Sensitivity Analysis of Linear Programming and Quadratic Programming Algorithms for Control Allocation

Science.gov (United States)

Frost, Susan A.; Bodson, Marc; Acosta, Diana M.

2009-01-01

The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming.

Management of linear quadratic regulator optimal control with full-vehicle control case study

Directory of Open Access Journals (Sweden)

Rodrigue Tchamna

2016-09-01

Full Text Available Linear quadratic regulator is a powerful technique for dealing with the control design of any linear and nonlinear system after linearization of the system around an operating point. For small systems, which have fewer state variables, the transformation of the performance index from scalar to matrix form can be straightforward. On the other hand, as the system becomes large with many state variables and controllers, appropriate design and notations should be defined to make it easy to automatically implement the technique for any large system without the need to redesign from scratch every time one requires a new system. The main aim of this article was to deal with this issue. This article shows how to automatically obtain the matrix form of the performance index matrices from the scalar version of the performance index. Control of a full-vehicle in cornering was taken as a case study in this article.

Optimal linear-quadratic control of coupled parabolic-hyperbolic PDEs

Science.gov (United States)

Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

2017-10-01

This paper focuses on the optimal control design for a system of coupled parabolic-hypebolic partial differential equations by using the infinite-dimensional state-space description and the corresponding operator Riccati equation. Some dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the linear-quadratic (LQ)-optimal control problem. A state LQ-feedback operator is computed by solving the operator Riccati equation, which is converted into a set of algebraic and differential Riccati equations, thanks to the eigenvalues and the eigenvectors of the parabolic operator. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ-optimal controller designed in the early portion of the paper is implemented for the original nonlinear model. Numerical simulations are performed to show the controller performances.

Quantum Optimal Control of Single Harmonic Oscillator under Quadratic Controls together with Linear Dipole Polarizability: A Fluctuation Free Expectation Value Dynamical Perspective

International Nuclear Information System (INIS)

Ayvaz, Muzaffer; Demiralp, Metin

2011-01-01

In this study, the optimal control equations for one dimensional quantum harmonic oscillator under the quadratic control operators together with linear dipole polarizability effects are constructed in the sense of Heisenberg equation of motion. A numerical technique based on the approximation to the non-commuting quantum mechanical operators from the fluctuation free expectation value dynamics perspective in the classical limit is also proposed for the solution of optimal control equations which are ODEs with accompanying boundary conditions. The dipole interaction of the system is considered to be linear, and the observable whose expectation value will be suppressed during the control process is considered to be quadratic in terms of position operator x. The objective term operator is also assumed to be quadratic.

Parallel Implementation of Riccati Recursion for Solving Linear-Quadratic Control Problems

DEFF Research Database (Denmark)

Frison, Gianluca; Jørgensen, John Bagterp

2013-01-01

In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper...... an alternative version of the Riccati recursion solver for LQ control problems is presented. The performance of both the classical and the alternative version is analyzed from a theoretical as well as a numerical point of view, and the alternative version is found to be approximately 50% faster than...

The regular indefinite linear-quadratic problem with linear endpoint constraints

NARCIS (Netherlands)

Soethoudt, J.M.; Trentelman, H.L.

1989-01-01

This paper deals with the infinite horizon linear-quadratic problem with indefinite cost. Given a linear system, a quadratic cost functional and a subspace of the state space, we consider the problem of minimizing the cost functional over all inputs for which the state trajectory converges to that

Neural network-based nonlinear model predictive control vs. linear quadratic gaussian control

Science.gov (United States)

Cho, C.; Vance, R.; Mardi, N.; Qian, Z.; Prisbrey, K.

1997-01-01

One problem with the application of neural networks to the multivariable control of mineral and extractive processes is determining whether and how to use them. The objective of this investigation was to compare neural network control to more conventional strategies and to determine if there are any advantages in using neural network control in terms of set-point tracking, rise time, settling time, disturbance rejection and other criteria. The procedure involved developing neural network controllers using both historical plant data and simulation models. Various control patterns were tried, including both inverse and direct neural network plant models. These were compared to state space controllers that are, by nature, linear. For grinding and leaching circuits, a nonlinear neural network-based model predictive control strategy was superior to a state space-based linear quadratic gaussian controller. The investigation pointed out the importance of incorporating state space into neural networks by making them recurrent, i.e., feeding certain output state variables into input nodes in the neural network. It was concluded that neural network controllers can have better disturbance rejection, set-point tracking, rise time, settling time and lower set-point overshoot, and it was also concluded that neural network controllers can be more reliable and easy to implement in complex, multivariable plants.

Design of Linear-Quadratic-Regulator for a CSTR process

Science.gov (United States)

Meghna, P. R.; Saranya, V.; Jaganatha Pandian, B.

2017-11-01

This paper aims at creating a Linear Quadratic Regulator (LQR) for a Continuous Stirred Tank Reactor (CSTR). A CSTR is a common process used in chemical industries. It is a highly non-linear system. Therefore, in order to create the gain feedback controller, the model is linearized. The controller is designed for the linearized model and the concentration and volume of the liquid in the reactor are kept at a constant value as required.

Radiotherapy treatment planning linear-quadratic radiobiology

CERN Document Server

Chapman, J Donald

2015-01-01

Understand Quantitative Radiobiology from a Radiation Biophysics PerspectiveIn the field of radiobiology, the linear-quadratic (LQ) equation has become the standard for defining radiation-induced cell killing. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology describes tumor cell inactivation from a radiation physics perspective and offers appropriate LQ parameters for modeling tumor and normal tissue responses.Explore the Latest Cell Killing Numbers for Defining Iso-Effective Cancer TreatmentsThe book compil

Linear quadratic Gaussian balancing for discrete-time infinite-dimensional linear systems

NARCIS (Netherlands)

Opmeer, MR; Curtain, RF

2004-01-01

In this paper, we study the existence of linear quadratic Gaussian (LQG)-balanced realizations for discrete-time infinite-dimensional systems. LQG-balanced realizations are those for which the smallest nonnegative self-adjoint solutions of the control and filter Riccati equations are equal. We show

Robust optimal control design using a differential game approach for open-loop linear quadratic descriptor systems

NARCIS (Netherlands)

Musthofa, M.W.; Salmah, S.; Engwerda, Jacob; Suparwanto, A.

This paper studies the robust optimal control problem for descriptor systems. We applied differential game theory to solve the disturbance attenuation problem. The robust control problem was converted into a reduced ordinary zero-sum game. Within a linear quadratic setting, we solved the problem for

Decentralized linear quadratic power system stabilizers for multi ...

Indian Academy of Sciences (India)

Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead–lag power system stabilizers. However, they have not seen much of practical importance as the state variables are generally not measurable; especially the generator rotor angle measurement is not ...

On a linear-quadratic problem with Caputo derivative

Directory of Open Access Journals (Sweden)

Dariusz Idczak

2016-01-01

Full Text Available In this paper, we study a linear-quadratic optimal control problem with a fractional control system containing a Caputo derivative of unknown function. First, we derive the formulas for the differential and gradient of the cost functional under given constraints. Next, we prove an existence result and derive a maximum principle. Finally, we describe the gradient and projection of the gradient methods for the problem under consideration.

Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

Science.gov (United States)

Ito, Kazufumi; Teglas, Russell

1987-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

A non-linear programming approach to the computer-aided design of regulators using a linear-quadratic formulation

Science.gov (United States)

Fleming, P.

1985-01-01

A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.

Efficient Implementation of the Riccati Recursion for Solving Linear-Quadratic Control Problems

DEFF Research Database (Denmark)

Frison, Gianluca; Jørgensen, John Bagterp

2013-01-01

In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is typically the main computational effort at each iteration....... In this paper, we compare a number of solvers for an extended formulation of the LQ control problem: a Riccati recursion based solver can be considered the best choice for the general problem with dense matrices. Furthermore, we present a novel version of the Riccati solver, that makes use of the Cholesky...... factorization of the Pn matrices to reduce the number of flops. When combined with regularization and mixed precision, this algorithm can solve large instances of the LQ control problem up to 3 times faster than the classical Riccati solver....

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

Science.gov (United States)

Ito, K.; Teglas, R.

1984-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Results of radiotherapy in craniopharyngiomas analysed by the linear quadratic model

Energy Technology Data Exchange (ETDEWEB)

Guerkaynak, M. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey); Oezyar, E. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey); Zorlu, F. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey); Akyol, F.H. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey); Lale Atahan, I. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey)

1994-12-31

In 23 craniopharyngioma patients treated by limited surgery and external radiotherapy, the results concerning local control were analysed by linear quadratic formula. A biologically effective dose (BED) of 55 Gy, calculated with time factor and an {alpha}/{beta} value of 10 Gy, seemed to be adequate for local control. (orig.).

A Quasi-Dynamic Optimal Control Strategy for Non-Linear Multivariable Processes Based upon Non-Quadratic Objective Functions

Directory of Open Access Journals (Sweden)

Jens G. Balchen

1984-10-01

Full Text Available The problem of systematic derivation of a quasi-dynamic optimal control strategy for a non-linear dynamic process based upon a non-quadratic objective function is investigated. The wellknown LQG-control algorithm does not lead to an optimal solution when the process disturbances have non-zero mean. The relationships between the proposed control algorithm and LQG-control are presented. The problem of how to constrain process variables by means of 'penalty' - terms in the objective function is dealt with separately.

Burgers' turbulence problem with linear or quadratic external potential

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole Eiler; Leonenko, N.N.

2005-01-01

We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.......We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions....

Quadratic Interpolation and Linear Lifting Design

Directory of Open Access Journals (Sweden)

Joel Solé

2007-03-01

Full Text Available A quadratic image interpolation method is stated. The formulation is connected to the optimization of lifting steps. This relation triggers the exploration of several interpolation possibilities within the same context, which uses the theory of convex optimization to minimize quadratic functions with linear constraints. The methods consider possible knowledge available from a given application. A set of linear equality constraints that relate wavelet bases and coefficients with the underlying signal is introduced in the formulation. As a consequence, the formulation turns out to be adequate for the design of lifting steps. The resulting steps are related to the prediction minimizing the detail signal energy and to the update minimizing the l2-norm of the approximation signal gradient. Results are reported for the interpolation methods in terms of PSNR and also, coding results are given for the new update lifting steps.

Staff turnover in hotels : exploring the quadratic and linear relationships.

OpenAIRE

Mohsin, A.; Lengler, J.F.B.; Aguzzoli, R.L.

2015-01-01

The aim of this study is to assess whether the relationship between intention to leave the job and its antecedents is quadratic or linear. To explore those relationships a theoretical model (see Fig. 1) and eight hypotheses are proposed. Each linear hypothesis is followed by an alternative quadratic hypothesis. The alternative hypotheses propose that the relationship between the four antecedent constructs and intention to leave the job might not be linear, as the existing literature suggests....

A smart rotor configuration with linear quadratic control of adaptive trailing edge flaps for active load alleviation

DEFF Research Database (Denmark)

Bergami, Leonardo; Poulsen, Niels Kjølstad

2015-01-01

The paper proposes a smart rotor configuration where adaptive trailing edge flaps (ATEFs) are employed for active alleviation of the aerodynamic loads on the blades of the NREL 5 MW reference turbine. The flaps extend for 20% of the blade length and are controlled by a linear quadratic (LQ....... The effects of active flap control are assessed with aeroelastic simulations of the turbine in normal operation conditions, as prescribed by the International Electrotechnical Commission standard. The turbine lifetime fatigue damage equivalent loads provide a convenient summary of the results achieved...

Quadratic theory and feedback controllers for linear time delay systems

International Nuclear Information System (INIS)

Lee, E.B.

1976-01-01

Recent research on the design of controllers for systems having time delays is discussed. Results for the ''open loop'' and ''closed loop'' designs will be presented. In both cases results for minimizing a quadratic cost functional are given. The usefulness of these results is not known, but similar results for the non-delay case are being routinely applied. (author)

LQG/LTR [linear quadratic Gaussian with loop transfer recovery] robust control system design for a low-pressure feedwater heater train

International Nuclear Information System (INIS)

Murphy, G.V.; Bailey, J.M.

1990-01-01

This paper uses the linear quadratic Gaussian with loop transfer recovery (LQG/LTR) control system design method to obtain a level control system for a low-pressure feedwater heater train. The control system performance and stability robustness are evaluated for a given set of system design specifications. The tools for analysis are the return ratio, return difference, and inverse return difference singular-valve plots for a loop break at the plant output. 3 refs., 7 figs., 2 tabs

On misclassication probabilities of linear and quadratic classiers ...

African Journals Online (AJOL)

We study the theoretical misclassication probability of linear and quadratic classiers and examine the performance of these classiers under distributional variations in theory and using simulation. We derive expression for Bayes errors for some competing distributions from the same family under location shift. Keywords: ...

Linear and Quadratic Interpolators Using Truncated-Matrix Multipliers and Squarers

Directory of Open Access Journals (Sweden)

E. George Walters III

2015-11-01

Full Text Available This paper presents a technique for designing linear and quadratic interpolators for function approximation using truncated multipliers and squarers. Initial coefficient values are found using a Chebyshev-series approximation and then adjusted through exhaustive simulation to minimize the maximum absolute error of the interpolator output. This technique is suitable for any function and any precision up to 24 bits (IEEE single precision. Designs for linear and quadratic interpolators that implement the 1/x, 1/ √ x, log2(1+2x, log2(x and 2x functions are presented and analyzed as examples. Results show that a proposed 24-bit interpolator computing 1/x with a design specification of ±1 unit in the last place of the product (ulp error uses 16.4% less area and 15.3% less power than a comparable standard interpolator with the same error specification. Sixteen-bit linear interpolators for other functions are shown to use up to 17.3% less area and 12.1% less power, and 16-bit quadratic interpolators are shown to use up to 25.8% less area and 24.7% less power.

Local hyperspectral data multisharpening based on linear/linear-quadratic nonnegative matrix factorization by integrating lidar data

Science.gov (United States)

Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

2015-10-01

In this paper, a new Spectral-Unmixing-based approach, using Nonnegative Matrix Factorization (NMF), is proposed to locally multi-sharpen hyperspectral data by integrating a Digital Surface Model (DSM) obtained from LIDAR data. In this new approach, the nature of the local mixing model is detected by using the local variance of the object elevations. The hyper/multispectral images are explored using small zones. In each zone, the variance of the object elevations is calculated from the DSM data in this zone. This variance is compared to a threshold value and the adequate linear/linearquadratic spectral unmixing technique is used in the considered zone to independently unmix hyperspectral and multispectral data, using an adequate linear/linear-quadratic NMF-based approach. The obtained spectral and spatial information thus respectively extracted from the hyper/multispectral images are then recombined in the considered zone, according to the selected mixing model. Experiments based on synthetic hyper/multispectral data are carried out to evaluate the performance of the proposed multi-sharpening approach and literature linear/linear-quadratic approaches used on the whole hyper/multispectral data. In these experiments, real DSM data are used to generate synthetic data containing linear and linear-quadratic mixed pixel zones. The DSM data are also used for locally detecting the nature of the mixing model in the proposed approach. Globally, the proposed approach yields good spatial and spectral fidelities for the multi-sharpened data and significantly outperforms the used literature methods.

linear-quadratic-linear model

Directory of Open Access Journals (Sweden)

Tanwiwat Jaikuna

2017-02-01

Full Text Available Purpose: To develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL model. Material and methods : The Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR, and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD2 was calculated using biological effective dose (BED based on the LQL model. The software calculation and the manual calculation were compared for EQD2 verification with pair t-test statistical analysis using IBM SPSS Statistics version 22 (64-bit. Results: Two and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV determined by D90%, 0.56% in the bladder, 1.74% in the rectum when determined by D2cc, and less than 1% in Pinnacle. The difference in the EQD2 between the software calculation and the manual calculation was not significantly different with 0.00% at p-values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT and 0.240, 0.320, and 0.849 for brachytherapy (BT in HR-CTV, bladder, and rectum, respectively. Conclusions : The Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT.

Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks

KAUST Repository

Li, Yanning

2014-03-01

This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network. © 2014 IEEE.

Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks

KAUST Repository

Li, Yanning; Canepa, Edward S.; Claudel, Christian

2014-01-01

This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network. © 2014 IEEE.

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

Pareto optimality in infinite horizon linear quadratic differential games

NARCIS (Netherlands)

Reddy, P.V.; Engwerda, J.C.

2013-01-01

In this article we derive conditions for the existence of Pareto optimal solutions for linear quadratic infinite horizon cooperative differential games. First, we present a necessary and sufficient characterization for Pareto optimality which translates to solving a set of constrained optimal

Application of Linear Quadratic Gaussian and Coefficient Diagram Techniques to Distributed Load Frequency Control of Power Systems

Directory of Open Access Journals (Sweden)

Tarek Hassan Mohamed

2015-12-01

Full Text Available This paper presented both the linear quadratic Gaussian technique (LQG and the coefficient diagram method (CDM as load frequency controllers in a multi-area power system to deal with the problem of variations in system parameters and load demand change. The full states of the system including the area frequency deviation have been estimated using the Kalman filter technique. The efficiency of the proposed control method has been checked using a digital simulation. Simulation results indicated that, with the proposed CDM + LQG technique, the system is robust in the face of parameter uncertainties and load disturbances. A comparison between the proposed technique and other schemes is carried out, confirming the superiority of the proposed CDM + LQG technique.

Hyperspectral and multispectral data fusion based on linear-quadratic nonnegative matrix factorization

Science.gov (United States)

Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

2017-04-01

This paper proposes three multisharpening approaches to enhance the spatial resolution of urban hyperspectral remote sensing images. These approaches, related to linear-quadratic spectral unmixing techniques, use a linear-quadratic nonnegative matrix factorization (NMF) multiplicative algorithm. These methods begin by unmixing the observable high-spectral/low-spatial resolution hyperspectral and high-spatial/low-spectral resolution multispectral images. The obtained high-spectral/high-spatial resolution features are then recombined, according to the linear-quadratic mixing model, to obtain an unobservable multisharpened high-spectral/high-spatial resolution hyperspectral image. In the first designed approach, hyperspectral and multispectral variables are independently optimized, once they have been coherently initialized. These variables are alternately updated in the second designed approach. In the third approach, the considered hyperspectral and multispectral variables are jointly updated. Experiments, using synthetic and real data, are conducted to assess the efficiency, in spatial and spectral domains, of the designed approaches and of linear NMF-based approaches from the literature. Experimental results show that the designed methods globally yield very satisfactory spectral and spatial fidelities for the multisharpened hyperspectral data. They also prove that these methods significantly outperform the used literature approaches.

Robust Weak Chimeras in Oscillator Networks with Delayed Linear and Quadratic Interactions

Science.gov (United States)

Bick, Christian; Sebek, Michael; Kiss, István Z.

2017-10-01

We present an approach to generate chimera dynamics (localized frequency synchrony) in oscillator networks with two populations of (at least) two elements using a general method based on a delayed interaction with linear and quadratic terms. The coupling design yields robust chimeras through a phase-model-based design of the delay and the ratio of linear and quadratic components of the interactions. We demonstrate the method in the Brusselator model and experiments with electrochemical oscillators. The technique opens the way to directly bridge chimera dynamics in phase models and real-world oscillator networks.

Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource

Energy Technology Data Exchange (ETDEWEB)

Graber, P. Jameson, E-mail: jameson-graber@baylor.edu [Baylor University, Department of Mathematics (United States)

2016-12-15

We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of Riccati equations. In certain cases, the solution to the mean field type control is also the equilibrium strategy for a class of mean field games. We use this fact to study an economic model of production of exhaustible resources.

Feedback nash equilibria for linear quadratic descriptor differential games

NARCIS (Netherlands)

Engwerda, J.C.; Salmah, S.

2012-01-01

In this paper, we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a

Feedback Nash Equilibria for Linear Quadratic Descriptor Differential Games

NARCIS (Netherlands)

Engwerda, J.C.; Salmah, Y.

2010-01-01

In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a

Linear and quadratic in temperature resistivity from holography

Energy Technology Data Exchange (ETDEWEB)

Ge, Xian-Hui [Department of Physics, Shanghai University, Shanghai 200444 (China); Shanghai Key Laboratory of High Temperature Superconductors,Shanghai 200444 (China); Shanghai Key Lab for Astrophysics,100 Guilin Road, 200234 Shanghai (China); Tian, Yu [School of Physics, University of Chinese Academy of Sciences,Beijing, 100049 (China); Shanghai Key Laboratory of High Temperature Superconductors,Shanghai 200444 (China); Wu, Shang-Yu [Department of Electrophysics, National Chiao Tung University,Hsinchu 300 (China); Wu, Shao-Feng [Department of Physics, Shanghai University, Shanghai 200444 (China); Shanghai Key Laboratory of High Temperature Superconductors,Shanghai 200444 (China); Shanghai Key Lab for Astrophysics,100 Guilin Road, 200234 Shanghai (China)

2016-11-22

We present a new black hole solution in the asymptotic Lifshitz spacetime with a hyperscaling violating factor. A novel computational method is introduced to compute the DC thermoelectric conductivities analytically. We find that both the linear-T and quadratic-T contributions to the resistivity can be realized, indicating that a more detailed comparison with experimental phenomenology can be performed in this scenario.

An application of nonlinear programming to the design of regulators of a linear-quadratic formulation

Science.gov (United States)

Fleming, P.

1983-01-01

A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a nonlinear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.

A nonlinear plate control without linearization

Directory of Open Access Journals (Sweden)

Yildirim Kenan

2017-03-01

Full Text Available In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

Model Predictive Control for Linear Complementarity and Extended Linear Complementarity Systems

Directory of Open Access Journals (Sweden)

Bambang Riyanto

2005-11-01

Full Text Available In this paper, we propose model predictive control method for linear complementarity and extended linear complementarity systems by formulating optimization along prediction horizon as mixed integer quadratic program. Such systems contain interaction between continuous dynamics and discrete event systems, and therefore, can be categorized as hybrid systems. As linear complementarity and extended linear complementarity systems finds applications in different research areas, such as impact mechanical systems, traffic control and process control, this work will contribute to the development of control design method for those areas as well, as shown by three given examples.

Quadratic Stabilization of LPV System by an LTI Controller Based on ILMI Algorithm

Directory of Open Access Journals (Sweden)

Wei Xie

2007-01-01

Full Text Available A linear time-invariant (LTI output feedback controller is designed for a linear parameter-varying (LPV control system to achieve quadratic stability. The LPV system includes immeasurable dependent parameters that are assumed to vary in a polytopic space. To solve this control problem, a heuristic algorithm is proposed in the form of an iterative linear matrix inequality (ILMI formulation. Furthermore, an effective method of setting an initial value of the ILMI algorithm is also proposed to increase the probability of getting an admissible solution for the controller design problem.

