directory of Open Access Journals (Sweden)

Yuzheng Yang

2014-01-01

Full Text Available An adaptive sliding controller using radial basis function (RBF network to approximate the unknown system dynamics microelectromechanical systems (MEMS gyroscope sensor is proposed. Neural controller is proposed to approximate the unknown system model and sliding controller is employed to eliminate the approximation error and attenuate the model uncertainties and external disturbances. Online neural network (NN weight tuning algorithms, including correction terms, are designed based on Lyapunov stability theory, which can guarantee bounded tracking errors as well as bounded NN weights. The tracking error bound can be made arbitrarily small by increasing a certain feedback gain. Numerical simulation for a MEMS angular velocity sensor is investigated to verify the effectiveness of the proposed adaptive neural control scheme and demonstrate the satisfactory tracking performance and robustness.

Hybrid Chaos Synchronization of Four-Scroll Systems via Active Control

Science.gov (United States)

Karthikeyan, Rajagopal; Sundarapandian, Vaidyanathan

2014-03-01

This paper investigates the hybrid chaos synchronization of identical Wang four-scroll systems (Wang, 2009), identical Liu-Chen four-scroll systems (Liu and Chen, 2004) and non-identical Wang and Liu-Chen four-scroll systems. Active control method is the method adopted to achieve the hybrid chaos synchronization of the four-scroll chaotic systems addressed in this paper and our synchronization results are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is effective and convenient to hybrid synchronize identical and different Wang and Liu-Chen four-scroll chaotic systems. Numerical simulations are also shown to illustrate and validate the hybrid synchronization results derived in this paper.

Guaranteed Cost Finite-Time Control of Discrete-Time Positive Impulsive Switched Systems

Directory of Open Access Journals (Sweden)

Leipo Liu

2018-01-01

Full Text Available This paper considers the guaranteed cost finite-time boundedness of discrete-time positive impulsive switched systems. Firstly, the definition of guaranteed cost finite-time boundedness is introduced. By using the multiple linear copositive Lyapunov function (MLCLF and average dwell time (ADT approach, a state feedback controller is designed and sufficient conditions are obtained to guarantee that the corresponding closed-loop system is guaranteed cost finite-time boundedness (GCFTB. Such conditions can be solved by linear programming. Finally, a numerical example is provided to show the effectiveness of the proposed method.

Automatic control design procedures for restructurable aircraft control

Science.gov (United States)

Looze, D. P.; Krolewski, S.; Weiss, J.; Barrett, N.; Eterno, J.

1985-01-01

A simple, reliable automatic redesign procedure for restructurable control is discussed. This procedure is based on Linear Quadratic (LQ) design methodologies. It employs a robust control system design for the unfailed aircraft to minimize the effects of failed surfaces and to extend the time available for restructuring the Flight Control System. The procedure uses the LQ design parameters for the unfailed system as a basis for choosing the design parameters of the failed system. This philosophy alloys the engineering trade-offs that were present in the nominal design to the inherited by the restructurable design. In particular, it alloys bandwidth limitations and performance trade-offs to be incorporated in the redesigned system. The procedure also has several other desirable features. It effectively redistributes authority among the available control effectors to maximize the system performance subject to actuator limitations and constraints. It provides a graceful performance degradation as the amount of control authority lessens. When given the parameters of the unfailed aircraft, the automatic redesign procedure reproduces the nominal control system design.

Adaptive Backstepping-Based Neural Tracking Control for MIMO Nonlinear Switched Systems Subject to Input Delays.

Science.gov (United States)

Niu, Ben; Li, Lu

2018-06-01

This brief proposes a new neural-network (NN)-based adaptive output tracking control scheme for a class of disturbed multiple-input multiple-output uncertain nonlinear switched systems with input delays. By combining the universal approximation ability of radial basis function NNs and adaptive backstepping recursive design with an improved multiple Lyapunov function (MLF) scheme, a novel adaptive neural output tracking controller design method is presented for the switched system. The feature of the developed design is that different coordinate transformations are adopted to overcome the conservativeness caused by adopting a common coordinate transformation for all subsystems. It is shown that all the variables of the resulting closed-loop system are semiglobally uniformly ultimately bounded under a class of switching signals in the presence of MLF and that the system output can follow the desired reference signal. To demonstrate the practicability of the obtained result, an adaptive neural output tracking controller is designed for a mass-spring-damper system.

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