Trajectory generation for manipulators using linear quadratic optimal tracking

Directory of Open Access Journals (Sweden)

Olav Egeland

1989-04-01

Full Text Available The reference trajectory is normally known in advance in manipulator control which makes it possible to apply linear quadratic optimal tracking. This gives a control system which rounds corners and generates optimal feedforward. The method may be used for references consisting of straight-line segments as an alternative to the two-step method of using splines to smooth the reference and then applying feedforward. In addition, the method can be used for more complex trajectories. The actual dynamics of the manipulator are taken into account, and this results in smooth and accurate tracking. The method has been applied in combination with the computed torque technique and excellent performance was demonstrated in a simulation study. The method has also been applied experimentally to an industrial spray-painting robot where a saw-tooth reference was tracked. The corner was rounded extremely well, and the steady-state tracking error was eliminated by the optimal feedforward.

Quadratic Blind Linear Unmixing: A Graphical User Interface for Tissue Characterization

OpenAIRE

Gutierrez-Navarro, O.; Campos-Delgado, D.U.; Arce-Santana, E. R.; Jo, Javier A.

2015-01-01

Spectral unmixing is the process of breaking down data from a sample into its basic components and their abundances. Previous work has been focused on blind unmixing of multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) datasets under a linear mixture model and quadratic approximations. This method provides a fast linear decomposition and can work without a limitation in the maximum number of components or end-members. Hence this work presents an interactive software which imple...

TUNING PARAMETER LINEAR QUADRATIC TRACKING MENGGUNAKAN ALGORITMA GENETIKA UNTUK PENGENDALIAN GERAK LATERAL QUADCOPTER

Directory of Open Access Journals (Sweden)

Farid Choirul Akbar

2016-04-01

Full Text Available Gerakan lateral quadcopter dapat dilakukan apabila quadcopter dapat menjaga kestabilan pada saat hover, sehingga quadcopter dapat melakukan gerak rotasi. Perubahan sudut roll akan mengakibatkan gerak translasi pada sumbu Y, sedangkan perubahan sudut pitch akan mengakibatkan gerak translasi pada sumbu X. Disisi lain, quadcopter merupakan suatu sistem non-linear dan memiliki kestabilan yang rendah sehingga rentan terhadap gangguan. Pada penelitian Tugas Akhir ini dirancang pengendalian gerak rotasi quadcopter menggunakan Linear Quadratic Regulator (LQR dan Linear Quadratic Tracking (LQT untuk pengendalian gerak translasi. Untuk mendapatkan parameter dari LQT digunakan Algoritma Genetika (GA. Hasil tuning GA yang digunakan pada LQT memiliki nilai Qx 700,1884, nilai Qy 700,6315, nilai Rx 0,1568, dan  nilai Ry 0,1579. Respon LQT tersebut memiliki RMSE pada sumbu X dan sumbu Y sebesar 1,99 % serta memiliki time lagging 0,35 detik. Dengan hasil tersebut quadcopter mampu men-tracking trajectory berbentuk segitigaTekni

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

Energy Technology Data Exchange (ETDEWEB)

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at [University of Innsbruck, Department of Mathematics (Austria); Tuffaha, Amjad, E-mail: atufaha@aus.edu [American University of Sharjah, Department of Mathematics (United Arab Emirates)

2017-06-15

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.

Quadratic algebras

CERN Document Server

Polishchuk, Alexander

2005-01-01

Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, noncommutative geometry, K-theory, number theory, and noncommutative linear algebra. The book offers a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincar�-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes.

Interlink Converter with Linear Quadratic Regulator Based Current Control for Hybrid AC/DC Microgrid

Directory of Open Access Journals (Sweden)

Dwi Riana Aryani

2017-11-01

Full Text Available A hybrid alternate current/direct current (AC/DC microgrid consists of an AC subgrid and a DC subgrid, and the subgrids are connected through the interlink bidirectional AC/DC converter. In the stand-alone operation mode, it is desirable that the interlink bidirectional AC/DC converter manages proportional power sharing between the subgrids by transferring power from the under-loaded subgrid to the over-loaded one. In terms of system security, the interlink bidirectional AC/DC converter takes an important role, so proper control strategies need to be established. In addition, it is assumed that a battery energy storage system is installed in one subgrid, and the coordinated control of interlink bidirectional AC/DC converter and battery energy storage system converter is required so that the power sharing scheme between subgrids becomes more efficient. For the purpose of designing a tracking controller for the power sharing by interlink bidirectional AC/DC converter in a hybrid AC/DC microgrid, a droop control method generates a power reference for interlink bidirectional AC/DC converter based on the deviation of the system frequency and voltages first and then interlink bidirectional AC/DC converter needs to transfer the power reference to the over-loaded subgrid. For efficiency of this power transferring, a linear quadratic regulator with exponential weighting for the current regulation of interlink bidirectional AC/DC converter is designed in such a way that the resulting microgrid can operate robustly against various uncertainties and the power sharing is carried out quickly. Simulation results show that the proposed interlink bidirectional AC/DC converter control strategy provides robust and efficient power sharing scheme between the subgrids without deteriorating the secure system operation.

Universality of quadratic to linear magnetoresistance crossover in disordered conductors

Science.gov (United States)

Lara, Silvia; Ramakrishnan, Navneeth; Lai, Ying Tong; Adam, Shaffique

Many experiments measuring Magnetoresistance (MR) showed unsaturating linear behavior at high magnetic fields and quadratic behavior at low fields. In the literature, two very different theoretical models have been used to explain this classical MR as a consequence of sample disorder. The phenomenological Random Resistor Network (RRN) model constructs a grid of four-terminal resistors each with a varying random resistance. The Effective Medium Theory (EMT) model imagines a smoothly varying disorder potential that causes a continuous variation of the local conductivity. In this theoretical work, we demonstrate numerically that both the RRN and EMT models belong to the same universality class, and that a single parameter (the ratio of the fluctuations in the carrier density to the average carrier density) completely determines both the magnitude of the MR and the B-field scale for the crossover from quadratic to linear MR. By considering several experimental data sets in the literature, ranging from thin films of InSb to graphene to Weyl semimetals like Na3Bi, we show that this disorder-induced mechanism for MR is in good agreement with the experiments, and that this comparison of MR with theory reveals information about the spatial carrier density inhomogeneity. This work was supported by the National Research Foundation of Singapore (NRF-NRFF2012-01).

Separable quadratic stochastic operators

International Nuclear Information System (INIS)

Rozikov, U.A.; Nazir, S.

2009-04-01

We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)

The application of LQR synthesis techniques to the turboshaft engine control problem. [Linear Quadratic Regulator

Science.gov (United States)

Pfeil, W. H.; De Los Reyes, G.; Bobula, G. A.

1985-01-01

A power turbine governor was designed for a recent-technology turboshaft engine coupled to a modern, articulated rotor system using Linear Quadratic Regulator (LQR) and Kalman Filter (KF) techniques. A linear, state-space model of the engine and rotor system was derived for six engine power settings from flight idle to maximum continuous. An integrator was appended to the fuel flow input to reduce the steady-state governor error to zero. Feedback gains were calculated for the system states at each power setting using the LQR technique. The main rotor tip speed state is not measurable, so a Kalman Filter of the rotor was used to estimate this state. The crossover of the system was increased to 10 rad/s compared to 2 rad/sec for a current governor. Initial computer simulations with a nonlinear engine model indicate a significant decrease in power turbine speed variation with the LQR governor compared to a conventional governor.

Quadratic blind linear unmixing: A graphical user interface for tissue characterization.

Science.gov (United States)

Gutierrez-Navarro, O; Campos-Delgado, D U; Arce-Santana, E R; Jo, Javier A

2016-02-01

Spectral unmixing is the process of breaking down data from a sample into its basic components and their abundances. Previous work has been focused on blind unmixing of multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) datasets under a linear mixture model and quadratic approximations. This method provides a fast linear decomposition and can work without a limitation in the maximum number of components or end-members. Hence this work presents an interactive software which implements our blind end-member and abundance extraction (BEAE) and quadratic blind linear unmixing (QBLU) algorithms in Matlab. The options and capabilities of our proposed software are described in detail. When the number of components is known, our software can estimate the constitutive end-members and their abundances. When no prior knowledge is available, the software can provide a completely blind solution to estimate the number of components, the end-members and their abundances. The characterization of three case studies validates the performance of the new software: ex-vivo human coronary arteries, human breast cancer cell samples, and in-vivo hamster oral mucosa. The software is freely available in a hosted webpage by one of the developing institutions, and allows the user a quick, easy-to-use and efficient tool for multi/hyper-spectral data decomposition. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Linear and quadratic exponential modulation of the solutions of the paraxial wave equation

International Nuclear Information System (INIS)

Torre, A

2010-01-01

A review of well-known transformations, which allow us to pass from one solution of the paraxial wave equation (PWE) (in one transverse space variable) to another, is presented. Such transformations are framed within the unifying context of the Lie algebra formalism, being related indeed to symmetries of the PWE. Due to the closure property of the symmetry group of the PWE we are led to consider as not trivial only the linear and the quadratic exponential modulation (accordingly, accompanied by a suitable shift or scaling of the space variables) of the original solutions of the PWE, which are seen to be just conveyed by a linear and a quadratic exponential modulation of the relevant 'source' functions. We will see that recently introduced solutions of the 1D PWE in both rectangular and polar coordinates can be deduced from already known solutions through the resulting symmetry transformation related schemes

Overlapping quadratic optimal control of linear time-varying commutative systems

Czech Academy of Sciences Publication Activity Database

Bakule, Lubomír; Rodellar, J.; Rossell, J. M.

2002-01-01

Roč. 40, č. 5 (2002), s. 1611-1627 ISSN 0363-0129 R&D Projects: GA AV ČR IAA2075802 Institutional research plan: CEZ:AV0Z1075907 Keywords : overlapping * optimal control * linear time-varying systems Subject RIV: BC - Control Systems Theory Impact factor: 1.441, year: 2002

A linear-quadratic model of cell survival considering both sublethal and potentially lethal radiation damage

International Nuclear Information System (INIS)

Rutz, H.P.; Coucke, P.A.; Mirimanoff, R.O.

1991-01-01

The authors assessed the dose-dependence of repair of potentially lethal damage in Chinese hamster ovary cells x-irradiated in vitro. The recovery ratio (RR) by which survival (SF) of the irradiated cells was enhanced increased exponentially with a linear and a quadratic component namely ζ and ψ: RR=exp(ζD+ψD 2 ). Survival of irradiated cells can thus be expressed by a combined linear-quadratic model considering 4 variables, namely α and β for the capacity of the cells to accumulate sublethal damage, and ζ and ψ for their capacity to repair potentially lethal damage: SF=exp((ζ-α)D+ (ψ-β)D 2 ). author. 26 refs.; 1 fig.; 1 tab

On using the linear-quadratic model in daily clinical practice

International Nuclear Information System (INIS)

Yaes, R.J.; Patel, P.; Maruyama, Y.

1991-01-01

To facilitate its use in the clinic, Barendsen's formulation of the Linear-Quadratic (LQ) model is modified by expressing isoeffect doses in terms of the Standard Effective Dose, Ds, the isoeffective dose for the standard fractionation schedule of 2 Gy fractions given once per day, 5 days per week. For any arbitrary fractionation schedule, where total dose D is given in N fractions of size d in a total time T, the corresponding Standard Effective Dose, Ds, will be proportional to the total dose D and the proportionality constant will be called the Standard Relative Effectiveness, SRE, to distinguish it from Barendsen's Relative Effectiveness, RE. Thus, Ds = SRE.D. The constant SRE depends on the parameters of the fractionation schedule, and on the tumor or normal tissue being irradiated. For the simple LQ model with no time dependence, which is applicable to late reacting tissue, SRE = [(d + delta)/(2 + delta)], where d is the fraction size and delta = alpha/beta is the alpha/beta ratio for the tissue of interest, with both d and delta expressed in units of Gy. Application of this method to the Linear Quadratic model with a time dependence, the LQ + time model, and to low dose rate brachytherapy will be discussed. To clarify the method of calculation, and to demonstrate its simplicity, examples from the clinical literature will be used

Quadratic obstructions to small-time local controllability for scalar-input systems

Science.gov (United States)

Beauchard, Karine; Marbach, Frédéric

2018-03-01

We consider nonlinear finite-dimensional scalar-input control systems in the vicinity of an equilibrium. When the linearized system is controllable, the nonlinear system is smoothly small-time locally controllable: whatever m > 0 and T > 0, the state can reach a whole neighborhood of the equilibrium at time T with controls arbitrary small in Cm-norm. When the linearized system is not controllable, we prove that: either the state is constrained to live within a smooth strict manifold, up to a cubic residual, or the quadratic order adds a signed drift with respect to it. This drift holds along a Lie bracket of length (2 k + 1), is quantified in terms of an H-k-norm of the control, holds for controls small in W 2 k , ∞-norm and these spaces are optimal. Our proof requires only C3 regularity of the vector field. This work underlines the importance of the norm used in the smallness assumption on the control, even in finite dimension.

Underprediction of human skin erythema at low doses per fraction by the linear quadratic model

International Nuclear Information System (INIS)

Hamilton, Christopher S.; Denham, James W.; O'Brien, Maree; Ostwald, Patricia; Kron, Tomas; Wright, Suzanne; Doerr, Wolfgang

1996-01-01

Background and purpose. The erythematous response of human skin to radiotherapy has proven useful for testing the predictions of the linear quadratic (LQ) model in terms of fractionation sensitivity and repair half time. No formal investigation of the response of human skin to doses less than 2 Gy per fraction has occurred. This study aims to test the validity of the LQ model for human skin at doses ranging from 0.4 to 5.2 Gy per fraction. Materials and methods. Complete erythema reaction profiles were obtained using reflectance spectrophotometry in two patient populations: 65 patients treated palliatively with 5, 10, 12 and 20 daily treatment fractions (varying thicknesses of bolus, various body sites) and 52 patients undergoing prostatic irradiation for localised carcinoma of the prostate (no bolus, 30-32 fractions). Results and conclusions. Gender, age, site and prior sun exposure influence pre- and post-treatment erythema values independently of dose administered. Out-of-field effects were also noted. The linear quadratic model significantly underpredicted peak erythema values at doses less than 1.5 Gy per fraction. This suggests that either the conventional linear quadratic model does not apply for low doses per fraction in human skin or that erythema is not exclusively initiated by radiation damage to the basal layer. The data are potentially explained by an induced repair model

Optimal Quadratic Programming Algorithms

CERN Document Server

Dostal, Zdenek

2009-01-01

Quadratic programming (QP) is one technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This title presents various algorithms for solving large QP problems. It is suitable as an introductory text on quadratic programming for graduate students and researchers

Quadratic Plus Linear Operators which Preserve Pure States of Quantum Systems: Small Dimensions

International Nuclear Information System (INIS)

Saburov, Mansoor

2014-01-01

A mathematical formalism of quantum mechanics says that a pure state of a quantum system corresponds to a vector of norm 1 and an observable is a self-adjoint operator on the space of states. It is of interest to describe all linear or nonlinear operators which preserve the pure states of the system. In the linear case, it is nothing more than isometries of Hilbert spaces. In the nonlinear case, this problem was open. In this paper, in the small dimensional spaces, we shall describe all quadratic plus linear operators which preserve pure states of the quantum system

Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation

International Nuclear Information System (INIS)

Kolesov, Andrei Yu; Rozov, Nikolai Kh

2002-01-01

For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied

Design a software real-time operation platform for wave piercing catamarans motion control using linear quadratic regulator based genetic algorithm.

Science.gov (United States)

Liang, Lihua; Yuan, Jia; Zhang, Songtao; Zhao, Peng

2018-01-01

This work presents optimal linear quadratic regulator (LQR) based on genetic algorithm (GA) to solve the two degrees of freedom (2 DoF) motion control problem in head seas for wave piercing catamarans (WPC). The proposed LQR based GA control strategy is to select optimal weighting matrices (Q and R). The seakeeping performance of WPC based on proposed algorithm is challenged because of multi-input multi-output (MIMO) system of uncertain coefficient problems. Besides the kinematical constraint problems of WPC, the external conditions must be considered, like the sea disturbance and the actuators (a T-foil and two flaps) control. Moreover, this paper describes the MATLAB and LabVIEW software plats to simulate the reduction effects of WPC. Finally, the real-time (RT) NI CompactRIO embedded controller is selected to test the effectiveness of the actuators based on proposed techniques. In conclusion, simulation and experimental results prove the correctness of the proposed algorithm. The percentage of heave and pitch reductions are more than 18% in different high speeds and bad sea conditions. And the results also verify the feasibility of NI CompactRIO embedded controller.

Analysis of a monetary union enlargement in the framework of linear-quadratic differential games

NARCIS (Netherlands)

Plasmans, J.E.J.; Engwerda, J.C.; van Aarle, B.; Michalak, T.

2009-01-01

"This paper studies the effects of a monetary union enlargement using the techniques and outcomes from an extensive research project on macroeconomic policy coordination in the EMU. Our approach is characterized by two main pillars: (i) linear-quadratic differential games to capture externalities,

Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise

Directory of Open Access Journals (Sweden)

Huiying Sun

2014-01-01

Full Text Available We mainly consider the stability of discrete-time Markovian jump linear systems with state-dependent noise as well as its linear quadratic (LQ differential games. A necessary and sufficient condition involved with the connection between stochastic Tn-stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochastic Tn-stability, we give the optimal strategies and the optimal cost values for infinite horizon LQ stochastic differential games. It is demonstrated that the solutions of infinite horizon LQ stochastic differential games are concerned with four coupled generalized algebraic Riccati equations (GAREs. Finally, an iterative algorithm is presented to solve the four coupled GAREs and a simulation example is given to illustrate the effectiveness of it.

The Model and Quadratic Stability Problem of Buck Converter in DCM

Directory of Open Access Journals (Sweden)

Li Xiaojing

2016-01-01

Full Text Available Quadratic stability is an important performance for control systems. At first, the model of Buck Converter in DCM is built based on the theories of hybrid systems and switched linear systems primarily. Then quadratic stability of SLS and hybrid feedback switching rule are introduced. The problem of Buck Converter’s quadratic stability is researched afterwards. In the end, the simulation analysis and verification are provided. Both experimental verification and theoretical analysis results indicate that the output of Buck Converter in DCM has an excellent performance via quadratic stability control and switching rules.

Dynamical invariants for variable quadratic Hamiltonians

International Nuclear Information System (INIS)

Suslov, Sergei K

2010-01-01

We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.

On Optimal Feedback Control for Stationary Linear Systems

International Nuclear Information System (INIS)

Russell, David L.

2010-01-01

We study linear-quadratic optimal control problems for finite dimensional stationary linear systems AX+BU=Z with output Y=CX+DU from the viewpoint of linear feedback solution. We interpret solutions in relation to system robustness with respect to disturbances Z and relate them to nonlinear matrix equations of Riccati type and eigenvalue-eigenvector problems for the corresponding Hamiltonian system. Examples are included along with an indication of extensions to continuous, i.e., infinite dimensional, systems, primarily of elliptic type.

A computer tool for daily application of the linear quadratic model

International Nuclear Information System (INIS)

Macias Jaen, J.; Galan Montenegro, P.; Bodineau Gil, C.; Wals Zurita, A.; Serradilla Gil, A.M.

2001-01-01

The aim of this paper is to indicate the relevance of the criteria A.S.A.R.A. (As Short As Reasonably Achievable) in the optimization of a fractionated radiotherapy schedule and the presentation of a Windows computer program as an easy tool in order to: Evaluate the Biological Equivalent Dose (BED) in a fractionated schedule; Make comparison between different treatments; Compensate a treatment when a delay has been happened with a version of the Linear Quadratic model that has into account the factor of accelerated repopulation. Conclusions: Delays in the normal radiotherapy schedule are items that have to be controlled as much as possible because it is able to be a very important parameter in order to release a good application of treatment, principally when the tumour is fast growing. It is necessary to evaluate them. ASARA criteria is useful to indicate the relevance of this aspect. Also, computer tools like this one could help us in order to achieve this. (author)

A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems

Science.gov (United States)

Banks, H. T.; Ito, K.

1991-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.

H 2 guaranteed cost control of discrete linear systems

Directory of Open Access Journals (Sweden)

Colmenares W.

2000-01-01

Full Text Available This paper presents necessary and sufficient conditions for the existence of a quadratically stabilizing output feedback controller which also assures H 2 guaranteed cost performance on a discrete linear uncertain system where the uncertainty is of the norm bounded type. The conditions are presented as a collection of linear matrix inequalities.The solution, however requires a search over a scalar parameter space.

Controller design approach based on linear programming.

Science.gov (United States)

Tanaka, Ryo; Shibasaki, Hiroki; Ogawa, Hiromitsu; Murakami, Takahiro; Ishida, Yoshihisa

2013-11-01

This study explains and demonstrates the design method for a control system with a load disturbance observer. Observer gains are determined by linear programming (LP) in terms of the Routh-Hurwitz stability criterion and the final-value theorem. In addition, the control model has a feedback structure, and feedback gains are determined to be the linear quadratic regulator. The simulation results confirmed that compared with the conventional method, the output estimated by our proposed method converges to a reference input faster when a load disturbance is added to a control system. In addition, we also confirmed the effectiveness of the proposed method by performing an experiment with a DC motor. © 2013 ISA. Published by ISA. All rights reserved.

On the Cauchy problem for a Sobolev-type equation with quadratic non-linearity

International Nuclear Information System (INIS)

Aristov, Anatoly I

2011-01-01

We investigate the asymptotic behaviour as t→∞ of the solution of the Cauchy problem for a Sobolev-type equation with quadratic non-linearity and develop ideas used by I. A. Shishmarev and other authors in the study of classical and Sobolev-type equations. Conditions are found under which it is possible to consider the case of an arbitrary dimension of the spatial variable.

Optimal Piecewise-Linear Approximation of the Quadratic Chaotic Dynamics

Directory of Open Access Journals (Sweden)

J. Petrzela

2012-04-01

Full Text Available This paper shows the influence of piecewise-linear approximation on the global dynamics associated with autonomous third-order dynamical systems with the quadratic vector fields. The novel method for optimal nonlinear function approximation preserving the system behavior is proposed and experimentally verified. This approach is based on the calculation of the state attractor metric dimension inside a stochastic optimization routine. The approximated systems are compared to the original by means of the numerical integration. Real electronic circuits representing individual dynamical systems are derived using classical as well as integrator-based synthesis and verified by time-domain analysis in Orcad Pspice simulator. The universality of the proposed method is briefly discussed, especially from the viewpoint of the higher-order dynamical systems. Future topics and perspectives are also provided

Quadratic genetic modifications: a streamlined route to cosmological simulations with controlled merger history

Science.gov (United States)

Rey, Martin P.; Pontzen, Andrew

2018-02-01

Recent work has studied the interplay between a galaxy's history and its observable properties using `genetically modified' cosmological zoom simulations. The approach systematically generates alternative histories for a halo, while keeping its cosmological environment fixed. Applications to date altered linear properties of the initial conditions, such as the mean overdensity of specified regions; we extend the formulation to include quadratic features, such as local variance, that determines the overall importance of smooth accretion relative to mergers in a galaxy's history. We introduce an efficient algorithm for this new class of modification and demonstrate its ability to control the variance of a region in a one-dimensional toy model. Outcomes of this work are twofold: (i) a clarification of the formulation of genetic modifications and (ii) a proof of concept for quadratic modifications leading the way to a forthcoming implementation in cosmological simulations.

Linear parameter varying representations for nonlinear control design

Science.gov (United States)

Carter, Lance Huntington

Linear parameter varying (LPV) systems are investigated as a framework for gain-scheduled control design and optimal hybrid control. An LPV system is defined as a linear system whose dynamics depend upon an a priori unknown but measurable exogenous parameter. A gain-scheduled autopilot design is presented for a bank-to-turn (BTT) missile. The method is novel in that the gain-scheduled design does not involve linearizations about operating points. Instead, the missile dynamics are brought to LPV form via a state transformation. This idea is applied to the design of a coupled longitudinal/lateral BTT missile autopilot. The pitch and yaw/roll dynamics are separately transformed to LPV form, where the cross axis states are treated as "exogenous" parameters. These are actually endogenous variables, so such a plant is called "quasi-LPV." Once in quasi-LPV form, a family of robust controllers using mu synthesis is designed for both the pitch and yaw/roll channels, using angle-of-attack and roll rate as the scheduling variables. The closed-loop time response is simulated using the original nonlinear model and also using perturbed aerodynamic coefficients. Modeling and control of engine idle speed is investigated using LPV methods. It is shown how generalized discrete nonlinear systems may be transformed into quasi-LPV form. A discrete nonlinear engine model is developed and expressed in quasi-LPV form with engine speed as the scheduling variable. An example control design is presented using linear quadratic methods. Simulations are shown comparing the LPV based controller performance to that using PID control. LPV representations are also shown to provide a setting for hybrid systems. A hybrid system is characterized by control inputs consisting of both analog signals and discrete actions. A solution is derived for the optimal control of hybrid systems with generalized cost functions. This is shown to be computationally intensive, so a suboptimal strategy is proposed that

Application of the linear-quadratic model to myelotoxicity associated with radioimmunotherapy

International Nuclear Information System (INIS)

Wilder, R.B.; DeNardo, G.L.; Sheri, S.; Fowler, J.F.; Wessels, B.W.; DeNardo, S.J.

1996-01-01

The purposes of this study were: To use the linear-quadratic model to determine time-dependent biologically effective doses (BEDs) that were delivered to the bone marrow by multiple infusions of radiolabeled antibodies, and (2) to determine whether granulocyte and platelet counts correlate better with BED than administered radioactivity. Twenty patients with B-cell malignancies that had progressed despite intensive chemotherapy and who had a significant number of malignant cells in their bone marrow were treated with multiple 0.7-3.7 GBq/m 2 intravenous infusions of Lym-1, a murine monoclonal antibody that binds to a tumour-associated antigen, labeled with iodine-131. Granulocyte and platelet counts were measured in order to assess bone marrow toxicity. The cumulative 131 I-Lym-1 radioactivity administered to each patient was calculated. BEDs from multiple 131 I-Lym-1 infusions were summated in order to arrive at a total BED for each patient. There was a weak association between granulocyte and platelet counts and radioactivity. Likewise, there was a weak association between granulocyte and platelet counts and BED. The attempt to take bone marrow absorbed doses and overall treatment time into consideration with the linear-quadratic model did not produce a stronger association than was observed between peripheral blood counts and administered radioactivity. The association between granulocyte and platelet counts and BED may have been weakened by several factors, including variable bone marrow reserve at the start of 131 I-Lym-1 therapy and the delivery of heterogeneous, absorbed doses of radiation to the bone marrow. (orig./MG)

Optimal Operation of Distribution Electronic Power Transformer Using Linear Quadratic Regulator Method

Directory of Open Access Journals (Sweden)

Mohammad Hosein Rezaei

2011-10-01

Full Text Available Transformers perform many functions such as voltage transformation, isolation and noise decoupling. They are indispensable components in electric power distribution system. However, at low frequencies (50 Hz, they are one of the heaviest and the most expensive equipment in an electrical distribution system. Nowadays, electronic power transformers are used instead of conventional power transformers that do voltage transformation and power delivery in power system by power electronic converter. In this paper, the structure of distribution electronic power transformer (DEPT are analized and then paid attention on the design of a linear-quadratic-regulator (LQR with integral action to improve dynamic performance of DEPT with voltage unbalance, voltage sags, voltage harmonics and voltage flicker. The presentation control strategy is simulated by MATLAB/SIMULINK. In addition, the results that are in terms of dc-link reference voltage, input and output voltages clearly show that a better dynamic performance can be achieved by using the LQR method when compared to other techniques.

Self-Tuning Linear Quadratic Supervisory Regulation of a Diesel Generator using Large-Signal State Estimation

DEFF Research Database (Denmark)

Knudsen, Jesper Viese; Bendtsen, Jan Dimon; Andersen, Palle

2016-01-01

In this paper, a self-tuning linear quadratic supervisory regulator using a large-signal state estimator for a diesel driven generator set is proposed. The regulator improves operational efficiency, in comparison to current implementations, by (i) automating the initial tuning process and (ii...... throughout the operating range of the diesel generator....

New hybrid non-linear transformations of divergent perturbation series for quadratic Zeeman effects

International Nuclear Information System (INIS)

Belkic, D.

1989-01-01

The problem of hydrogen atoms in an external uniform magnetic field (quadratic Zeeman effect) is studied by means of perturbation theory. The power series for the ground-state energy in terms of magnetic-field strength B is divergent. Nevertheless, it is possible to induce convergence of this divergent series by applying various non-linear transformations. These transformations of originally divergent perturbation series yield new sequences, which then converge. The induced convergence is, however, quite slow. A new hybrid Shanks-Levin non-linear transform is devised here for accelerating these slowly converging series and sequences. Significant improvement in the convergence rate is obtained. Agreement with the exact results is excellent. (author)

A Finite Continuation Algorithm for Bound Constrained Quadratic Programming

DEFF Research Database (Denmark)

Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.

1999-01-01

The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems...

The Increase in Animal Mortality Risk following Exposure to Sparsely Ionizing Radiation Is Not Linear Quadratic with Dose.

Directory of Open Access Journals (Sweden)

Benjamin M Haley

Full Text Available The US government regulates allowable radiation exposures relying, in large part, on the seventh report from the committee to estimate the Biological Effect of Ionizing Radiation (BEIR VII, which estimated that most contemporary exposures- protracted or low-dose, carry 1.5 fold less risk of carcinogenesis and mortality per Gy than acute exposures of atomic bomb survivors. This correction is known as the dose and dose rate effectiveness factor for the life span study of atomic bomb survivors (DDREFLSS. It was calculated by applying a linear-quadratic dose response model to data from Japanese atomic bomb survivors and a limited number of animal studies.We argue that the linear-quadratic model does not provide appropriate support to estimate the risk of contemporary exposures. In this work, we re-estimated DDREFLSS using 15 animal studies that were not included in BEIR VII's original analysis. Acute exposure data led to a DDREFLSS estimate from 0.9 to 3.0. By contrast, data that included both acute and protracted exposures led to a DDREFLSS estimate from 4.8 to infinity. These two estimates are significantly different, violating the assumptions of the linear-quadratic model, which predicts that DDREFLSS values calculated in either way should be the same.Therefore, we propose that future estimates of the risk of protracted exposures should be based on direct comparisons of data from acute and protracted exposures, rather than from extrapolations from a linear-quadratic model. The risk of low dose exposures may be extrapolated from these protracted estimates, though we encourage ongoing debate as to whether this is the most valid approach. We also encourage efforts to enlarge the datasets used to estimate the risk of protracted exposures by including both human and animal data, carcinogenesis outcomes, a wider range of exposures, and by making more radiobiology data publicly accessible. We believe that these steps will contribute to better estimates

Observer-based linear parameter varying H∞ tracking control for hypersonic vehicles

Directory of Open Access Journals (Sweden)

Yiqing Huang

2016-11-01

Full Text Available This article aims to develop observer-based linear parameter varying output feedback H∞ tracking controller for hypersonic vehicles. Due to the complexity of an original nonlinear model of the hypersonic vehicle dynamics, a slow–fast loop linear parameter varying polytopic model is introduced for system stability analysis and controller design. Then, a state observer is developed by linear parameter varying technique in order to estimate the unmeasured attitude angular for slow loop system. Also, based on the designed linear parameter varying state observer, a kind of attitude tracking controller is presented to reduce tracking errors for all bounded reference attitude angular inputs. The closed-loop linear parameter varying system is proved to be quadratically stable by Lypapunov function technique. Finally, simulation results show that the developed linear parameter varying H∞ controller has good tracking capability for reference commands.

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

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Xiaobing Kong

2013-01-01

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

An improved robust model predictive control for linear parameter-varying input-output models

NARCIS (Netherlands)

Abbas, H.S.; Hanema, J.; Tóth, R.; Mohammadpour, J.; Meskin, N.

2018-01-01

This paper describes a new robust model predictive control (MPC) scheme to control the discrete-time linear parameter-varying input-output models subject to input and output constraints. Closed-loop asymptotic stability is guaranteed by including a quadratic terminal cost and an ellipsoidal terminal

Slab albedo for linearly and quadratically anisotropic scattering kernel with modified F{sub N} method

Energy Technology Data Exchange (ETDEWEB)

Tuereci, R. Goekhan [Kirikkale Univ. (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministry of Education, Ankara (Turkey). 75th year Anatolia High School

2017-11-15

One speed, time independent and homogeneous medium neutron transport equation is solved with the anisotropic scattering which includes both the linearly and the quadratically anisotropic scattering kernel. Having written Case's eigenfunctions and the orthogonality relations among of these eigenfunctions, slab albedo problem is investigated as numerically by using Modified F{sub N} method. Selected numerical results are presented in tables.

Technical report. The application of probability-generating functions to linear-quadratic radiation survival curves.

Science.gov (United States)

Kendal, W S

2000-04-01

To illustrate how probability-generating functions (PGFs) can be employed to derive a simple probabilistic model for clonogenic survival after exposure to ionizing irradiation. Both repairable and irreparable radiation damage to DNA were assumed to occur by independent (Poisson) processes, at intensities proportional to the irradiation dose. Also, repairable damage was assumed to be either repaired or further (lethally) injured according to a third (Bernoulli) process, with the probability of lethal conversion being directly proportional to dose. Using the algebra of PGFs, these three processes were combined to yield a composite PGF that described the distribution of lethal DNA lesions in irradiated cells. The composite PGF characterized a Poisson distribution with mean, chiD+betaD2, where D was dose and alpha and beta were radiobiological constants. This distribution yielded the conventional linear-quadratic survival equation. To test the composite model, the derived distribution was used to predict the frequencies of multiple chromosomal aberrations in irradiated human lymphocytes. The predictions agreed well with observation. This probabilistic model was consistent with single-hit mechanisms, but it was not consistent with binary misrepair mechanisms. A stochastic model for radiation survival has been constructed from elementary PGFs that exactly yields the linear-quadratic relationship. This approach can be used to investigate other simple probabilistic survival models.

Time-dependent tumour repopulation factors in linear-quadratic equations

International Nuclear Information System (INIS)

Dale, R.G.

1989-01-01

Tumour proliferation effects can be tentatively quantified in the linear-quadratic (LQ) method by the incorporation of a time-dependent factor, the magnitude of which is related both to the value of α in the tumour α/β ratio, and to the tumour doubling time. The method, the principle of which has been suggested by a numbre of other workers for use in fractionated therapy, is here applied to both fractionated and protracted radiotherapy treatments, and examples of its uses are given. By assuming that repopulation of late-responding tissues is significant during normal treatment strategies in terms of the behaviour of the Extrapolated Response Dose (ERD). Although the numerical credibility of the analysis used here depends on the reliability of the LQ model, and on the assumption that the rate of repopulation is constant throughout treatment, the predictions are consistent with other lines of reasoning which point to the advantages of accelerated hyperfractionation. In particular, it is demonstrated that accelerated fractionation represents a relatively 'foregiving' treatment which enables tumours of a variety of sensitivities and clonogenic growth rates to be treated moderately successfully, even though the critical cellular parameters may not be known in individual cases. The analysis also suggests that tumours which combine low intrinsic sensitivity with a very short doubling time might be bettter controlled by low dose-rate continuous therapy than by almost any form of accelerated hyperfractionation. (author). 24 refs.; 5 figs

Reference-tracking feedforward control design for linear dynamical systems through signal decomposition

NARCIS (Netherlands)

Kasemsinsup, Y.; Romagnoli, R.; Heertjes, M.F.; Weiland, S.; Butler, H.

2017-01-01

In this work, we study a novel approach towards the reference-tracking feedforward control design for linear dynamical systems. By utilizing the superposition property and exploiting signal decomposition together with a quadratic optimization process, we obtain a feedforward design procedure for

Quadratic-linear pattern in cancer fractional radiotherapy. Equations for a computering program

International Nuclear Information System (INIS)

Burgos, D.; Bullejos, J.; Garcia Puche, J.L.; Pedraza, V.

1990-01-01

Knowledge of equivalence between different tratment schemes with the same iso-effect is the essential thing in clinical cancer radiotherapy. For this purpose it is very useful the group of ideas derived from quadratic-linear pattern (Q-L) proposed in order to analyze cell survival curve to radiation. Iso-effect definition caused by several irradiation rules is done by extrapolated tolerance dose (ETD). Because equations for ETD are complex, a computering program have been carried out. In this paper, iso-effect equations for well defined therapeutic situations and flow diagram proposed for resolution, have been studied. (Author)

Optimality Conditions for Fuzzy Number Quadratic Programming with Fuzzy Coefficients

Directory of Open Access Journals (Sweden)

Xue-Gang Zhou

2014-01-01

Full Text Available The purpose of the present paper is to investigate optimality conditions and duality theory in fuzzy number quadratic programming (FNQP in which the objective function is fuzzy quadratic function with fuzzy number coefficients and the constraint set is fuzzy linear functions with fuzzy number coefficients. Firstly, the equivalent quadratic programming of FNQP is presented by utilizing a linear ranking function and the dual of fuzzy number quadratic programming primal problems is introduced. Secondly, we present optimality conditions for fuzzy number quadratic programming. We then prove several duality results for fuzzy number quadratic programming problems with fuzzy coefficients.

Combining support vector machines with linear quadratic regulator adaptation for the online design of an automotive active suspension system

International Nuclear Information System (INIS)

Chiou, J-S; Liu, M-T

2008-01-01

As a powerful machine-learning approach to pattern recognition problems, the support vector machine (SVM) is known to easily allow generalization. More importantly, it works very well in a high-dimensional feature space. This paper presents a nonlinear active suspension controller which achieves a high level performance by compensating for actuator dynamics. We use a linear quadratic regulator (LQR) to ensure optimal control of nonlinear systems. An LQR is used to solve the problem of state feedback and an SVM is used to address the question of the estimation and examination of the state. These two are then combined and designed in a way that outputs feedback control. The real-time simulation demonstrates that an active suspension using the combined SVM-LQR controller provides passengers with a much more comfortable ride and better road handling

A Linear Programming Reformulation of the Standard Quadratic Optimization Problem

NARCIS (Netherlands)

de Klerk, E.; Pasechnik, D.V.

2005-01-01

The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem (SQO).It is NPhard, and contains the maximum stable set problem in graphs as a special case.In this note we show that the SQO problem may be reformulated as an (exponentially

A perturbative solution for gravitational waves in quadratic gravity

International Nuclear Information System (INIS)

Neto, Edgard C de Rey; Aguiar, Odylio D; Araujo, Jose C N de

2003-01-01

We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einstein's linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einstein's general relativity. The perturbative solution is written as a power series in the β parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency ω, the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 1/2 . This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin

On the analysis of clonogenic survival data: Statistical alternatives to the linear-quadratic model

International Nuclear Information System (INIS)

Unkel, Steffen; Belka, Claus; Lauber, Kirsten

2016-01-01

The most frequently used method to quantitatively describe the response to ionizing irradiation in terms of clonogenic survival is the linear-quadratic (LQ) model. In the LQ model, the logarithm of the surviving fraction is regressed linearly on the radiation dose by means of a second-degree polynomial. The ratio of the estimated parameters for the linear and quadratic term, respectively, represents the dose at which both terms have the same weight in the abrogation of clonogenic survival. This ratio is known as the α/β ratio. However, there are plausible scenarios in which the α/β ratio fails to sufficiently reflect differences between dose-response curves, for example when curves with similar α/β ratio but different overall steepness are being compared. In such situations, the interpretation of the LQ model is severely limited. Colony formation assays were performed in order to measure the clonogenic survival of nine human pancreatic cancer cell lines and immortalized human pancreatic ductal epithelial cells upon irradiation at 0-10 Gy. The resulting dataset was subjected to LQ regression and non-linear log-logistic regression. Dimensionality reduction of the data was performed by cluster analysis and principal component analysis. Both the LQ model and the non-linear log-logistic regression model resulted in accurate approximations of the observed dose-response relationships in the dataset of clonogenic survival. However, in contrast to the LQ model the non-linear regression model allowed the discrimination of curves with different overall steepness but similar α/β ratio and revealed an improved goodness-of-fit. Additionally, the estimated parameters in the non-linear model exhibit a more direct interpretation than the α/β ratio. Dimensionality reduction of clonogenic survival data by means of cluster analysis was shown to be a useful tool for classifying radioresistant and sensitive cell lines. More quantitatively, principal component analysis allowed

Linear versus quadratic portfolio optimization model with transaction cost

Science.gov (United States)

Razak, Norhidayah Bt Ab; Kamil, Karmila Hanim; Elias, Siti Masitah

2014-06-01

Optimization model is introduced to become one of the decision making tools in investment. Hence, it is always a big challenge for investors to select the best model that could fulfill their goal in investment with respect to risk and return. In this paper we aims to discuss and compare the portfolio allocation and performance generated by quadratic and linear portfolio optimization models namely of Markowitz and Maximin model respectively. The application of these models has been proven to be significant and popular among others. However transaction cost has been debated as one of the important aspects that should be considered for portfolio reallocation as portfolio return could be significantly reduced when transaction cost is taken into consideration. Therefore, recognizing the importance to consider transaction cost value when calculating portfolio' return, we formulate this paper by using data from Shariah compliant securities listed in Bursa Malaysia. It is expected that, results from this paper will effectively justify the advantage of one model to another and shed some lights in quest to find the best decision making tools in investment for individual investors.

Stochastic multiresonance for a fractional linear oscillator with time-delayed kernel and quadratic noise

Science.gov (United States)

Guo, Feng; Wang, Xue-Yuan; Zhu, Cheng-Yin; Cheng, Xiao-Feng; Zhang, Zheng-Yu; Huang, Xu-Hui

2017-12-01

The stochastic resonance for a fractional oscillator with time-delayed kernel and quadratic trichotomous noise is investigated. Applying linear system theory and Laplace transform, the system output amplitude (SPA) for the fractional oscillator is obtained. It is found that the SPA is a periodical function of the kernel delayed-time. Stochastic multiplicative phenomenon appears on the SPA versus the driving frequency, versus the noise amplitude, and versus the fractional exponent. The non-monotonous dependence of the SPA on the system parameters is also discussed.

Mechanistic formulation of a lineal-quadratic-linear (LQL) model: Split-dose experiments and exponentially decaying sources

International Nuclear Information System (INIS)

Guerrero, Mariana; Carlone, Marco

2010-01-01

Purpose: In recent years, several models were proposed that modify the standard linear-quadratic (LQ) model to make the predicted survival curve linear at high doses. Most of these models are purely phenomenological and can only be applied in the particular case of acute doses per fraction. The authors consider a mechanistic formulation of a linear-quadratic-linear (LQL) model in the case of split-dose experiments and exponentially decaying sources. This model provides a comprehensive description of radiation response for arbitrary dose rate and fractionation with only one additional parameter. Methods: The authors use a compartmental formulation of the LQL model from the literature. They analytically solve the model's differential equations for the case of a split-dose experiment and for an exponentially decaying source. They compare the solutions of the survival fraction with the standard LQ equations and with the lethal-potentially lethal (LPL) model. Results: In the case of the split-dose experiment, the LQL model predicts a recovery ratio as a function of dose per fraction that deviates from the square law of the standard LQ. The survival fraction as a function of time between fractions follows a similar exponential law as the LQ but adds a multiplicative factor to the LQ parameter β. The LQL solution for the split-dose experiment is very close to the LPL prediction. For the decaying source, the differences between the LQL and the LQ solutions are negligible when the half-life of the source is much larger than the characteristic repair time, which is the clinically relevant case. Conclusions: The compartmental formulation of the LQL model can be used for arbitrary dose rates and provides a comprehensive description of dose response. When the survival fraction for acute doses is linear for high dose, a deviation of the square law formula of the recovery ratio for split doses is also predicted.

Zhang neural network for online solution of time-varying convex quadratic program subject to time-varying linear-equality constraints

International Nuclear Information System (INIS)

Zhang Yunong; Li Zhan

2009-01-01

In this Letter, by following Zhang et al.'s method, a recurrent neural network (termed as Zhang neural network, ZNN) is developed and analyzed for solving online the time-varying convex quadratic-programming problem subject to time-varying linear-equality constraints. Different from conventional gradient-based neural networks (GNN), such a ZNN model makes full use of the time-derivative information of time-varying coefficient. The resultant ZNN model is theoretically proved to have global exponential convergence to the time-varying theoretical optimal solution of the investigated time-varying convex quadratic program. Computer-simulation results further substantiate the effectiveness, efficiency and novelty of such ZNN model and method.

Linear algebra

CERN Document Server

Shilov, Georgi E

1977-01-01

Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

Study of load change control in PWRs using the methods of linear optimal control

International Nuclear Information System (INIS)

Yang, T.

1983-01-01

This thesis investigates the application of modern control theory to the problem of controlling load changes in PWR power plants. A linear optimal state feedback scheme resulting from linear optimal control theory with a quadratic cost function is reduced to a partially decentralized control system using mode preservation techniques. Minimum information transfer among major components of the plant is investigated to provide an adequate coordination, simple implementation, and a reliable control system. Two control approaches are proposed: servo and model following. Each design considers several information structures for performance comparison. Integrated output error has been included in the control systems to accommodate external and plant parameter disturbances. In addition, the cross limit feature, specific to certain modern reactor control systems, is considered in the study to prevent low pressure reactor trip conditions. An 11th order nonlinear model for the reactor and boiler is derived based on theoretical principles, and simulation tests are performed for 10% load change as an illustration of system performance

Operator approach to linear control systems

CERN Document Server

Cheremensky, A

1996-01-01

Within the framework of the optimization problem for linear control systems with quadratic performance index (LQP), the operator approach allows the construction of a systems theory including a number of particular infinite-dimensional optimization problems with hardly visible concreteness. This approach yields interesting interpretations of these problems and more effective feedback design methods. This book is unique in its emphasis on developing methods for solving a sufficiently general LQP. Although this is complex material, the theory developed here is built on transparent and relatively simple principles, and readers with less experience in the field of operator theory will find enough material to give them a good overview of the current state of LQP theory and its applications. Audience: Graduate students and researchers in the fields of mathematical systems theory, operator theory, cybernetics, and control systems.

The Linear Quadratic Gaussian Multistage Game with Nonclassical Information Pattern Using a Direct Solution Method

Science.gov (United States)

Clemens, Joshua William

Game theory has application across multiple fields, spanning from economic strategy to optimal control of an aircraft and missile on an intercept trajectory. The idea of game theory is fascinating in that we can actually mathematically model real-world scenarios and determine optimal decision making. It may not always be easy to mathematically model certain real-world scenarios, nonetheless, game theory gives us an appreciation for the complexity involved in decision making. This complexity is especially apparent when the players involved have access to different information upon which to base their decision making (a nonclassical information pattern). Here we will focus on the class of adversarial two-player games (sometimes referred to as pursuit-evasion games) with nonclassical information pattern. We present a two-sided (simultaneous) optimization solution method for the two-player linear quadratic Gaussian (LQG) multistage game. This direct solution method allows for further interpretation of each player's decision making (strategy) as compared to previously used formal solution methods. In addition to the optimal control strategies, we present a saddle point proof and we derive an expression for the optimal performance index value. We provide some numerical results in order to further interpret the optimal control strategies and to highlight real-world application of this game-theoretic optimal solution.

Quadratic independence of coordinate functions of certain ...

Indian Academy of Sciences (India)

... are `quadratically independent' in the sense that they do not satisfy any nontrivial homogeneous quadratic relations among them. Using this, it is proved that there is no genuine compact quantum group which can act faithfully on C ( M ) such that the action leaves invariant the linear span of the above coordinate functions.

A Trust-region-based Sequential Quadratic Programming Algorithm

DEFF Research Database (Denmark)

Henriksen, Lars Christian; Poulsen, Niels Kjølstad

This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints.......This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints....

Half-space albedo problem with modified F{sub N} method for linear and quadratic anisotropic scattering

Energy Technology Data Exchange (ETDEWEB)

Tuereci, R.G. [Kirikkale Univ., Kirikkale (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministry of Education, Ankara (Turkey). 75th year Anatolia High School

2017-05-15

One speed, time independent and homogeneous medium neutron transport equation can be solved with the anisotropic scattering which includes both the linear anisotropic and the quadratic anisotropic scattering properties. Having solved Case's eigenfunctions and the orthogonality relations among these eigenfunctions, some neutron transport problems such as albedo problem can be calculated as numerically by using numerical or semi-analytic methods. In this study the half-space albedo problem is investigated by using the modified F{sub N} method.

Biological equivalence between LDR and PDR in cervical cancer: multifactor analysis using the linear-quadratic model

OpenAIRE

José Guilherme Couto; Isabel Bravo; Rui Pirraco

2011-01-01

Purpose The purpose of this work was the biological comparison between Low Dose Rate (LDR) and Pulsed Dose Rate (PDR) in cervical cancer regarding the discontinuation of the afterloading system used for the LDR treatments at our Institution since December 2009. Material and methods In the first phase we studied the influence of the pulse dose and the pulse time in the biological equivalence between LDR and PDR treatments using the Linear Quadratic Model (LQM). In the second phase, the equival...

A Design of a Hybrid Non-Linear Control Algorithm

Directory of Open Access Journals (Sweden)

Farinaz Behrooz

2017-11-01

Full Text Available One of the high energy consuming devices in the buildings is the air-conditioning system. Designing a proper controller to consider the thermal comfort and simultaneously control the energy usage of the device will impact on the system energy efficiency and its performance. The aim of this study was to design a Multiple-Input and Multiple-Output (MIMO, non-linear, and intelligent controller on direct expansion air-conditioning system The control algorithm uses the Fuzzy Cognitive Map method as a main controller and the Generalized Predictive Control method is used for assigning the initial weights of the main controller. The results of the proposed controller shows that the controller was successfully designed and works in set point tracking and under disturbance rejection tests. The obtained results of the Generalized Predictive Control-Fuzzy Cognitive Map controller are compared with the previous MIMO Linear Quadratic Gaussian control design on the same direct expansion air-conditioning system under the same conditions. The comparative results indicate energy savings would be achieved with the proposed controller with long-term usage. Energy efficiency and thermal comfort conditions are achieved by the proposed controller.

Rainfall induced landslide susceptibility mapping using weight-of-evidence, linear and quadratic discriminant and logistic model tree method

Science.gov (United States)

Hong, H.; Zhu, A. X.

2017-12-01

Climate change is a common phenomenon and it is very serious all over the world. The intensification of rainfall extremes with climate change is of key importance to society and then it may induce a large impact through landslides. This paper presents GIS-based new ensemble data mining techniques that weight-of-evidence, logistic model tree, linear and quadratic discriminant for landslide spatial modelling. This research was applied in Anfu County, which is a landslide-prone area in Jiangxi Province, China. According to a literature review and research the study area, we select the landslide influencing factor and their maps were digitized in a GIS environment. These landslide influencing factors are the altitude, plan curvature, profile curvature, slope degree, slope aspect, topographic wetness index (TWI), Stream Power Index (SPI), Topographic Wetness Index (SPI), distance to faults, distance to rivers, distance to roads, soil, lithology, normalized difference vegetation index and land use. According to historical information of individual landslide events, interpretation of the aerial photographs, and field surveys supported by the government of Jiangxi Meteorological Bureau of China, 367 landslides were identified in the study area. The landslide locations were divided into two subsets, namely, training and validating (70/30), based on a random selection scheme. In this research, Pearson's correlation was used for the evaluation of the relationship between the landslides and influencing factors. In the next step, three data mining techniques combined with the weight-of-evidence, logistic model tree, linear and quadratic discriminant, were used for the landslide spatial modelling and its zonation. Finally, the landslide susceptibility maps produced by the mentioned models were evaluated by the ROC curve. The results showed that the area under the curve (AUC) of all of the models was > 0.80. At the same time, the highest AUC value was for the linear and quadratic

Adaptive Finite Element Method for Optimal Control Problem Governed by Linear Quasiparabolic Integrodifferential Equations

Directory of Open Access Journals (Sweden)

Wanfang Shen

2012-01-01

Full Text Available The mathematical formulation for a quadratic optimal control problem governed by a linear quasiparabolic integrodifferential equation is studied. The control constrains are given in an integral sense: Uad={u∈X;∫ΩUu⩾0, t∈[0,T]}. Then the a posteriori error estimates in L∞(0,T;H1(Ω-norm and L2(0,T;L2(Ω-norm for both the state and the control approximation are given.

Finite element method with quadratic quadrilateral unit for solving two dimensional incompressible N-S equation

International Nuclear Information System (INIS)

Tao Ganqiang; Yu Qing; Xiao Xiao

2011-01-01

Viscous and incompressible fluid flow is important for numerous engineering mechanics problems. Because of high non linear and incompressibility for Navier-Stokes equation, it is very difficult to solve Navier-Stokes equation by numerical method. According to its characters of Navier-Stokes equation, quartic derivation controlling equation of the two dimensional incompressible Navier-Stokes equation is set up firstly. The method solves the problem for dealing with vorticity boundary and automatically meets incompressibility condition. Then Finite Element equation for Navier-Stokes equation is proposed by using quadratic quadrilateral unit with 8 nodes in which the unit function is quadratic and non linear.-Based on it, the Finite Element program of quadratic quadrilateral unit with 8 nodes is developed. Lastly, numerical experiment proves the accuracy and dependability of the method and also shows the method has good application prospect in computational fluid mechanics. (authors)

On Active Surge Control of Compression Systems via Characteristic Linearization and Model Nonlinearity Cancellation

Directory of Open Access Journals (Sweden)

Yohannes S.M. Simamora

2014-09-01

Full Text Available A simple approach of active surge control of compression systems is presented. Specifically, nonlinear components of the pressure ratio and rotating speed states of the Moore-Greitzer model are transferred into the input vectors. Subsequently, the compressor characteristic is linearized into two modes, which describe the stable region and the unstable region respectively. As a result, the system’s state and input matrices both appear linear, to which linear realization and analysis are applicable. A linear quadratic regulator plus integrator is then chosen as closed-loop controller. By simulation it was shown that the modified model and characteristics can describe surge behavior, while the closed-loop controller can stabilize the system in the unstable operating region. The last-mentioned was achieved when massflow was 5.38 per cent less than the surge point.

A new formalism for modelling parameters α and β of the linear-quadratic model of cell survival for hadron therapy

Science.gov (United States)

Vassiliev, Oleg N.; Grosshans, David R.; Mohan, Radhe

2017-10-01

We propose a new formalism for calculating parameters α and β of the linear-quadratic model of cell survival. This formalism, primarily intended for calculating relative biological effectiveness (RBE) for treatment planning in hadron therapy, is based on a recently proposed microdosimetric revision of the single-target multi-hit model. The main advantage of our formalism is that it reliably produces α and β that have correct general properties with respect to their dependence on physical properties of the beam, including the asymptotic behavior for very low and high linear energy transfer (LET) beams. For example, in the case of monoenergetic beams, our formalism predicts that, as a function of LET, (a) α has a maximum and (b) the α/β ratio increases monotonically with increasing LET. No prior models reviewed in this study predict both properties (a) and (b) correctly, and therefore, these prior models are valid only within a limited LET range. We first present our formalism in a general form, for polyenergetic beams. A significant new result in this general case is that parameter β is represented as an average over the joint distribution of energies E 1 and E 2 of two particles in the beam. This result is consistent with the role of the quadratic term in the linear-quadratic model. It accounts for the two-track mechanism of cell kill, in which two particles, one after another, damage the same site in the cell nucleus. We then present simplified versions of the formalism, and discuss predicted properties of α and β. Finally, to demonstrate consistency of our formalism with experimental data, we apply it to fit two sets of experimental data: (1) α for heavy ions, covering a broad range of LETs, and (2) β for protons. In both cases, good agreement is achieved.

The bounds of feasible space on constrained nonconvex quadratic programming

Science.gov (United States)

Zhu, Jinghao

2008-03-01

This paper presents a method to estimate the bounds of the radius of the feasible space for a class of constrained nonconvex quadratic programmingsE Results show that one may compute a bound of the radius of the feasible space by a linear programming which is known to be a P-problem [N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984) 373-395]. It is proposed that one applies this method for using the canonical dual transformation [D.Y. Gao, Canonical duality theory and solutions to constrained nonconvex quadratic programming, J. Global Optimization 29 (2004) 377-399] for solving a standard quadratic programming problem.

Approximative analytic eigenvalues for orbital excitations in the case of a coulomb potential plus linear and quadratic radial terms

International Nuclear Information System (INIS)

Rekab, S.; Zenine, N.

2006-01-01

We consider the three dimensional non relativistic eigenvalue problem in the case of a Coulomb potential plus linear and quadratic radial terms. In the framework of the Rayleigh-Schrodinger Perturbation Theory, using a specific choice of the unperturbed Hamiltonian, we obtain approximate analytic expressions for the eigenvalues of orbital excitations. The implications and the range of validity of the obtained analytic expression are discussed

Solitons in quadratic nonlinear photonic crystals

DEFF Research Database (Denmark)

Corney, Joel Frederick; Bang, Ole

2001-01-01

We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families....... Because of these induced cubic terms, solitons still exist even when the effective quadratic nonlinearity vanishes and conventional theory predicts that there can be no soliton. We demonstrate that both bright and dark forms of these solitons can propagate stably....

Study on TVD parameters sensitivity of a crankshaft using multiple scale and state space method considering quadratic and cubic non-linearities

Directory of Open Access Journals (Sweden)

R. Talebitooti

Full Text Available In this paper the effect of quadratic and cubic non-linearities of the system consisting of the crankshaft and torsional vibration damper (TVD is taken into account. TVD consists of non-linear elastomer material used for controlling the torsional vibration of crankshaft. The method of multiple scales is used to solve the governing equations of the system. Meanwhile, the frequency response of the system for both harmonic and sub-harmonic resonances is extracted. In addition, the effects of detuning parameters and other dimensionless parameters for a case of harmonic resonance are investigated. Moreover, the external forces including both inertia and gas forces are simultaneously applied into the model. Finally, in order to study the effectiveness of the parameters, the dimensionless governing equations of the system are solved, considering the state space method. Then, the effects of the torsional damper as well as all corresponding parameters of the system are discussed.

Decay constants for pulsed monoenergetic neutron systems with quadratically anisotropic scattering

International Nuclear Information System (INIS)

Sjoestrand, N.G.

1977-06-01

The eigenvalues of the time-dependent transport equation for monoenergetic neutrons have been studied numerically for various combinations of linearly and quadratically anisotropic scattering assuming a space dependence of e β . The results, presented in the form of tables and graphs, show that quadratic anisotropy leads to a more complicated eigenvalue spectrum. However, no drastic changes occur in comparison to purely linear anistropy.(author)

ORACLS- OPTIMAL REGULATOR ALGORITHMS FOR THE CONTROL OF LINEAR SYSTEMS (CDC VERSION)

Science.gov (United States)

Armstrong, E. S.

1994-01-01

This control theory design package, called Optimal Regulator Algorithms for the Control of Linear Systems (ORACLS), was developed to aid in the design of controllers and optimal filters for systems which can be modeled by linear, time-invariant differential and difference equations. Optimal linear quadratic regulator theory, currently referred to as the Linear-Quadratic-Gaussian (LQG) problem, has become the most widely accepted method of determining optimal control policy. Within this theory, the infinite duration time-invariant problems, which lead to constant gain feedback control laws and constant Kalman-Bucy filter gains for reconstruction of the system state, exhibit high tractability and potential ease of implementation. A variety of new and efficient methods in the field of numerical linear algebra have been combined into the ORACLS program, which provides for the solution to time-invariant continuous or discrete LQG problems. The ORACLS package is particularly attractive to the control system designer because it provides a rigorous tool for dealing with multi-input and multi-output dynamic systems in both continuous and discrete form. The ORACLS programming system is a collection of subroutines which can be used to formulate, manipulate, and solve various LQG design problems. The ORACLS program is constructed in a manner which permits the user to maintain considerable flexibility at each operational state. This flexibility is accomplished by providing primary operations, analysis of linear time-invariant systems, and control synthesis based on LQG methodology. The input-output routines handle the reading and writing of numerical matrices, printing heading information, and accumulating output information. The basic vector-matrix operations include addition, subtraction, multiplication, equation, norm construction, tracing, transposition, scaling, juxtaposition, and construction of null and identity matrices. The analysis routines provide for the following

Comments on a time-dependent version of the linear-quadratic model

International Nuclear Information System (INIS)

Tucker, S.L.; Travis, E.L.

1990-01-01

The accuracy and interpretation of the 'LQ + time' model are discussed. Evidence is presented, based on data in the literature, that this model does not accurately describe the changes in isoeffect dose occurring with protraction of the overall treatment time during fractionated irradiation of the lung. This lack of fit of the model explains, in part, the surprisingly large values of γ/α that have been derived from experimental lung data. The large apparent time factors for lung suggested by the model are also partly explained by the fact that γT/α, despite having units of dose, actually measures the influence of treatment time on the effect scale, not the dose scale, and is shown to consistently overestimate the change in total dose. The unusually high values of α/β that have been derived for lung using the model are shown to be influenced by the method by which the model was fitted to data. Reanalyses of the data using a more statistically valid regression procedure produce estimates of α/β more typical of those usually cited for lung. Most importantly, published isoeffect data from lung indicate that the true deviation from the linear-quadratic (LQ) model is nonlinear in time, instead of linear, and also depends on other factors such as the effect level and the size of dose per fraction. Thus, the authors do not advocate the use of the 'LQ + time' expression as a general isoeffect model. (author). 32 refs.; 3 figs.; 1 tab

A revisit to quadratic programming with fuzzy parameters

International Nuclear Information System (INIS)

Liu, S.-T.

2009-01-01

Quadratic programming has been widely applied to solving real-world problems. Recently, Liu describes a solution method for solving a class of fuzzy quadratic programming problems, where the cost coefficients of the linear terms in objective function, constraint coefficients, and right-hand sides are fuzzy numbers [Liu ST. Quadratic programming with fuzzy parameters: a membership function approach. Chaos, Solitons and Fractals 2009;40:237-45]. In this paper, we generalize Liu's method to a more general fuzzy quadratic programming problem, where the cost coefficients in objective function, constraint coefficients, and right-hand sides are all fuzzy numbers. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. With the ability of calculating the fuzzy objective value developed in this paper, it might help initiate wider applications.

Quadratic prediction of factor scores

NARCIS (Netherlands)

Wansbeek, T

1999-01-01

Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. II is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic

Designing Camera Networks by Convex Quadratic Programming

KAUST Repository

Ghanem, Bernard; Wonka, Peter; Cao, Yuanhao

2015-01-01

be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution

A Genetic-Algorithms-Based Approach for Programming Linear and Quadratic Optimization Problems with Uncertainty

Directory of Open Access Journals (Sweden)

Weihua Jin

2013-01-01

Full Text Available This paper proposes a genetic-algorithms-based approach as an all-purpose problem-solving method for operation programming problems under uncertainty. The proposed method was applied for management of a municipal solid waste treatment system. Compared to the traditional interactive binary analysis, this approach has fewer limitations and is able to reduce the complexity in solving the inexact linear programming problems and inexact quadratic programming problems. The implementation of this approach was performed using the Genetic Algorithm Solver of MATLAB (trademark of MathWorks. The paper explains the genetic-algorithms-based method and presents details on the computation procedures for each type of inexact operation programming problems. A comparison of the results generated by the proposed method based on genetic algorithms with those produced by the traditional interactive binary analysis method is also presented.

ORACLS- OPTIMAL REGULATOR ALGORITHMS FOR THE CONTROL OF LINEAR SYSTEMS (DEC VAX VERSION)

Science.gov (United States)

Frisch, H.

1994-01-01

This control theory design package, called Optimal Regulator Algorithms for the Control of Linear Systems (ORACLS), was developed to aid in the design of controllers and optimal filters for systems which can be modeled by linear, time-invariant differential and difference equations. Optimal linear quadratic regulator theory, currently referred to as the Linear-Quadratic-Gaussian (LQG) problem, has become the most widely accepted method of determining optimal control policy. Within this theory, the infinite duration time-invariant problems, which lead to constant gain feedback control laws and constant Kalman-Bucy filter gains for reconstruction of the system state, exhibit high tractability and potential ease of implementation. A variety of new and efficient methods in the field of numerical linear algebra have been combined into the ORACLS program, which provides for the solution to time-invariant continuous or discrete LQG problems. The ORACLS package is particularly attractive to the control system designer because it provides a rigorous tool for dealing with multi-input and multi-output dynamic systems in both continuous and discrete form. The ORACLS programming system is a collection of subroutines which can be used to formulate, manipulate, and solve various LQG design problems. The ORACLS program is constructed in a manner which permits the user to maintain considerable flexibility at each operational state. This flexibility is accomplished by providing primary operations, analysis of linear time-invariant systems, and control synthesis based on LQG methodology. The input-output routines handle the reading and writing of numerical matrices, printing heading information, and accumulating output information. The basic vector-matrix operations include addition, subtraction, multiplication, equation, norm construction, tracing, transposition, scaling, juxtaposition, and construction of null and identity matrices. The analysis routines provide for the following

An Analysis and Design for Nonlinear Quadratic Systems Subject to Nested Saturation

Directory of Open Access Journals (Sweden)

Minsong Zhang

2013-01-01

Full Text Available This paper considers the stability problem for nonlinear quadratic systems with nested saturation input. The interesting treatment method proposed to nested saturation here is put into use a well-established linear differential control tool. And the new conclusions include the existing conclusion on this issue and have less conservatism than before. Simulation example illustrates the effectiveness of the established methodologies.

Quadratic Lagrangians and Legendre transformation

International Nuclear Information System (INIS)

Magnano, G.

1988-01-01

In recent years interest is grown about the so-called non-linear Lagrangians for gravitation. In particular, the quadratic lagrangians are currently believed to play a fundamental role both for quantum gravity and for the super-gravity approach. The higher order and high degree of non-linearity of these theories make very difficult to extract physical information out of them. The author discusses how the Legendre transformation can be applied to a wide class of non-linear theories: it corresponds to a conformal transformation whenever the Lagrangian depends only on the scalar curvature, while it has a more general form if the Lagrangian depends on the full Ricci tensor

Evaluation of linearly solvable Markov decision process with dynamic model learning in a mobile robot navigation task.

Science.gov (United States)

Kinjo, Ken; Uchibe, Eiji; Doya, Kenji

2013-01-01

Linearly solvable Markov Decision Process (LMDP) is a class of optimal control problem in which the Bellman's equation can be converted into a linear equation by an exponential transformation of the state value function (Todorov, 2009b). In an LMDP, the optimal value function and the corresponding control policy are obtained by solving an eigenvalue problem in a discrete state space or an eigenfunction problem in a continuous state using the knowledge of the system dynamics and the action, state, and terminal cost functions. In this study, we evaluate the effectiveness of the LMDP framework in real robot control, in which the dynamics of the body and the environment have to be learned from experience. We first perform a simulation study of a pole swing-up task to evaluate the effect of the accuracy of the learned dynamics model on the derived the action policy. The result shows that a crude linear approximation of the non-linear dynamics can still allow solution of the task, despite with a higher total cost. We then perform real robot experiments of a battery-catching task using our Spring Dog mobile robot platform. The state is given by the position and the size of a battery in its camera view and two neck joint angles. The action is the velocities of two wheels, while the neck joints were controlled by a visual servo controller. We test linear and bilinear dynamic models in tasks with quadratic and Guassian state cost functions. In the quadratic cost task, the LMDP controller derived from a learned linear dynamics model performed equivalently with the optimal linear quadratic regulator (LQR). In the non-quadratic task, the LMDP controller with a linear dynamics model showed the best performance. The results demonstrate the usefulness of the LMDP framework in real robot control even when simple linear models are used for dynamics learning.

Binary classification posed as a quadratically constrained quadratic ...

Indian Academy of Sciences (India)

Binary classification is posed as a quadratically constrained quadratic problem and solved using the proposed method. Each class in the binary classification problem is modeled as a multidimensional ellipsoid to forma quadratic constraint in the problem. Particle swarms help in determining the optimal hyperplane or ...

Quadratic tracer dynamical models tobacco growth

International Nuclear Information System (INIS)

Qiang Jiyi; Hua Cuncai; Wang Shaohua

2011-01-01

In order to study the non-uniformly transferring process of some tracer dosages, we assume that the absorption of some tracer by tobacco is a quadratic function of the tracer quantity of the tracer in the case of fast absorption, whereas the exclusion of the tracer from tobacco is a linear function of the tracer quantity in the case of slow exclusion, after the tracer is introduced into tobacco once at zero time. A single-compartment quadratic dynamical model of Logistic type is established for the leaves of tobacco. Then, a two-compartment quadratic dynamical model is established for leaves and calms of the tobacco. Qualitative analysis of the models shows that the tracer applied to the leaves of the tobacco is excluded finally; however, the tracer stays at the tobacco for finite time. Two methods are also given for computing the parameters in the models. Finally, the results of the models are verified by the 32 P experiment for the absorption of tobacco. (authors)

Quadratic temporal finite element method for linear elastic structural dynamics based on mixed convolved action

International Nuclear Information System (INIS)

Kim, Jin Kyu; Kim, Dong Keon

2016-01-01

A common approach for dynamic analysis in current practice is based on a discrete time-integration scheme. This approach can be largely attributed to the absence of a true variational framework for initial value problems. To resolve this problem, a new stationary variational principle was recently established for single-degree-of-freedom oscillating systems using mixed variables, fractional derivatives and convolutions of convolutions. In this mixed convolved action, all the governing differential equations and initial conditions are recovered from the stationarity of a single functional action. Thus, the entire description of linear elastic dynamical systems is encapsulated. For its practical application to structural dynamics, this variational formalism is systemically extended to linear elastic multidegree- of-freedom systems in this study, and a corresponding weak form is numerically implemented via a quadratic temporal finite element method. The developed numerical method is symplectic and unconditionally stable with respect to a time step for the underlying conservative system. For the forced-damped vibration, a three-story shear building is used as an example to investigate the performance of the developed numerical method, which provides accurate results with good convergence characteristics

Quadratic temporal finite element method for linear elastic structural dynamics based on mixed convolved action

Energy Technology Data Exchange (ETDEWEB)

Kim, Jin Kyu [School of Architecture and Architectural Engineering, Hanyang University, Ansan (Korea, Republic of); Kim, Dong Keon [Dept. of Architectural Engineering, Dong A University, Busan (Korea, Republic of)

2016-09-15

A common approach for dynamic analysis in current practice is based on a discrete time-integration scheme. This approach can be largely attributed to the absence of a true variational framework for initial value problems. To resolve this problem, a new stationary variational principle was recently established for single-degree-of-freedom oscillating systems using mixed variables, fractional derivatives and convolutions of convolutions. In this mixed convolved action, all the governing differential equations and initial conditions are recovered from the stationarity of a single functional action. Thus, the entire description of linear elastic dynamical systems is encapsulated. For its practical application to structural dynamics, this variational formalism is systemically extended to linear elastic multidegree- of-freedom systems in this study, and a corresponding weak form is numerically implemented via a quadratic temporal finite element method. The developed numerical method is symplectic and unconditionally stable with respect to a time step for the underlying conservative system. For the forced-damped vibration, a three-story shear building is used as an example to investigate the performance of the developed numerical method, which provides accurate results with good convergence characteristics.

Moving Horizon Estimation and Control

DEFF Research Database (Denmark)

Jørgensen, John Bagterp

successful and applied methodology beyond PID-control for control of industrial processes. The main contribution of this thesis is introduction and definition of the extended linear quadratic optimal control problem for solution of numerical problems arising in moving horizon estimation and control...... problems. Chapter 1 motivates moving horizon estimation and control as a paradigm for control of industrial processes. It introduces the extended linear quadratic control problem and discusses its central role in moving horizon estimation and control. Introduction, application and efficient solution....... It provides an algorithm for computation of the maximal output admissible set for linear model predictive control. Appendix D provides results concerning linear regression. Appendix E discuss prediction error methods for identification of linear models tailored for model predictive control....

Quadratic reactivity fuel cycle model

International Nuclear Information System (INIS)

Lewins, J.D.

1985-01-01

For educational purposes it is highly desirable to provide simple yet realistic models for fuel cycle and fuel economy. In particular, a lumped model without recourse to detailed spatial calculations would be very helpful in providing the student with a proper understanding of the purposes of fuel cycle calculations. A teaching model for fuel cycle studies based on a lumped model assuming the summability of partial reactivities with a linear dependence of reactivity usefully illustrates fuel utilization concepts. The linear burnup model does not satisfactorily represent natural enrichment reactors. A better model, showing the trend of initial plutonium production before subsequent fuel burnup and fission product generation, is a quadratic fit. The study of M-batch cycles, reloading 1/Mth of the core at end of cycle, is now complicated by nonlinear equations. A complete account of the asymptotic cycle for any order of M-batch refueling can be given and compared with the linear model. A complete account of the transient cycle can be obtained readily in the two-batch model and this exact solution would be useful in verifying numerical marching models. It is convenient to treat the parabolic fit rho = 1 - tau 2 as a special case of the general quadratic fit rho = 1 - C/sub tau/ - (1 - C)tau 2 in suitably normalized reactivity and cycle time units. The parabolic results are given in this paper

Evaluation of linearly solvable Markov decision process with dynamic model learning in a mobile robot navigation task

Directory of Open Access Journals (Sweden)

Ken eKinjo

2013-04-01

Full Text Available Linearly solvable Markov Decision Process (LMDP is a class of optimal control problem in whichthe Bellman’s equation can be converted into a linear equation by an exponential transformation ofthe state value function (Todorov, 2009. In an LMDP, the optimal value function and the correspondingcontrol policy are obtained by solving an eigenvalue problem in a discrete state space or an eigenfunctionproblem in a continuous state using the knowledge of the system dynamics and the action, state, andterminal cost functions.In this study, we evaluate the effectiveness of the LMDP framework in real robot control, in whichthe dynamics of the body and the environment have to be learned from experience. We first perform asimulation study of a pole swing-up task to evaluate the effect of the accuracy of the learned dynam-ics model on the derived the action policy. The result shows that a crude linear approximation of thenonlinear dynamics can still allow solution of the task, despite with a higher total cost.We then perform real robot experiments of a battery-catching task using our Spring Dog mobile robotplatform. The state is given by the position and the size of a battery in its camera view and two neck jointangles. The action is the velocities of two wheels, while the neck joints were controlled by a visual servocontroller. We test linear and bilinear dynamic models in tasks with quadratic and Guassian state costfunctions. In the quadratic cost task, the LMDP controller derived from a learned linear dynamics modelperformed equivalently with the optimal linear quadratic controller (LQR. In the non-quadratic task, theLMDP controller with a linear dynamics model showed the best performance. The results demonstratethe usefulness of the LMDP framework in real robot control even when simple linear models are usedfor dynamics learning.

Estimation of transition doses for human glioblastoma, neuroblastoma and prostate cell lines using the linear-quadratic formalism

Directory of Open Access Journals (Sweden)

John Akudugu

2015-09-01

Full Text Available Purpose: The introduction of stereotactic radiotherapy has raised concerns regarding the use of the linear-quadratic (LQ model for predicting radiation response for large fractional doses. To partly address this issue, a transition dose D* below which the LQ model retains its predictive strength has been proposed. Estimates of D* which depends on the a, β, and D0 parameters are much lower than fractional doses typically encountered in stereotactic radiotherapy. D0, often referred to as the final slope of the cell survival curve, is thought to be constant. In vitro cell survival curves generally extend over the first few logs of cell killing, where D0-values derived from the multi-target formalism may be overestimated and can lead to low transition doses. Methods:  D0-values were calculated from first principles for each decade of cell killing, using experimentally-determined a and β parameters for 17 human glioblastoma, neuroblastoma, and prostate cell lines, and corresponding transition doses were derived.Results: D0 was found to decrease exponentially with cell killing. Using D0-values at cell surviving fractions of the order of 10-10 yielded transition doses ~3-fold higher than those obtained from D0-values obtained from conventional approaches. D* was found to increase from 7.84 ± 0.56, 8.91 ± 1.20, and 6.55 ± 0.91 Gy to 26.84 ± 2.83, 23.95 ± 2.03, and 22.49 ± 2.31 Gy for the glioblastoma, neuroblastoma, and prostate cell lines, respectively. Conclusion: These findings suggest that the linear-quadratic formalism might be valid for estimating the effect of stereotactic radiotherapy with fractional doses in excess of 20 Gy.

Frequency of micronuclei in hepatocytes following X and fast-neutron irradiations--an analysis by a linear-quadratic model

International Nuclear Information System (INIS)

Ono, K.; Nagata, Y.; Akuta, K.; Abe, M.; Ando, K.; Koike, S.

1990-01-01

The usefulness of the micronucleus assay for investigating the radiation response of hepatocytes was examined. The frequency was defined as the ratio of the total number of micronuclei to the number of hepatocytes examined. The dose-response curves were curvilinear after X rays and linear after neutrons. These dose-response curves were analyzed by a linear-quadratic model, frequency = aD + bD2 + c. The a/b ratio was 3.03 +/- 1.26 Gy following X irradiation. This value is within the range of the alpha/beta ratios reported by others using the clonogenic assay of hepatocytes. While the a/b value for neutrons was 24.3 +/- 11.7 Gy, the maximum relative biological effectiveness of neutrons was 6.30 +/- 2.53. Since the micronucleus assay is simple and rapid, it may be a good tool for evaluating the radiation response of hepatocytes in vivo

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

Science.gov (United States)

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

Science.gov (United States)

Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740

Fitness analysis method for magnesium in drinking water with atomic absorption using quadratic curve calibration

Directory of Open Access Journals (Sweden)

Esteban Pérez-López

2014-11-01

Full Text Available Because of the importance of quantitative chemical analysis in research, quality control, sales of services and other areas of interest , and the limiting of some instrumental analysis methods for quantification with linear calibration curve, sometimes because the short linear dynamic ranges of the analyte, and sometimes by limiting the technique itself, is that there is a need to investigate a little more about the convenience of using quadratic curves for analytical quantification, which seeks demonstrate that it is a valid calculation model for chemical analysis instruments. To this was taken as an analysis method based on the technique and atomic absorption spectroscopy in particular a determination of magnesium in a sample of drinking water Tacares sector Northern Grecia, employing a nonlinear calibration curve and a curve specific quadratic behavior, which was compared with the test results obtained for the same analysis with a linear calibration curve. The results show that the methodology is valid for the determination referred to, with all confidence, since the concentrations are very similar, and as used hypothesis testing can be considered equal.

Robust Control Design of Wheeled Inverted Pendulum Assistant Robot

Institute of Scientific and Technical Information of China (English)

Magdi S.Mahmoud; Mohammad T.Nasir

2017-01-01

This paper examines the design concept and mobile control strategy of the human assistant robot I-PENTAR（inverted pendulum type assistant robot）. The motion equation is derived considering the non-holonomic constraint of the twowheeled mobile robot. Different optimal control approaches are applied to a linearized model of I-PENTAR. These include linear quadratic regulator（LQR）, linear quadratic Gaussian control（LQG）, H2 control and H∞ control. Simulation is performed for all the approaches yielding good performance results.

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.

Directory of Open Access Journals (Sweden)

Xiangrong Li

Full Text Available It is generally acknowledged that the conjugate gradient (CG method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.

Science.gov (United States)

Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

2015-01-01

It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.

Hidden conic quadratic representation of some nonconvex quadratic optimization problems

NARCIS (Netherlands)

Ben-Tal, A.; den Hertog, D.

The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated

Linear–Quadratic Mean-Field-Type Games: A Direct Method

Directory of Open Access Journals (Sweden)

Tyrone E. Duncan

2018-02-01

Full Text Available In this work, a multi-person mean-field-type game is formulated and solved that is described by a linear jump-diffusion system of mean-field type and a quadratic cost functional involving the second moments, the square of the expected value of the state, and the control actions of all decision-makers. We propose a direct method to solve the game, team, and bargaining problems. This solution approach does not require solving the Bellman–Kolmogorov equations or backward–forward stochastic differential equations of Pontryagin’s type. The proposed method can be easily implemented by beginners and engineers who are new to the emerging field of mean-field-type game theory. The optimal strategies for decision-makers are shown to be in a state-and-mean-field feedback form. The optimal strategies are given explicitly as a sum of the well-known linear state-feedback strategy for the associated deterministic linear–quadratic game problem and a mean-field feedback term. The equilibrium cost of the decision-makers are explicitly derived using a simple direct method. Moreover, the equilibrium cost is a weighted sum of the initial variance and an integral of a weighted variance of the diffusion and the jump process. Finally, the method is used to compute global optimum strategies as well as saddle point strategies and Nash bargaining solution in state-and-mean-field feedback form.

H∞ control for uncertain linear system over networks with Bernoulli data dropout and actuator saturation.

Science.gov (United States)

Yu, Jimin; Yang, Chenchen; Tang, Xiaoming; Wang, Ping

2018-03-01

This paper investigates the H ∞ control problems for uncertain linear system over networks with random communication data dropout and actuator saturation. The random data dropout process is modeled by a Bernoulli distributed white sequence with a known conditional probability distribution and the actuator saturation is confined in a convex hull by introducing a group of auxiliary matrices. By constructing a quadratic Lyapunov function, effective conditions for the state feedback-based H ∞ controller and the observer-based H ∞ controller are proposed in the form of non-convex matrix inequalities to take the random data dropout and actuator saturation into consideration simultaneously, and the problem of non-convex feasibility is solved by applying cone complementarity linearization (CCL) procedure. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed new design techniques. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Approximate analytical relationships for linear optimal aeroelastic flight control laws

Science.gov (United States)

Kassem, Ayman Hamdy

1998-09-01

This dissertation introduces new methods to uncover functional relationships between design parameters of a contemporary control design technique and the resulting closed-loop properties. Three new methods are developed for generating such relationships through analytical expressions: the Direct Eigen-Based Technique, the Order of Magnitude Technique, and the Cost Function Imbedding Technique. Efforts concentrated on the linear-quadratic state-feedback control-design technique applied to an aeroelastic flight control task. For this specific application, simple and accurate analytical expressions for the closed-loop eigenvalues and zeros in terms of basic parameters such as stability and control derivatives, structural vibration damping and natural frequency, and cost function weights are generated. These expressions explicitly indicate how the weights augment the short period and aeroelastic modes, as well as the closed-loop zeros, and by what physical mechanism. The analytical expressions are used to address topics such as damping, nonminimum phase behavior, stability, and performance with robustness considerations, and design modifications. This type of knowledge is invaluable to the flight control designer and would be more difficult to formulate when obtained from numerical-based sensitivity analysis.

Longitudinal mathematics development of students with learning disabilities and students without disabilities: a comparison of linear, quadratic, and piecewise linear mixed effects models.

Science.gov (United States)

Kohli, Nidhi; Sullivan, Amanda L; Sadeh, Shanna; Zopluoglu, Cengiz

2015-04-01

Effective instructional planning and intervening rely heavily on accurate understanding of students' growth, but relatively few researchers have examined mathematics achievement trajectories, particularly for students with special needs. We applied linear, quadratic, and piecewise linear mixed-effects models to identify the best-fitting model for mathematics development over elementary and middle school and to ascertain differences in growth trajectories of children with learning disabilities relative to their typically developing peers. The analytic sample of 2150 students was drawn from the Early Childhood Longitudinal Study - Kindergarten Cohort, a nationally representative sample of United States children who entered kindergarten in 1998. We first modeled students' mathematics growth via multiple mixed-effects models to determine the best fitting model of 9-year growth and then compared the trajectories of students with and without learning disabilities. Results indicate that the piecewise linear mixed-effects model captured best the functional form of students' mathematics trajectories. In addition, there were substantial achievement gaps between students with learning disabilities and students with no disabilities, and their trajectories differed such that students without disabilities progressed at a higher rate than their peers who had learning disabilities. The results underscore the need for further research to understand how to appropriately model students' mathematics trajectories and the need for attention to mathematics achievement gaps in policy. Copyright © 2015 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.

Electron laser acceleration in vacuum by a quadratically chirped laser pulse

International Nuclear Information System (INIS)

Salamin, Yousef I; Jisrawi, Najeh M

2014-01-01

Single MeV electrons in vacuum subjected to single high-intensity quadratically chirped laser pulses are shown to gain multi-GeV energies. The laser pulses are modelled by finite-duration trapezoidal and cos  2 pulse-shapes and the equations of motion are solved numerically. It is found that, typically, the maximum energy gain from interaction with a quadratic chirp is about half of what would be gained from a linear chirp. (paper)

Biologically effective dose distribution based on the linear quadratic model and its clinical relevance

International Nuclear Information System (INIS)

Lee, Steve P.; Leu, Min Y.; Smathers, James B.; McBride, William H.; Parker, Robert G.; Withers, H. Rodney

1995-01-01

Purpose: Radiotherapy plans based on physical dose distributions do not necessarily entirely reflect the biological effects under various fractionation schemes. Over the past decade, the linear-quadratic (LQ) model has emerged as a convenient tool to quantify biological effects for radiotherapy. In this work, we set out to construct a mechanism to display biologically oriented dose distribution based on the LQ model. Methods and Materials: A computer program that converts a physical dose distribution calculated by a commercially available treatment planning system to a biologically effective dose (BED) distribution has been developed and verified against theoretical calculations. This software accepts a user's input of biological parameters for each structure of interest (linear and quadratic dose-response and repopulation kinetic parameters), as well as treatment scheme factors (number of fractions, fractional dose, and treatment time). It then presents a two-dimensional BED display in conjunction with anatomical structures. Furthermore, to facilitate clinicians' intuitive comparison with conventional fractionation regimen, a conversion of BED to normalized isoeffective dose (NID) is also allowed. Results: Two sample cases serve to illustrate the application of our tool in clinical practice. (a) For an orthogonal wedged pair of x-ray beams treating a maxillary sinus tumor, the biological effect at the ipsilateral mandible can be quantified, thus illustrates the so-called 'double-trouble' effects very well. (b) For a typical four-field, evenly weighted prostate treatment using 10 MV x-rays, physical dosimetry predicts a comparable dose at the femoral necks between an alternate two-fields/day and four-fields/day schups. However, our BED display reveals an approximate 21% higher BED for the two-fields/day scheme. This excessive dose to the femoral necks can be eliminated if the treatment is delivered with a 3:2 (anterio-posterior/posterio-anterior (AP

Learning quadratic receptive fields from neural responses to natural stimuli.

Science.gov (United States)

Rajan, Kanaka; Marre, Olivier; Tkačik, Gašper

2013-07-01

Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are selective for only a small number of linear projections of a potentially high-dimensional input. In this review, we explore recent modeling approaches where the neural response depends on the quadratic form of the input rather than on its linear projection, that is, the neuron is sensitive to the local covariance structure of the signal preceding the spike. To infer this quadratic dependence in the presence of arbitrary (e.g., naturalistic) stimulus distribution, we review several inference methods, focusing in particular on two information theory-based approaches (maximization of stimulus energy and of noise entropy) and two likelihood-based approaches (Bayesian spike-triggered covariance and extensions of generalized linear models). We analyze the formal relationship between the likelihood-based and information-based approaches to demonstrate how they lead to consistent inference. We demonstrate the practical feasibility of these procedures by using model neurons responding to a flickering variance stimulus.

DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

Science.gov (United States)

Mokhtari, Aryan; Shi, Wei; Ling, Qing; Ribeiro, Alejandro

2016-10-01

This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with neighbors only. A decentralized version of the alternating directions method of multipliers (DADMM) is a common method for solving this category of problems. DADMM exhibits linear convergence rate to the optimal objective but its implementation requires solving a convex optimization problem at each iteration. This can be computationally costly and may result in large overall convergence times. The decentralized quadratically approximated ADMM algorithm (DQM), which minimizes a quadratic approximation of the objective function that DADMM minimizes at each iteration, is proposed here. The consequent reduction in computational time is shown to have minimal effect on convergence properties. Convergence still proceeds at a linear rate with a guaranteed constant that is asymptotically equivalent to the DADMM linear convergence rate constant. Numerical results demonstrate advantages of DQM relative to DADMM and other alternatives in a logistic regression problem.

Input-constrained model predictive control via the alternating direction method of multipliers

DEFF Research Database (Denmark)

Sokoler, Leo Emil; Frison, Gianluca; Andersen, Martin S.

2014-01-01

This paper presents an algorithm, based on the alternating direction method of multipliers, for the convex optimal control problem arising in input-constrained model predictive control. We develop an efficient implementation of the algorithm for the extended linear quadratic control problem (LQCP......) with input and input-rate limits. The algorithm alternates between solving an extended LQCP and a highly structured quadratic program. These quadratic programs are solved using a Riccati iteration procedure, and a structure-exploiting interior-point method, respectively. The computational cost per iteration...... is quadratic in the dimensions of the controlled system, and linear in the length of the prediction horizon. Simulations show that the approach proposed in this paper is more than an order of magnitude faster than several state-of-the-art quadratic programming algorithms, and that the difference in computation...

Smoothing optimization of supporting quadratic surfaces with Zernike polynomials

Science.gov (United States)

Zhang, Hang; Lu, Jiandong; Liu, Rui; Ma, Peifu

2018-03-01

A new optimization method to get a smooth freeform optical surface from an initial surface generated by the supporting quadratic method (SQM) is proposed. To smooth the initial surface, a 9-vertex system from the neighbor quadratic surface and the Zernike polynomials are employed to establish a linear equation system. A local optimized surface to the 9-vertex system can be build by solving the equations. Finally, a continuous smooth optimization surface is constructed by stitching the above algorithm on the whole initial surface. The spot corresponding to the optimized surface is no longer discrete pixels but a continuous distribution.

Design of an Optimal Preview Controller for Linear Discrete-Time Descriptor Noncausal Multirate Systems

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Mengjuan Cao

2014-01-01

Full Text Available The linear discrete-time descriptor noncausal multirate system is considered for the presentation of a new design approach for optimal preview control. First, according to the characteristics of causal controllability and causal observability, the descriptor noncausal system is constructed into a descriptor causal closed-loop system. Second, by using the characteristics of the causal system and elementary transformation, the descriptor causal closed-loop system is transformed into a normal system. Then, taking advantage of the discrete lifting technique, the normal multirate system is converted to a single-rate system. By making use of the standard preview control method, we construct the descriptor augmented error system. The quadratic performance index for the multirate system is given, which can be changed into one for the single-rate system. In addition, a new single-rate system is obtained, the optimal control law of which is given. Returning to the original system, the optimal preview controller for linear discrete-time descriptor noncausal multirate systems is derived. The stabilizability and detectability of the lifted single-rate system are discussed in detail. The optimal preview control design techniques are illustrated by simulation results for a simple example.

Delayed Stochastic Linear-Quadratic Control Problem and Related Applications

Directory of Open Access Journals (Sweden)

Li Chen

2012-01-01

stochastic differential equations (FBSDEs with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem.

Self-Replicating Quadratics

Science.gov (United States)

Withers, Christopher S.; Nadarajah, Saralees

2012-01-01

We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…

Periodic feedback stabilization for linear periodic evolution equations

CERN Document Server

Wang, Gengsheng

2016-01-01

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

A Quadratically Convergent O(square root of nL-Iteration Algorithm for Linear Programming

National Research Council Canada - National Science Library

Ye, Y; Gueler, O; Tapia, Richard A; Zhang, Y

1991-01-01

...)-iteration complexity while exhibiting superlinear convergence of the duality gap to zero under the assumption that the iteration sequence converges, and quadratic convergence of the duality gap...

Evaluation of uneven fractionation radiotherapy of cervical lymph node-metastases by linear quadratic model

International Nuclear Information System (INIS)

Sasaki, Takehito; Kamata, Rikisaburo; Urahashi, Shingo; Yamaguchi, Tetsuji.

1993-01-01

One hundred and sixty-nine cervical lymph node-metastases from head and neck squamous cell carcinomas treated with either even fractionation or uneven fractionation regimens were analyzed in the present investigation. Logistic multivariate regression analysis indicated that: type of fractionation (even vs uneven), size of metastases, T value of primary tumors, and total dose are independent variables out of 18 variables that significantly influenced the rate of tumor clearance. The data, with statistical bias corrected by the regression equation, indicated that the uneven fractionation scheme significantly improved the rate of tumor clearance for the same size of metastases, total dose, and overall time compared to the even fractionation scheme. Further analysis by a linear-quadratic cell survival model indicated that the clinical improvement by uneven fractionation might not be explained entirely by a larger dose per fraction. It is suggested that tumor cells irradiated with an uneven fractionation regimen might repopulate more slowly, or they might be either less hypoxic or redistributed in a more radiosensitive phase in the cell cycle than those irradiated with even fractionation. This conclusion is clearly not definite, but it is suitable, pending the results of further investigation. (author)

Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps

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Minsong Zhang

2014-01-01

Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.

Isobio software: biological dose distribution and biological dose volume histogram from physical dose conversion using linear-quadratic-linear model.

Science.gov (United States)

Jaikuna, Tanwiwat; Khadsiri, Phatchareewan; Chawapun, Nisa; Saekho, Suwit; Tharavichitkul, Ekkasit

2017-02-01

To develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL) model. The Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR), and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD 2 ) was calculated using biological effective dose (BED) based on the LQL model. The software calculation and the manual calculation were compared for EQD 2 verification with pair t -test statistical analysis using IBM SPSS Statistics version 22 (64-bit). Two and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS) in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV) determined by D 90% , 0.56% in the bladder, 1.74% in the rectum when determined by D 2cc , and less than 1% in Pinnacle. The difference in the EQD 2 between the software calculation and the manual calculation was not significantly different with 0.00% at p -values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT) and 0.240, 0.320, and 0.849 for brachytherapy (BT) in HR-CTV, bladder, and rectum, respectively. The Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT.

Adaptive dynamic programming for discrete-time linear quadratic regulation based on multirate generalised policy iteration

Science.gov (United States)

Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho

2018-06-01

In this paper, we propose two multirate generalised policy iteration (GPI) algorithms applied to discrete-time linear quadratic regulation problems. The proposed algorithms are extensions of the existing GPI algorithm that consists of the approximate policy evaluation and policy improvement steps. The two proposed schemes, named heuristic dynamic programming (HDP) and dual HDP (DHP), based on multirate GPI, use multi-step estimation (M-step Bellman equation) at the approximate policy evaluation step for estimating the value function and its gradient called costate, respectively. Then, we show that these two methods with the same update horizon can be considered equivalent in the iteration domain. Furthermore, monotonically increasing and decreasing convergences, so called value iteration (VI)-mode and policy iteration (PI)-mode convergences, are proved to hold for the proposed multirate GPIs. Further, general convergence properties in terms of eigenvalues are also studied. The data-driven online implementation methods for the proposed HDP and DHP are demonstrated and finally, we present the results of numerical simulations performed to verify the effectiveness of the proposed methods.

Dhage Iteration Method for Generalized Quadratic Functional Integral Equations

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Bapurao C. Dhage

2015-01-01

Full Text Available In this paper we prove the existence as well as approximations of the solutions for a certain nonlinear generalized quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting at a lower or upper solution converges monotonically to the solutions of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our main result on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.

A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions

International Nuclear Information System (INIS)

Jian Jinbao; Hu Qingjie; Tang Chunming; Zheng Haiyan

2007-01-01

In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported

Quadratic algebras in the noncommutative integration method of wave equation

International Nuclear Information System (INIS)

Varaksin, O.L.

1995-01-01

The paper deals with the investigation of applications of the method of noncommutative integration of linear differential equations by partial derivatives. Nontrivial example was taken for integration of three-dimensions wave equation with the use of non-Abelian quadratic algebras

Quadratic Damping

Science.gov (United States)

Fay, Temple H.

2012-01-01

Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…

Quadratic interaction effect on the dark energy density in the universe

International Nuclear Information System (INIS)

Deveci, Derya G; Aydiner, Ekrem

2017-01-01

In this study, we deal with the holographic model of interacting dark components of dark energy and dark matter quadratic case of the equation of state parameter (EoS). The effective equations of states for the interacting holographic energy density are derived and the results are analyzed and compared with the solution of the linear form in the literature. The result of our work shows that the value of interaction term between dark components affects the fixed points at far future in the DE-dominated universe in the case of quadratic EoS parameter; it is a different result from the linear case in the theoretical results in the literature, and as the Quintom scenario the equations of state had coincidence at the cosmological constant boundary of –1 from above to below. (paper)

Quad-copter UAV BLDC Motor Control: Linear v/s non-linear control maps

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Deep Parikh

2015-08-01

Full Text Available This paper presents some investigations and comparison of using linear versus non-linear static motor-control maps for the speed control of a BLDC (Brush Less Direct Current motors used in quad-copter UAV (Unmanned Aerial Vehicles. The motor-control map considered here is the inverse of the static map relating motor-speed output to motor-voltage input for a typical out-runner type Brushless DC Motors (BLDCM.  Traditionally, quad-copter BLDC motor speed control uses simple linear motor-control map defined by the motor-constant specification. However, practical BLDC motors show non-linear characteristic, particularly when operated across wide operating speed-range as is commonly required in quad-copter UAV flight operations. In this paper, our investigations to compare performance of linear versus non-linear motor-control maps are presented. The investigations cover simulation-based and experimental study of BLDC motor speed control systems for  quad-copter vehicle available. First the non-linear map relating rotor RPM to motor voltage for quad-copter BLDC motor is obtained experimentally using an optical speed encoder. The performance of the linear versus non-linear motor-control-maps for the speed control are studied. The investigations also cover study of time-responses for various standard test input-signals e.g. step, ramp and pulse inputs, applied as the reference speed-commands. Also, simple 2-degree of freedom test-bed is developed in our laboratory to help test the open-loop and closed-loop experimental investigations. The non-linear motor-control map is found to perform better in BLDC motor speed tracking control performance and thereby helping achieve better quad-copter roll-angle attitude control.

Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

Energy Technology Data Exchange (ETDEWEB)

Szederkenyi, Gabor; Hangos, Katalin M

2004-04-26

We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.

Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

Science.gov (United States)

Szederkényi, Gábor; Hangos, Katalin M.

2004-04-01

We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.

Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

International Nuclear Information System (INIS)

Szederkenyi, Gabor; Hangos, Katalin M.

2004-01-01

We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities

Quadratic soliton self-reflection at a quadratically nonlinear interface

Science.gov (United States)

Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai

2003-11-01

The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.

A separation theorem for the stochastic sampled-data LQG problem. [control of continuous linear plant disturbed by white noise

Science.gov (United States)

Halyo, N.; Caglayan, A. K.

1976-01-01

This paper considers the control of a continuous linear plant disturbed by white plant noise when the control is constrained to be a piecewise constant function of time; i.e. a stochastic sampled-data system. The cost function is the integral of quadratic error terms in the state and control, thus penalizing errors at every instant of time while the plant noise disturbs the system continuously. The problem is solved by reducing the constrained continuous problem to an unconstrained discrete one. It is shown that the separation principle for estimation and control still holds for this problem when the plant disturbance and measurement noise are Gaussian.

Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC

Directory of Open Access Journals (Sweden)

Morten Hovd

2010-04-01

Full Text Available Explicit MPC of constrained linear systems is known to result in a piecewise affine controller and therefore also piecewise affine closed loop dynamics. The complexity of such analytic formulations of the control law can grow exponentially with the prediction horizon. The suboptimal solutions offer a trade-off in terms of complexity and several approaches can be found in the literature for the construction of approximate MPC laws. In the present paper a piecewise quadratic (PWQ Lyapunov function is used for the stability verification of an of approximate explicit Model Predictive Control (MPC. A novel relaxation method is proposed for the LMI criteria on the Lyapunov function design. This relaxation is applicable to the design of PWQ Lyapunov functions for discrete-time piecewise affine systems in general.

Sub-optimal control of fuzzy linear dynamical systems under granular differentiability concept.

Science.gov (United States)

Mazandarani, Mehran; Pariz, Naser

2018-05-01

This paper deals with sub-optimal control of a fuzzy linear dynamical system. The aim is to keep the state variables of the fuzzy linear dynamical system close to zero in an optimal manner. In the fuzzy dynamical system, the fuzzy derivative is considered as the granular derivative; and all the coefficients and initial conditions can be uncertain. The criterion for assessing the optimality is regarded as a granular integral whose integrand is a quadratic function of the state variables and control inputs. Using the relative-distance-measure (RDM) fuzzy interval arithmetic and calculus of variations, the optimal control law is presented as the fuzzy state variables feedback. Since the optimal feedback gains are obtained as fuzzy functions, they need to be defuzzified. This will result in the sub-optimal control law. This paper also sheds light on the restrictions imposed by the approaches which are based on fuzzy standard interval arithmetic (FSIA), and use strongly generalized Hukuhara and generalized Hukuhara differentiability concepts for obtaining the optimal control law. The granular eigenvalues notion is also defined. Using an RLC circuit mathematical model, it is shown that, due to their unnatural behavior in the modeling phenomenon, the FSIA-based approaches may obtain some eigenvalues sets that might be different from the inherent eigenvalues set of the fuzzy dynamical system. This is, however, not the case with the approach proposed in this study. The notions of granular controllability and granular stabilizability of the fuzzy linear dynamical system are also presented in this paper. Moreover, a sub-optimal control for regulating a Boeing 747 in longitudinal direction with uncertain initial conditions and parameters is gained. In addition, an uncertain suspension system of one of the four wheels of a bus is regulated using the sub-optimal control introduced in this paper. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Quadratic inner element subgrid scale discretisation of the Boltzmann transport equation

International Nuclear Information System (INIS)

Baker, C.M.J.; Buchan, A.G.; Pain, C.C.; Tollit, B.; Eaton, M.D.; Warner, P.

2012-01-01

This paper explores the application of the inner element subgrid scale method to the Boltzmann transport equation using quadratic basis functions. Previously, only linear basis functions for both the coarse scale and the fine scale were considered. This paper, therefore, analyses the advantages of using different coarse and subgrid basis functions for increasing the accuracy of the subgrid scale method. The transport of neutral particle radiation may be described by the Boltzmann transport equation (BTE) which, due to its 7 dimensional phase space, is computationally expensive to resolve. Multi-scale methods offer an approach to efficiently resolve the spatial dimensions of the BTE by separating the solution into its coarse and fine scales and formulating a solution whereby only the computationally efficient coarse scales need to be solved. In previous work an inner element subgrid scale method was developed that applied a linear continuous and discontinuous finite element method to represent the solution’s coarse and fine scale components. This approach was shown to generate efficient and stable solutions, and so this article continues its development by formulating higher order quadratic finite element expansions over the continuous and discontinuous scales. Here it is shown that a solution’s convergence can be improved significantly using higher order basis functions. Furthermore, by using linear finite elements to represent coarse scales in combination with quadratic fine scales, convergence can also be improved with only a modest increase in computational expense.

Wind turbine power tracking using an improved multimodel quadratic approach.

Science.gov (United States)

Khezami, Nadhira; Benhadj Braiek, Naceur; Guillaud, Xavier

2010-07-01

In this paper, an improved multimodel optimal quadratic control structure for variable speed, pitch regulated wind turbines (operating at high wind speeds) is proposed in order to integrate high levels of wind power to actively provide a primary reserve for frequency control. On the basis of the nonlinear model of the studied plant, and taking into account the wind speed fluctuations, and the electrical power variation, a multimodel linear description is derived for the wind turbine, and is used for the synthesis of an optimal control law involving a state feedback, an integral action and an output reference model. This new control structure allows a rapid transition of the wind turbine generated power between different desired set values. This electrical power tracking is ensured with a high-performance behavior for all other state variables: turbine and generator rotational speeds and mechanical shaft torque; and smooth and adequate evolution of the control variables. 2010 ISA. Published by Elsevier Ltd. All rights reserved.

A nonlinear model for fluid flow in a multiple-zone composite reservoir including the quadratic gradient term

International Nuclear Information System (INIS)

Wang, Xiao-Lu; Fan, Xiang-Yu; Nie, Ren-Shi; Huang, Quan-Hua; He, Yong-Ming

2013-01-01

Based on material balance and Darcy's law, the governing equation with the quadratic pressure gradient term was deduced. Then the nonlinear model for fluid flow in a multiple-zone composite reservoir including the quadratic gradient term was established and solved using a Laplace transform. A series of standard log–log type curves of 1-zone (homogeneous), 2-zone and 3-zone reservoirs were plotted and nonlinear flow characteristics were analysed. The type curves governed by the coefficient of the quadratic gradient term (β) gradually deviate from those of a linear model with time elapsing. Qualitative and quantitative analyses were implemented to compare the solutions of the linear and nonlinear models. The results showed that differences of pressure transients between the linear and nonlinear models increase with elapsed time and β. At the end, a successful application of the theoretical model data against the field data shows that the nonlinear model will be a good tool to evaluate formation parameters more accurately. (paper)

Rescuing Quadratic Inflation

CERN Document Server

Ellis, John; Sueiro, Maria

2014-01-01

Inflationary models based on a single scalar field $\\phi$ with a quadratic potential $V = \\frac{1}{2} m^2 \\phi^2$ are disfavoured by the recent Planck constraints on the scalar index, $n_s$, and the tensor-to-scalar ratio for cosmological density perturbations, $r_T$. In this paper we study how such a quadratic inflationary model can be rescued by postulating additional fields with quadratic potentials, such as might occur in sneutrino models, which might serve as either curvatons or supplementary inflatons. Introducing a second scalar field reduces but does not remove the pressure on quadratic inflation, but we find a sample of three-field models that are highly compatible with the Planck data on $n_s$ and $r_T$. We exhibit a specific three-sneutrino example that is also compatible with the data on neutrino mass difference and mixing angles.

A ''quadratized'' augmented plane wave method

International Nuclear Information System (INIS)

Smrcka, L.

1982-02-01

The exact radial solution inside the muffin-tin sphere is replaced by its Taylor expansion with respect to the energy, truncated after the quadratic term. Making use of it the energy independent augmented plane waves are formed which lead to the secular equations linear in energy. The method resembles the currently used linearized APW method but yields higher accuracy. The analysis of solution inside one muffin-tin sphere shows that the eigenvalue error is proportional to (E-E 0 ) 6 as compared with (E-E 0 ) 4 for LAPW. The error of eigenfunctions is (E-E 0 ) 3 ((E-E 0 ) 2 for LAPW). These conclusions are confirmed by direct numerical calculation of band structure of Cu and Al. (author)

Non-chaotic behaviour for a class of quadratic jerk equations

International Nuclear Information System (INIS)

Malasoma, J.-M.

2009-01-01

It is shown that a class constituted by 27 different types of non-linear third-order differential equations of the form x - =j(x,x . ,x), where j is a quadratic polynomial with only one or two terms, and for which ∂j(x,y,z)/∂z is not a constant function of time, does not exhibit chaos. The three-dimensional dynamical systems associated to these equations are not necessarily dissipative everywhere nor conservative everywhere in the corresponding phase spaces. Our results include and improve some recent results obtained by Yang and Chen who only considered the case where j was a homogeneous quadratic polynomial with two terms.

Least Squares Problems with Absolute Quadratic Constraints

Directory of Open Access Journals (Sweden)

R. Schöne

2012-01-01

Full Text Available This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem by multiplications of Givens' rotations. Finally, four applications of this approach are presented.

Measurement of quadratic electrogyration effect in castor oil

Science.gov (United States)

Izdebski, Marek; Ledzion, Rafał; Górski, Piotr

2015-07-01

This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient β13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.

A Note on 5-bit Quadratic Permutations’ Classification

OpenAIRE

Božilov, Dušan; Bilgin, Begül; Sahin, Hacı Ali

2017-01-01

Classification of vectorial Boolean functions up to affine equivalence is used widely to analyze various cryptographic and implementation properties of symmetric-key algorithms. We show that there exist 75 affine equivalence classes of 5-bit quadratic permutations. Furthermore, we explore important cryptographic properties of these classes, such as linear and differential properties and degrees of their inverses, together with multiplicative complexity and existence of uniform threshold reali...

Application of a quadratic method of programming to a particular problem of a rational development of a waterflooded field

Energy Technology Data Exchange (ETDEWEB)

Korotkov, S F; Khalitov, N T

1965-01-01

he quadratic method of programming is used to solve the following type of problem. A circular reservoir is subjected to a peripheral waterflood. The reservoir is drained by wells arranged in 3 concentric circles. The objective is to control the operation of producing wells, that a maximum quantity of water-free oil will be produced. The wells are flowed so that bottomhole pressure is above the bubble point. A quadratic equation is used to express the essential features of the problem; a system of linear equations is used to express the boundary conditions. The problem is solved by means of the Wolf algorithm method. The method is demonstrated by an illustrative example.

Exact solutions for oscillators with quadratic damping and mixed-parity nonlinearity

International Nuclear Information System (INIS)

Lai, S K; Chow, K W

2012-01-01

Exact vibration modes of a nonlinear oscillator, which contains both quadratic friction and a mixed-parity restoring force, are derived analytically. Two families of exact solutions are obtained in terms of rational expressions for classical Jacobi elliptic functions. The present solutions allow the investigation of the dynamical behaviour of the system in response to changes in physical parameters that concern nonlinearity. The physical significance of the signs (i.e. attractive or repulsive nature) of the linear, quadratic and cubic restoring forces is discussed. A qualitative analysis is also conducted to provide valuable physical insight into the nature of the system. (paper)

Newton's method for solving a quadratic matrix equation with special coefficient matrices

International Nuclear Information System (INIS)

Seo, Sang-Hyup; Seo, Jong Hyun; Kim, Hyun-Min

2014-01-01

We consider the iterative method for solving a quadratic matrix equation with special coefficient matrices which arises in the quasi-birth-death problem. In this paper, we show that the elementwise minimal positive solvents to quadratic matrix equations can be obtained using Newton's method. We also prove that the convergence rate of the Newton iteration is quadratic if the Fréchet derivative at the elementwise minimal positive solvent is nonsingular. However, if the Fréchet derivative is singular, the convergence rate is at least linear. Numerical experiments of the convergence rate are given.(This is summarized a paper which is to appear in Honam Mathematical Journal.)

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

Science.gov (United States)

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

2009-12-01

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

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

Directory of Open Access Journals (Sweden)

Ian H Stevenson

2009-12-01

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

Selective Linear or Quadratic Optomechanical Coupling via Measurement

Directory of Open Access Journals (Sweden)

Michael R. Vanner

2011-11-01

Full Text Available The ability to engineer both linear and nonlinear coupling with a mechanical resonator is an important goal for the preparation and investigation of macroscopic mechanical quantum behavior. In this work, a measurement based scheme is presented where linear or square mechanical-displacement coupling can be achieved using the optomechanical interaction that is linearly proportional to the mechanical position. The resulting square-displacement measurement strength is compared to that attainable in the dispersive case that has a direct interaction with the mechanical-displacement squared. An experimental protocol and parameter set are discussed for the generation and observation of non-Gaussian states of motion of the mechanical element.

Faithfully quadratic rings

CERN Document Server

Dickmann, M

2015-01-01

In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where -1 is not a sum of squares and 2 is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of T-isometry, where T is a preorder of the given ring, A, or T = A^2. (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in

Inelastic scattering in a local polaron model with quadratic coupling to bosons

DEFF Research Database (Denmark)

Olsen, Thomas

2009-01-01

We calculate the inelastic scattering probabilities in the wide band limit of a local polaron model with quadratic coupling to bosons. The central object is a two-particle Green's function which is calculated exactly using a purely algebraic approach. Compared with the usual linear interaction term...... a quadratic interaction term gives higher probabilities for inelastic scattering involving a large number of bosons. As an application we consider the problem hot-electron-mediated energy transfer at surfaces and use the delta self-consistent field extension of density-functional theory to calculate...

Design of power controller in CDMA system with power and SIR error minimization

Institute of Scientific and Technical Information of China (English)

Shulan KONG; Huanshui ZHANG; Zhaosheng ZHANG; Hongxia WANG

2007-01-01

In this paper, an uplink power control problem is considered for code division multiple access (CDMA) systems. A distributed algorithm is proposed based on linear quadratic optimal control theory. The proposed scheme minimizes the sum of the power and the error of signal-to-interference ratio (SIR). A power controller is designed by constructing an optimization problem of a stochastic linear quadratic type in Krein space and solving a Kalman filter problem.

Gravitation and quadratic forms

International Nuclear Information System (INIS)

Ananth, Sudarshan; Brink, Lars; Majumdar, Sucheta; Mali, Mahendra; Shah, Nabha

2017-01-01

The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.

Gravitation and quadratic forms

Energy Technology Data Exchange (ETDEWEB)

Ananth, Sudarshan [Indian Institute of Science Education and Research,Pune 411008 (India); Brink, Lars [Department of Physics, Chalmers University of Technology,S-41296 Göteborg (Sweden); Institute of Advanced Studies and Department of Physics & Applied Physics,Nanyang Technological University,Singapore 637371 (Singapore); Majumdar, Sucheta [Indian Institute of Science Education and Research,Pune 411008 (India); Mali, Mahendra [School of Physics, Indian Institute of Science Education and Research,Thiruvananthapuram, Trivandrum 695016 (India); Shah, Nabha [Indian Institute of Science Education and Research,Pune 411008 (India)

2017-03-31

The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.

Genetic design of interpolated non-linear controllers for linear plants

International Nuclear Information System (INIS)

Ajlouni, N.

2000-01-01

The techniques of genetic algorithms are proposed as a means of designing non-linear PID control systems. It is shown that the use of genetic algorithms for this purpose results in highly effective non-linear PID control systems. These results are illustrated by using genetic algorithms to design a non-linear PID control system and contrasting the results with an optimally tuned linear PID controller. (author)

Model Predictive Controller Combined with LQG Controller and Velocity Feedback to Control the Stewart Platform

DEFF Research Database (Denmark)

Nadimi, Esmaeil Sharak; Bak, Thomas; Izadi-Zamanabadi, Roozbeh

2006-01-01

The main objective of this paper is to investigate the erformance and applicability of two GPC (generalized predictive control) based control methods on a complete benchmark model of the Stewart platform made in MATLAB V6.5. The first method involves an LQG controller (Linear Quadratic Gaussian...

Guises and disguises of quadratic divergences

Energy Technology Data Exchange (ETDEWEB)

Cherchiglia, A.L., E-mail: adriano@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Vieira, A.R., E-mail: arvieira@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Hiller, Brigitte, E-mail: brigitte@teor.fis.uc.pt [Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, 3004-516 Coimbra (Portugal); Baêta Scarpelli, A.P., E-mail: scarpelli.apbs@dpf.gov.br [Setor Técnico-Científico, Departamento de Polícia Federal, Rua Hugo D’Antola, 95 - Lapa, São Paulo (Brazil); Sampaio, Marcos, E-mail: marcos.sampaio@durham.ac.uk [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road Durham DH1 3LE (United Kingdom)

2014-12-15

In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

On the classification of elliptic foliations induced by real quadratic fields with center

Science.gov (United States)

Puchuri, Liliana; Bueno, Orestes

2016-12-01

Related to the study of Hilbert's infinitesimal problem, is the problem of determining the existence and estimating the number of limit cycles of the linear perturbation of Hamiltonian fields. A classification of the elliptic foliations in the projective plane induced by the fields obtained by quadratic fields with center was already studied by several authors. In this work, we devise a unified proof of the classification of elliptic foliations induced by quadratic fields with center. This technique involves using a formula due to Cerveau & Lins Neto to calculate the genus of the generic fiber of a first integral of foliations of these kinds. Furthermore, we show that these foliations induce several examples of linear families of foliations which are not bimeromorphically equivalent to certain remarkable examples given by Lins Neto.

A new accurate quadratic equation model for isothermal gas chromatography and its comparison with the linear model

Science.gov (United States)

Wu, Liejun; Chen, Maoxue; Chen, Yongli; Li, Qing X.

2013-01-01

The gas holdup time (tM) is a dominant parameter in gas chromatographic retention models. The difference equation (DE) model proposed by Wu et al. (J. Chromatogr. A 2012, http://dx.doi.org/10.1016/j.chroma.2012.07.077) excluded tM. In the present paper, we propose that the relationship between the adjusted retention time tRZ′ and carbon number z of n-alkanes follows a quadratic equation (QE) when an accurate tM is obtained. This QE model is the same as or better than the DE model for an accurate expression of the retention behavior of n-alkanes and model applications. The QE model covers a larger range of n-alkanes with better curve fittings than the linear model. The accuracy of the QE model was approximately 2–6 times better than the DE model and 18–540 times better than the LE model. Standard deviations of the QE model were approximately 2–3 times smaller than those of the DE model. PMID:22989489

The quadratic-form identity for constructing the Hamiltonian structure of integrable systems

International Nuclear Information System (INIS)

Guo Fukui; Zhang Yufeng

2005-01-01

A usual loop algebra, not necessarily the matrix form of the loop algebra A-tilde n-1 , is also made use of for constructing linear isospectral problems, whose compatibility conditions exhibit a zero-curvature equation from which integrable systems are derived. In order to look for the Hamiltonian structure of such integrable systems, a quadratic-form identity is created in the present paper whose special case is just the trace identity; that is, when taking the loop algebra A-tilde 1 , the quadratic-form identity presented in this paper is completely consistent with the trace identity

Satellite Formation Control Using Atmospheric Drag

National Research Council Canada - National Science Library

Hajovsky, Blake B

2007-01-01

This study investigates the use of a linear quadratic terminal controller to reconfigure satellite formations using atmospheric drag actuated control while minimizing the loss of energy of the formation...

Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

Science.gov (United States)

Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.

2018-04-01

Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.

Vibration control of large linear quadratic symmetric systems. Ph.D. Thesis

Science.gov (United States)

Jeon, G. J.

1983-01-01

Some unique properties on a class of the second order lambda matrices were found and applied to determine a damping matrix of the decoupled subsystem in such a way that the damped system would have preassigned eigenvalues without disturbing the stiffness matrix. The resulting system was realized as a time invariant velocity only feedback control system with desired poles. Another approach using optimal control theory was also applied to the decoupled system in such a way that the mode spillover problem could be eliminated. The procedures were tested successfully by numerical examples.

Dynamic Algorithm for LQGPC Predictive Control

DEFF Research Database (Denmark)

Hangstrup, M.; Ordys, A.W.; Grimble, M.J.

1998-01-01

In this paper the optimal control law is derived for a multi-variable state space Linear Quadratic Gaussian Predictive Controller (LQGPC). A dynamic performance index is utilized resulting in an optimal steady state controller. Knowledge of future reference values is incorporated into the control......In this paper the optimal control law is derived for a multi-variable state space Linear Quadratic Gaussian Predictive Controller (LQGPC). A dynamic performance index is utilized resulting in an optimal steady state controller. Knowledge of future reference values is incorporated...... into the controller design and the solution is derived using the method of Lagrange multipliers. It is shown how well-known GPC controller can be obtained as a special case of the LQGPC controller design. The important advantage of using the LQGPC framework for designing predictive, e.g. GPS is that LQGPC enables...

Integrated vehicle dynamics control using State Dependent Riccati Equations

NARCIS (Netherlands)

Bonsen, B.; Mansvelders, R.; Vermeer, E.

2010-01-01

In this paper we discuss a State Dependent Riccati Equations (SDRE) solution for Integrated Vehicle Dynamics Control (IVDC). The SDRE approach is a nonlinear variant of the well known Linear Quadratic Regulator (LQR) and implements a quadratic cost function optimization. A modified version of this

Fitness of the analysis method of magnesium in drinking water using atomic absorption with quadratic calibration curve

International Nuclear Information System (INIS)

Perez-Lopez, Esteban

2014-01-01

The quantitative chemical analysis has been importance in research. Also, aspects like: quality control, sales of services and other areas of interest. Some instrumental analysis methods for quantification with linear calibration curve have presented limitations, because the short liner dynamic ranges of the analyte, or sometimes, by limiting the technique itself. The need has been to investigate a little more about the convenience of using quadratic calibration curves for analytical quantification, with which it has seeked demonstrate that has been a valid calculation model for chemical analysis instruments. An analysis base method is used on the technique of atomic absorption spectroscopy and in particular a determination of magnesium in a drinking water sample of the Tacares sector North of Grecia. A nonlinear calibration curve was used and specifically a curve with quadratic behavior. The same was compared with the test results obtained for the equal analysis with a linear calibration curve. The results have showed that the methodology has been valid for the determination referred with all confidence, since the concentrations have been very similar and, according to the used hypothesis testing, can be considered equal. (author) [es

Tail-constraining stochastic linear–quadratic control: a large deviation and statistical physics approach

International Nuclear Information System (INIS)

Chertkov, Michael; Kolokolov, Igor; Lebedev, Vladimir

2012-01-01

The standard definition of the stochastic risk-sensitive linear–quadratic (RS-LQ) control depends on the risk parameter, which is normally left to be set exogenously. We reconsider the classical approach and suggest two alternatives, resolving the spurious freedom naturally. One approach consists in seeking for the minimum of the tail of the probability distribution function (PDF) of the cost functional at some large fixed value. Another option suggests minimizing the expectation value of the cost functional under a constraint on the value of the PDF tail. Under the assumption of resulting control stability, both problems are reduced to static optimizations over a stationary control matrix. The solutions are illustrated using the examples of scalar and 1D chain (string) systems. The large deviation self-similar asymptotic of the cost functional PDF is analyzed. (paper)

A program package for solving linear optimization problems

International Nuclear Information System (INIS)

Horikami, Kunihiko; Fujimura, Toichiro; Nakahara, Yasuaki

1980-09-01

Seven computer programs for the solution of linear, integer and quadratic programming (four programs for linear programming, one for integer programming and two for quadratic programming) have been prepared and tested on FACOM M200 computer, and auxiliary programs have been written to make it easy to use the optimization program package. The characteristics of each program are explained and the detailed input/output descriptions are given in order to let users know how to use them. (author)

Design of Linear - and Minimum-phase FIR-equalizers

DEFF Research Database (Denmark)

Bysted, Tommy Kristensen; Jensen, K.J.; Gaunholt, Hans

1996-01-01

an error function which is quadratic in the filtercoefficients. The advantage of the quadratic function is the ability to find the optimal coefficients solving a system of linear equations without iterations.The transformation to a minimum-phase equalizer is carried out by homomorphic deconvolution...

On bent and semi-bent quadratic Boolean functions

DEFF Research Database (Denmark)

Charpin, P.; Pasalic, Enes; Tavernier, C.

2005-01-01

correlation and high nonlinearity. We say that such a sequence is generated by a semi-bent function. Some new families of such function, represented by f(x) = Sigma(i=1)(n-1/2) c(i)Tr(x(2t+1)), n odd and c(i) is an element of F-2, have recently (2002) been introduced by Khoo et al. We first generalize......The maximum-length sequences, also called m-sequences, have received a lot of attention since the late 1960s. In terms of linear-feedback shift register (LFSR) synthesis they are usually generated by certain power polynomials over a finite field and in addition are characterized by a low cross...... their results to even n. We further investigate the conditions on the choice of ci for explicit definitions of new infinite families having three and four trace terms. Also, a class of nonpermutation polynomials whose composition with a quadratic function yields again a quadratic semi-bent function is specified...

New robust chaotic system with exponential quadratic term

International Nuclear Information System (INIS)

Bao Bocheng; Li Chunbiao; Liu Zhong; Xu Jianping

2008-01-01

This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic attractor with only two equilibria, and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent. Some basic dynamical properties and chaotic behaviour of novel attractor are studied. By numerical simulation, this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviours by a constant controller. (general)

Aspects of Quadratic Gravity

CERN Document Server

Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio

2016-01-01

We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...

Simulation of nonlinear benchmarks and sheet metal forming processes using linear and quadratic solid–shell elements combined with advanced anisotropic behavior models

Directory of Open Access Journals (Sweden)

Wang Peng

2016-01-01

Full Text Available A family of prismatic and hexahedral solid‒shell (SHB elements with their linear and quadratic versions is presented in this paper to model thin 3D structures. Based on reduced integration and special treatments to eliminate locking effects and to control spurious zero-energy modes, the SHB solid‒shell elements are capable of modeling most thin 3D structural problems with only a single element layer, while describing accurately the various through-thickness phenomena. In this paper, the SHB elements are combined with fully 3D behavior models, including orthotropic elastic behavior for composite materials and anisotropic plastic behavior for metallic materials, which allows describing the strain/stress state in the thickness direction, in contrast to traditional shell elements. All SHB elements are implemented into ABAQUS using both standard/quasi-static and explicit/dynamic solvers. Several benchmark tests have been conducted, in order to first assess the performance of the SHB elements in quasi-static and dynamic analyses. Then, deep drawing of a hemispherical cup is performed to demonstrate the capabilities of the SHB elements in handling various types of nonlinearities (large displacements and rotations, anisotropic plasticity, and contact. Compared to classical ABAQUS solid and shell elements, the results given by the SHB elements show good agreement with the reference solutions.

Spectral analysis of the SN approximations in a slab with quadratically anisotropic scattering

International Nuclear Information System (INIS)

Ourique, L.E.; Pazos, R.P.; Vilhena, M.T.; Barros, R.C.

2003-01-01

The spectral analysis of the S N approximations to the one-dimensional transport equation began with 3 and 4, following the studies of 1 and 2 about the discrete eigenvalues of the transport equation. In previous work about the influence of a parameter in the solutions of S N approximations, it was considered the total macroscopic cross section as a control parameter and was analyzed how its variation changes the nature of the eigenvalues of the S N transport matrix, in problems with linearly anisotropic scattering. It was showed the existence of bifurcations points, i.e., there exist some values of control parameters for which the S N transport matrix has only real eigenvalues while for other values the S N relation between the eigenvalues of S N transport matrix and control parameter, supposing quadratically anisotropic scattering. Numerical results are reported. (author)

An algorithm for the solution of dynamic linear programs

Science.gov (United States)

Psiaki, Mark L.

1989-01-01

The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation

Linear and quadratic models of point process systems: contributions of patterned input to output.

Science.gov (United States)

Lindsay, K A; Rosenberg, J R

2012-08-01

In the 1880's Volterra characterised a nonlinear system using a functional series connecting continuous input and continuous output. Norbert Wiener, in the 1940's, circumvented problems associated with the application of Volterra series to physical problems by deriving from it a new series of terms that are mutually uncorrelated with respect to Gaussian processes. Subsequently, Brillinger, in the 1970's, introduced a point-process analogue of Volterra's series connecting point-process inputs to the instantaneous rate of point-process output. We derive here a new series from this analogue in which its terms are mutually uncorrelated with respect to Poisson processes. This new series expresses how patterned input in a spike train, represented by third-order cross-cumulants, is converted into the instantaneous rate of an output point-process. Given experimental records of suitable duration, the contribution of arbitrary patterned input to an output process can, in principle, be determined. Solutions for linear and quadratic point-process models with one and two inputs and a single output are investigated. Our theoretical results are applied to isolated muscle spindle data in which the spike trains from the primary and secondary endings from the same muscle spindle are recorded in response to stimulation of one and then two static fusimotor axons in the absence and presence of a random length change imposed on the parent muscle. For a fixed mean rate of input spikes, the analysis of the experimental data makes explicit which patterns of two input spikes contribute to an output spike. Copyright © 2012 Elsevier Ltd. All rights reserved.

Basic concepts of control theory

International Nuclear Information System (INIS)

Markus, L.

1976-01-01

After a philosophical introduction on control theory and its position among various branches of science, mathematical control theory and its connection with functional analysis are discussed. A chapter on system theory concepts follows. After a summary of results and notations in the general theory of ordinary differential equations, a qualitative theory of control dynamical systems and chapters on the topological dynamics, and the controllability of linear systems are presented. As examples of autonomous linear systems, the switching locus for the synthesis of optimal controllers and linear dynamics with quadratic cost optimization are considered. (author)

COMPARISON OF LINEAR CONTROLLERS FOR A

DEFF Research Database (Denmark)

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

2005-01-01

on comparing different linear controllers, based on both simulation and experimental results, to determine what is obtainable when applying standard linear controllers to a hydraulic SISO servo system. The paper furthermore addresses how the performance may be improved by using internal pressure control......In many hydraulic control applications, classic linear controllers are still employed, although there exist a number of number of nonlinear control methods, which may be better suited for handling the intrensic non-linearities often found in hydraulic systems. The focus of this paper is therefore...... and model based information to include feedforward information. The control strategies considered are all based on measurement of piston position and pressure only....

Introduction to optimal control theory

International Nuclear Information System (INIS)

Agrachev, A.A.

2002-01-01

These are lecture notes of the introductory course in Optimal Control theory treated from the geometric point of view. Optimal Control Problem is reduced to the study of controls (and corresponding trajectories) leading to the boundary of attainable sets. We discuss Pontryagin Maximum Principle, basic existence results, and apply these tools to concrete simple optimal control problems. Special sections are devoted to the general theory of linear time-optimal problems and linear-quadratic problems. (author)

On Characterization of Quadratic Splines

DEFF Research Database (Denmark)

Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong

2005-01-01

that the representation can be refined in a neighborhood of a non-degenerate point and a set of non-degenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general....

An introduction to linear algebra

CERN Document Server

Mirsky, L

2003-01-01

Rigorous, self-contained coverage of determinants, vectors, matrices and linear equations, quadratic forms, more. Elementary, easily readable account with numerous examples and problems at the end of each chapter.

Diagonalizing quadratic bosonic operators by non-autonomous flow equations

CERN Document Server

Bach, Volker

2016-01-01

The authors study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. They specify assumptions that ensure the global existence of its solutions and allow them to derive its asymptotics at temporal infinity. They demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocketâe"Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous unitary flow. In fact, the solution of the non-linear flow equation leads to a diagonalization of Hamiltonian operators in boson quantum field theory which are quadratic in the field.

Complex eigenvalues for neutron transport equation with quadratically anisotropic scattering

International Nuclear Information System (INIS)

Sjoestrand, N.G.

1981-01-01

Complex eigenvalues for the monoenergetic neutron transport equation in the buckling approximation have been calculated for various combinations of linearly and quadratically anisotropic scattering. The results are discussed in terms of the time-dependent case. Tables are given of complex bucklings for real decay constants and of complex decay constants for real bucklings. The results fit nicely into the pattern of real and purely imaginary eigenvalues obtained earlier. (author)

Optimization for decision making linear and quadratic models

CERN Document Server

Murty, Katta G

2010-01-01

While maintaining the rigorous linear programming instruction required, Murty's new book is unique in its focus on developing modeling skills to support valid decision-making for complex real world problems, and includes solutions to brand new algorithms.

Quadratic third-order tensor optimization problem with quadratic constraints

Directory of Open Access Journals (Sweden)

Lixing Yang

2014-05-01

Full Text Available Quadratically constrained quadratic programs (QQPs problems play an important modeling role for many diverse problems. These problems are in general NP hard and numerically intractable. Semidenite programming (SDP relaxations often provide good approximate solutions to these hard problems. For several special cases of QQP, e.g., convex programs and trust region subproblems, SDP relaxation provides the exact optimal value, i.e., there is a zero duality gap. However, this is not true for the general QQP, or even the QQP with two convex constraints, but a nonconvex objective.In this paper, we consider a certain QQP where the variable is neither vector nor matrix but a third-order tensor. This problem can be viewed as a generalization of the ordinary QQP with vector or matrix as it's variant. Under some mild conditions, we rst show that SDP relaxation provides exact optimal solutions for the original problem. Then we focus on two classes of homogeneous quadratic tensor programming problems which have no requirements on the constraints number. For one, we provide an easily implemental polynomial time algorithm to approximately solve the problem and discuss the approximation ratio. For the other, we show there is no gap between the SDP relaxation and itself.

Decentralized linear quadratic power system stabilizers for multi ...

Indian Academy of Sciences (India)

Introduction. Modern excitation systems considerably enhance the overall transient stability of power systems ..... to the local bus rather than the angle δ measured with respect to the remote bus. ... With this in view, the linear and nonlinear per-.

Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

Science.gov (United States)

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.

Parametric optimal control of uncertain systems under an optimistic value criterion

Science.gov (United States)

Li, Bo; Zhu, Yuanguo

2018-01-01

It is well known that the optimal control of a linear quadratic model is characterized by the solution of a Riccati differential equation. In many cases, the corresponding Riccati differential equation cannot be solved exactly such that the optimal feedback control may be a complex time-oriented function. In this article, a parametric optimal control problem of an uncertain linear quadratic model under an optimistic value criterion is considered for simplifying the expression of optimal control. Based on the equation of optimality for the uncertain optimal control problem, an approximation method is presented to solve it. As an application, a two-spool turbofan engine optimal control problem is given to show the utility of the proposed model and the efficiency of the presented approximation method.

Quadratic algebras applied to noncommutative integration of the Klein-Gordon equation: Four-dimensional quadratic algebras containing three-dimensional nilpotent lie algebras

International Nuclear Information System (INIS)

Varaksin, O.L.; Firstov, V.V.; Shapovalov, A.V.

1995-01-01

The study is continued on noncommutative integration of linear partial differential equations in application to the exact integration of quantum-mechanical equations in a Riemann space. That method gives solutions to the Klein-Gordon equation when the set of noncommutative symmetry operations for that equation forms a quadratic algebra consisting of one second-order operator and of first-order operators forming a Lie algebra. The paper is a continuation of, where a single nontrivial example is used to demonstrate noncommutative integration of the Klein-Gordon equation in a Riemann space not permitting variable separation

[The enigma of the biological interpretation of the linear-quadratic model finally resolved? A summary for non-mathematicians].

Science.gov (United States)

Bodgi, L; Canet, A; Granzotto, A; Britel, M; Puisieux, A; Bourguignon, M; Foray, N

2016-06-01

The linear-quadratic (LQ) model is the only mathematical formula linking cellular survival and radiation dose that is sufficiently consensual to help radiation oncologists and radiobiologists in describing the radiation-induced events. However, this formula proposed in the 1970s and α and β parameters on which it is based remained without relevant biological meaning. From a collection of cutaneous fibroblasts with different radiosensitivity, built over 12 years by more than 50 French radiation oncologists, we recently pointed out that the ATM protein, major actor of the radiation response, diffuses from the cytoplasm to the nucleus after irradiation. The evidence of this nuclear shuttling of ATM allowed us to provide a biological interpretation of the LQ model in its mathematical features, validated by a hundred of radiosensitive cases. A mechanistic explanation of the radiosensitivity of syndromes caused by the mutation of cytoplasmic proteins and of the hypersensitivity to low-dose phenomenon has been proposed, as well. In this review, we present our resolution of the LQ model in the most didactic way. Copyright © 2016 Société française de radiothérapie oncologique (SFRO). Published by Elsevier SAS. All rights reserved.

Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

Science.gov (United States)

Acikmese, Ahmet Behcet; Corless, Martin

2004-01-01

We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

Linearizing feedforward/feedback attitude control

Science.gov (United States)

Paielli, Russell A.; Bach, Ralph E.

1991-01-01

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

Extending the Scope of Robust Quadratic Optimization

NARCIS (Netherlands)

Marandi, Ahmadreza; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand

In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in

Quadratic residues and non-residues selected topics

CERN Document Server

Wright, Steve

2016-01-01

This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.

Calculus of variations mechanics, control and other applications

CERN Document Server

MacCluer, Charles R

2012-01-01

First truly up-to-date treatment offers a simple introduction to optimal control, linear-quadratic control design, and more. Broad perspective features numerous exercises, hints, outlines, and appendixes, including a practical discussion of MATLAB. 2005 edition.

Partial Stator Overlap in a Linear Generator for Wave Power: An Experimental Study

Directory of Open Access Journals (Sweden)

Anna E. Frost

2017-11-01

Full Text Available This paper presents a study on how the power absorption and damping in a linear generator for wave energy conversion are affected by partial overlap between stator and translator. The theoretical study shows that the electrical power as well as the damping coefficient change quadratically with partial stator overlap, if inductance, friction and iron losses are assumed independent of partial stator overlap or can be neglected. Results from onshore experiments on a linear generator for wave energy conversion cannot reject the quadratic relationship. Measurements were done on the inductance of the linear generator and no dependence on partial stator overlap could be found. Simulations of the wave energy converter’s operation in high waves show that entirely neglecting partial stator overlap will overestimate the energy yield and underestimate the peak forces in the line between the buoy and the generator. The difference between assuming a linear relationship instead of a quadratic relationship is visible but small in the energy yield in the simulation. Since the theoretical deduction suggests a quadratic relationship, this is advisable to use during modeling. However, a linear assumption could be seen as an acceptable simplification when modeling since other relationships can be computationally costly.

Students' Understanding of Quadratic Equations

Science.gov (United States)

López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

2016-01-01

Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

Vacuum solutions of Bianchi cosmologies in quadratic gravity

International Nuclear Information System (INIS)

Deus, Juliano Alves de; Muller, Daniel

2011-01-01

Full text: In this work we solve numerically the vacuum solutions of field equations of Bianchi homogeneous universes in the context of Semiclassical theory. Our interest is to study the quadratic theory of gravity with regard in the cosmological description of our universe in periods of intense fields. Bianchi cosmologies are anisotropic homogeneous cosmological models, but can include the isotropic models as particular cases (Bianchi I, VII and IX include homogeneous and isotropic Friedmann models plane, hyperbolic and spherical, respectively). Homogeneous models are good cosmological representations of our universe. With focus in solutions for intense fields, like the early universe, where isotropy is not necessarily required, the adopted scenario is the vacuum solutions, where the geometry is dominant in determining the gravitation. Still following in this way, the Semiclassical theory, which considers quantum matter fields propagating in classical geometrical background, is addressed to give the field equations. This formalism leads to fourth-order ordinary differential equations, in contrast to second-order equations from General Relativity. The Lagrangian of the theory is quadratic in the Ricci scalar and in the Ricci tensor. The equations system is highly non-linear and can be only numerically solved, except perhaps for few particular cases. We obtained numerical solutions for Bianchi V II A evolving to Minkowski and to de Sitter solutions, and also to singularities. The both first and second solutions were obtained choosing initial conditions near from respective exact vacuum solutions from Einstein theory, which are also exact solutions of the quadratic theory. Other Bianchi types are still under study. (author)

Controllability analysis of decentralised linear controllers for polymeric fuel cells

Energy Technology Data Exchange (ETDEWEB)

Serra, Maria; Aguado, Joaquin; Ansede, Xavier; Riera, Jordi [Institut de Robotica i Informatica Industrial, Universitat Politecnica de Catalunya - Consejo Superior de Investigaciones Cientificas, C. Llorens i Artigas 4, 08028 Barcelona (Spain)

2005-10-10

This work deals with the control of polymeric fuel cells. It includes a linear analysis of the system at different operating points, the comparison and selection of different control structures, and the validation of the controlled system by simulation. The work is based on a complex non linear model which has been linearised at several operating points. The linear analysis tools used are the Morari resiliency index, the condition number, and the relative gain array. These techniques are employed to compare the controllability of the system with different control structures and at different operating conditions. According to the results, the most promising control structures are selected and their performance with PI based diagonal controllers is evaluated through simulations with the complete non linear model. The range of operability of the examined control structures is compared. Conclusions indicate good performance of several diagonal linear controllers. However, very few have a wide operability range. (author)

Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning.

Science.gov (United States)

Gorban, A N; Mirkes, E M; Zinovyev, A

2016-12-01

Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L 1 norm or even sub-linear potentials corresponding to quasinorms L p (0application of min-plus algebra. The approach can be applied in most of existing machine learning methods, including methods of data approximation and regularized and sparse regression, leading to the improvement in the computational cost/accuracy trade-off. We demonstrate that on synthetic and real-life datasets PQSQ-based machine learning methods achieve orders of magnitude faster computational performance than the corresponding state-of-the-art methods, having similar or better approximation accuracy. Copyright © 2016 Elsevier Ltd. All rights reserved.

Linear feedback controls the essentials

CERN Document Server

Haidekker, Mark A

2013-01-01

The design of control systems is at the very core of engineering. Feedback controls are ubiquitous, ranging from simple room thermostats to airplane engine control. Helping to make sense of this wide-ranging field, this book provides a new approach by keeping a tight focus on the essentials with a limited, yet consistent set of examples. Analysis and design methods are explained in terms of theory and practice. The book covers classical, linear feedback controls, and linear approximations are used when needed. In parallel, the book covers time-discrete (digital) control systems and juxtapos

Stochastic Control of Energy Efficient Buildings: A Semidefinite Programming Approach

Energy Technology Data Exchange (ETDEWEB)

Ma, Xiao [ORNL; Dong, Jin [ORNL; Djouadi, Seddik M [ORNL; Nutaro, James J [ORNL; Kuruganti, Teja [ORNL

2015-01-01

The key goal in energy efficient buildings is to reduce energy consumption of Heating, Ventilation, and Air- Conditioning (HVAC) systems while maintaining a comfortable temperature and humidity in the building. This paper proposes a novel stochastic control approach for achieving joint performance and power control of HVAC. We employ a constrained Stochastic Linear Quadratic Control (cSLQC) by minimizing a quadratic cost function with a disturbance assumed to be Gaussian. The problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. By using cSLQC, the problem is reduced to a semidefinite optimization problem, where the optimal control can be computed efficiently by Semidefinite programming (SDP). Simulation results are provided to demonstrate the effectiveness and power efficiency by utilizing the proposed control approach.

An efficient inverse radiotherapy planning method for VMAT using quadratic programming optimization.

Science.gov (United States)

Hoegele, W; Loeschel, R; Merkle, N; Zygmanski, P

2012-01-01

The purpose of this study is to investigate the feasibility of an inverse planning optimization approach for the Volumetric Modulated Arc Therapy (VMAT) based on quadratic programming and the projection method. The performance of this method is evaluated against a reference commercial planning system (eclipse(TM) for rapidarc(TM)) for clinically relevant cases. The inverse problem is posed in terms of a linear combination of basis functions representing arclet dose contributions and their respective linear coefficients as degrees of freedom. MLC motion is decomposed into basic motion patterns in an intuitive manner leading to a system of equations with a relatively small number of equations and unknowns. These equations are solved using quadratic programming under certain limiting physical conditions for the solution, such as the avoidance of negative dose during optimization and Monitor Unit reduction. The modeling by the projection method assures a unique treatment plan with beneficial properties, such as the explicit relation between organ weightings and the final dose distribution. Clinical cases studied include prostate and spine treatments. The optimized plans are evaluated by comparing isodose lines, DVH profiles for target and normal organs, and Monitor Units to those obtained by the clinical treatment planning system eclipse(TM). The resulting dose distributions for a prostate (with rectum and bladder as organs at risk), and for a spine case (with kidneys, liver, lung and heart as organs at risk) are presented. Overall, the results indicate that similar plan qualities for quadratic programming (QP) and rapidarc(TM) could be achieved at significantly more efficient computational and planning effort using QP. Additionally, results for the quasimodo phantom [Bohsung et al., "IMRT treatment planning: A comparative inter-system and inter-centre planning exercise of the estro quasimodo group," Radiother. Oncol. 76(3), 354-361 (2005)] are presented as an example

A numerical algorithm to find all feedback Nash equilibria in scalar affine quadratic differential games

NARCIS (Netherlands)

Engwerda, Jacob

2015-01-01

This note deals with solving scalar coupled algebraic Riccati equations. These equations arise in finding linear feedback Nash equilibria of the scalar N-player affine quadratic differential game. A numerical procedure is provided to compute all the stabilizing solutions. The main idea is to

A generalized linear-quadratic model incorporating reciprocal time pattern of radiation damage repair

International Nuclear Information System (INIS)

Huang, Zhibin; Mayr, Nina A.; Lo, Simon S.; Wang, Jian Z.; Jia Guang; Yuh, William T. C.; Johnke, Roberta

2012-01-01

Purpose: It has been conventionally assumed that the repair rate for sublethal damage (SLD) remains constant during the entire radiation course. However, increasing evidence from animal studies suggest that this may not the case. Rather, it appears that the repair rate for radiation-induced SLD slows down with increasing time. Such a slowdown in repair would suggest that the exponential repair pattern would not necessarily accurately predict repair process. As a result, the purpose of this study was to investigate a new generalized linear-quadratic (LQ) model incorporating a repair pattern with reciprocal time. The new formulas were tested with published experimental data. Methods: The LQ model has been widely used in radiation therapy, and the parameter G in the surviving fraction represents the repair process of sublethal damage with T r as the repair half-time. When a reciprocal pattern of repair process was adopted, a closed form of G was derived analytically for arbitrary radiation schemes. The published animal data adopted to test the reciprocal formulas. Results: A generalized LQ model to describe the repair process in a reciprocal pattern was obtained. Subsequently, formulas for special cases were derived from this general form. The reciprocal model showed a better fit to the animal data than the exponential model, particularly for the ED50 data (reduced χ 2 min of 2.0 vs 4.3, p = 0.11 vs 0.006), with the following gLQ parameters: α/β = 2.6-4.8 Gy, T r = 3.2-3.9 h for rat feet skin, and α/β = 0.9 Gy, T r = 1.1 h for rat spinal cord. Conclusions: These results of repair process following a reciprocal time suggest that the generalized LQ model incorporating the reciprocal time of sublethal damage repair shows a better fit than the exponential repair model. These formulas can be used to analyze the experimental and clinical data, where a slowing-down repair process appears during the course of radiation therapy.

Experiences with the quadratic Korringa-Kohn-Rostoker band theory method

International Nuclear Information System (INIS)

Faulkner, J.S.

1992-01-01

This paper reports on the Quadratic Korriga-Kohn-Rostoker method which is a fast band theory method in the sense that all eigenvalues for a given k are obtained from one matrix diagonalization, but it differs from other fast band theory methods in that it is derived entirely from multiple-scattering theory, without the introduction of a Rayleigh-Ritz variations step. In this theory, the atomic potentials are shifted by Δσ(r) with Δ equal to E-E 0 and σ(r) equal to one when r is inside the Wigner-Seitz cell and zero otherwise, and it turns out that the matrix of coefficients is an entire function of Δ. This matrix can be terminated to give a linear KKR, quadratic KKR, cubic KKR,..., or not terminated at all to give the pivoted multiple-scattering equations. Full potential are no harder to deal with than potentials with a shape approximation

Orthogonality preserving infinite dimensional quadratic stochastic operators

International Nuclear Information System (INIS)

Akın, Hasan; Mukhamedov, Farrukh

2015-01-01

In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators

Polyhedral combinatorics of the cardinality constrained quadratic knapsack problem and the quadratic selective travelling salesman problem

DEFF Research Database (Denmark)

Mak, Vicky; Thomadsen, Tommy

2006-01-01

This paper considers the cardinality constrained quadratic knapsack problem (QKP) and the quadratic selective travelling salesman problem (QSTSP). The QKP is a generalization of the knapsack problem and the QSTSP is a generalization of the travelling salesman problem. Thus, both problems are NP...

Quadratically convergent MCSCF scheme using Fock operators

International Nuclear Information System (INIS)

Das, G.

1981-01-01

A quadratically convergent formulation of the MCSCF method using Fock operators is presented. Among its advantages the present formulation is quadratically convergent unlike the earlier ones based on Fock operators. In contrast to other quadratically convergent schemes as well as the one based on generalized Brillouin's theorem, this method leads easily to a hybrid scheme where the weakly coupled orbitals (such as the core) are handled purely by Fock equations, while the rest of the orbitals are treated by a quadratically convergent approach with a truncated virtual space obtained by the use of the corresponding Fock equations

The maximally achievable accuracy of linear optimal regulators and linear optimal filters

NARCIS (Netherlands)

Kwakernaak, H.; Sivan, Raphael

1972-01-01

A linear system with a quadratic cost function, which is a weighted sum of the integral square regulation error and the integral square input, is considered. What happens to the integral square regulation error as the relative weight of the integral square input reduces to zero is investigated. In

PWR control system design using advanced linear and non-linear methodologies

International Nuclear Information System (INIS)

Rabindran, N.; Whitmarsh-Everiss, M.J.

2004-01-01

Consideration is here given to the methodology deployed for non-linear heuristic analysis in the time domain supported by multi-variable linear control system design methods for the purposes of operational dynamics and control system analysis. This methodology is illustrated by the application of structural singular value μ analysis to Pressurised Water Reactor control system design. (author)

Quadratic brackets from symplectic forms

International Nuclear Information System (INIS)

Alekseev, Anton Yu.; Todorov, Ivan T.

1994-01-01

We give a physicist oriented survey of Poisson-Lie symmetries of classical systems. We consider finite-dimensional geometric actions and the chiral WZNW model as examples for the general construction. An essential point is the appearance of quadratic Poisson brackets for group-like variables. It is believed that upon quantization they lead to quadratic exchange algebras. ((orig.))

Multivariable adaptive control of bio process

Energy Technology Data Exchange (ETDEWEB)

Maher, M.; Bahhou, B.; Roux, G. [Centre National de la Recherche Scientifique (CNRS), 31 - Toulouse (France); Maher, M. [Faculte des Sciences, Rabat (Morocco). Lab. de Physique

1995-12-31

This paper presents a multivariable adaptive control of a continuous-flow fermentation process for the alcohol production. The linear quadratic control strategy is used for the regulation of substrate and ethanol concentrations in the bioreactor. The control inputs are the dilution rate and the influent substrate concentration. A robust identification algorithm is used for the on-line estimation of linear MIMO model`s parameters. Experimental results of a pilot-plant fermenter application are reported and show the control performances. (authors) 8 refs.

Magneto-optical conductivity of Weyl semimetals with quadratic term in momentum

Directory of Open Access Journals (Sweden)

J. M. Shao

2016-02-01

Full Text Available Weyl semimetal is a three-dimensional Dirac material whose low energy dispersion is linear in momentum. Adding a quadratic (Schrödinger term to the Weyl node breaks the original particle-hole symmetry and also breaks the mirror symmetry between the positive and negative Landau levels in present of magnetic field. This asymmetry splits the absorption line of the longitudinal magneto-optical conductivity into a two peaks structure. It also results in an oscillation pattern in the absorption part of the Hall conductivity. The two split peaks in Reσxx (or the positive and negative oscillation in Imσxy just correspond to the absorptions of left-handed (σ− and right-handed (σ+ polarization light, respectively. The split in Reσxx and the displacement between the absorption of σ+ and σ− are decided by the magnitude of the quadratic term and the magnetic field.

Optimal estimation and scheduling in aquifer management using the rapid feedback control method

Science.gov (United States)

Ghorbanidehno, Hojat; Kokkinaki, Amalia; Kitanidis, Peter K.; Darve, Eric

2017-12-01

Management of water resources systems often involves a large number of parameters, as in the case of large, spatially heterogeneous aquifers, and a large number of "noisy" observations, as in the case of pressure observation in wells. Optimizing the operation of such systems requires both searching among many possible solutions and utilizing new information as it becomes available. However, the computational cost of this task increases rapidly with the size of the problem to the extent that textbook optimization methods are practically impossible to apply. In this paper, we present a new computationally efficient technique as a practical alternative for optimally operating large-scale dynamical systems. The proposed method, which we term Rapid Feedback Controller (RFC), provides a practical approach for combined monitoring, parameter estimation, uncertainty quantification, and optimal control for linear and nonlinear systems with a quadratic cost function. For illustration, we consider the case of a weakly nonlinear uncertain dynamical system with a quadratic objective function, specifically a two-dimensional heterogeneous aquifer management problem. To validate our method, we compare our results with the linear quadratic Gaussian (LQG) method, which is the basic approach for feedback control. We show that the computational cost of the RFC scales only linearly with the number of unknowns, a great improvement compared to the basic LQG control with a computational cost that scales quadratically. We demonstrate that the RFC method can obtain the optimal control values at a greatly reduced computational cost compared to the conventional LQG algorithm with small and controllable losses in the accuracy of the state and parameter estimation.

The Design of Optimal PID Control Method for Quadcopter Movement Control

Directory of Open Access Journals (Sweden)

Hanum Arrosida

2018-02-01

Full Text Available Nowadays, quadcopter motion control has become a popular research topic because of its versatile ability as an unmanned aircraft can be used to alleviate human labor and also be able to reach dangerous areas or areas which is unreachable to humans. On the other hand, the Optimal PID control method, which incorporates PID and Linear Quadratic Regulator (LQR control methods, has also been widely used in industry and research field because it has advantages that are easy to operate, easy design, and a good level of precision. In the PID control method, the main problem to be solved is the accuracy of the gain value Kp, Ki, and Kd because the inappropriateness of those value will result in an imprecise control action. Based on these problems and referring to the previous study, the optimal PID control method was developed by using PID controller structure with tuning gain parameter of PID through Linear Quadratic Regulator (LQR method. Through the integration of these two control methods, the optimum solutions can be obtained: easier controller design process for quadcopter control when crossing the determined trajectories, steady state error values less than 5% and a stable quadcopter movement with roll and pitch angle stabilization at position 0 radians with minimum energy function.

Linear-quadratic model underestimates sparing effect of small doses per fraction in rat spinal cord

International Nuclear Information System (INIS)

Shun Wong, C.; Toronto University; Minkin, S.; Hill, R.P.; Toronto University

1993-01-01

The application of the linear-quadratic (LQ) model to describe iso-effective fractionation schedules for dose fraction sizes less than 2 Gy has been controversial. Experiments are described in which the effect of daily fractionated irradiation given with a wide range of fraction sizes was assessed in rat cervical spine cord. The first group of rats was given doses in 1, 2, 4, 8 and 40 fractions/day. The second group received 3 initial 'top-up'doses of 9 Gy given once daily, representing 3/4 tolerance, followed by doses in 1, 2, 10, 20, 30 and 40 fractions/day. The fractionated portion of the irradiation schedule therefore constituted only the final quarter of the tolerance dose. The endpoint of the experiments was paralysis of forelimbs secondary to white matter necrosis. Direct analysis of data from experiments with full course fractionation up to 40 fractions/day (25.0-1.98 Gy/fraction) indicated consistency with the LQ model yielding an α/β value of 2.41 Gy. Analysis of data from experiments in which the 3 'top-up' doses were followed by up to 10 fractions (10.0-1.64 Gy/fraction) gave an α/β value of 3.41 Gy. However, data from 'top-up' experiments with 20, 30 and 40 fractions (1.60-0.55 Gy/fraction) were inconsistent with LQ model and gave a very small α/β of 0.48 Gy. It is concluded that LQ model based on data from large doses/fraction underestimates the sparing effect of small doses/fraction, provided sufficient time is allowed between each fraction for repair of sublethal damage. (author). 28 refs., 5 figs., 1 tab

Spectral analysis of the S{sub N} approximations in a slab with quadratically anisotropic scattering

Energy Technology Data Exchange (ETDEWEB)

Ourique, L.E.; Pazos, R.P. [Pontificia Univ. Catolica do Rio Grande do Sul, Porto Alegre, RS (Brazil)]. E-mail: ourique@pucrs.br; rpp@pucrs.br; Vilhena, M.T. [Rio Grande do Sul Univ., Porto Alegre, RS (Brazil). Escola de Engenharia); vilhena@cesup.ufrgs.br; Barros, R.C. [Universidade do Estado, Nova Friburgo, RJ (Brazil). Instituto Politecnico]. E-mail: dickbarros@uol.com.br

2003-07-01

The spectral analysis of the S{sub N} approximations to the one-dimensional transport equation began with 3 and 4, following the studies of 1 and 2 about the discrete eigenvalues of the transport equation. In previous work about the influence of a parameter in the solutions of S{sub N} approximations, it was considered the total macroscopic cross section as a control parameter and was analyzed how its variation changes the nature of the eigenvalues of the S{sub N} transport matrix, in problems with linearly anisotropic scattering. It was showed the existence of bifurcations points, i.e., there exist some values of control parameters for which the S{sub N} transport matrix has only real eigenvalues while for other values the S{sub N} relation between the eigenvalues of S{sub N} transport matrix and control parameter, supposing quadratically anisotropic scattering. Numerical results are reported. (author)

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.

Data Transmission Over Networks for Estimation and Control

OpenAIRE

Gupta, Vijay; Dana, Amir F.; Hespanha, Joao P.; Murray, Richard M.; Hassibi, Babak

2009-01-01

We consider the problem of controlling a linear time invariant process when the controller is located at a location remote from where the sensor measurements are being generated. The communication from the sensor to the controller is supported by a communication network with arbitrary topology composed of analog erasure channels. Using a separation principle, we prove that the optimal linear-quadratic-Gaussian (LQG) controller consists of an LQ optimal regulator along with an estimator that e...

A comparative study of stabilizing control of a planer electromagnetic levitation using PID and LQR controllers

Directory of Open Access Journals (Sweden)

Mundher H.A. Yaseen

Full Text Available Magnetic levitation is a technique to suspend an object without any mechanical support. The main objective of this study is to demonstrate stabilized closed loop control of 1-DOF Maglev experimentally using real-time control simulink feature of (SIMLAB microcontroller. Proportional Integral Derivative (PID and Linear Quadratic Regulator (LQR controllers are employed to examine the stability performance of the Maglev control system under effect of unbalanced change of load and wave signal on Maglev plane. The effect of unbalanced change of applied load on single point, line and plane are presented. Furthermore, in order to study the effect of sudden change in input signal, the input of wave signal has been applied on all points of the prototype maglev plate simultaneously. The results of pulse width modulation (PWM reveal that the control system using LQR controller provides faster response to adjust the levitated plane comparing to PID controller. Moreover, the air gap distance that controlled using PID controller is rather stable with little oscillation. Meanwhile, LQR controller provided more stability and homogeneous response. Keywords: Magnetic levitation (Maglev, Linear Quadratic Regulator (LQR, PID controller, SIMLAB Platform

A convex optimization approach for solving large scale linear systems

Directory of Open Access Journals (Sweden)

Debora Cores

2017-01-01

Full Text Available The well-known Conjugate Gradient (CG method minimizes a strictly convex quadratic function for solving large-scale linear system of equations when the coefficient matrix is symmetric and positive definite. In this work we present and analyze a non-quadratic convex function for solving any large-scale linear system of equations regardless of the characteristics of the coefficient matrix. For finding the global minimizers, of this new convex function, any low-cost iterative optimization technique could be applied. In particular, we propose to use the low-cost globally convergent Spectral Projected Gradient (SPG method, which allow us to extend this optimization approach for solving consistent square and rectangular linear system, as well as linear feasibility problem, with and without convex constraints and with and without preconditioning strategies. Our numerical results indicate that the new scheme outperforms state-of-the-art iterative techniques for solving linear systems when the symmetric part of the coefficient matrix is indefinite, and also for solving linear feasibility problems.

Robustness analysis of the Zhang neural network for online time-varying quadratic optimization

International Nuclear Information System (INIS)

Zhang Yunong; Ruan Gongqin; Li Kene; Yang Yiwen

2010-01-01

A general type of recurrent neural network (termed as Zhang neural network, ZNN) has recently been proposed by Zhang et al for the online solution of time-varying quadratic-minimization (QM) and quadratic-programming (QP) problems. Global exponential convergence of the ZNN could be achieved theoretically in an ideal error-free situation. In this paper, with the normal differentiation and dynamics-implementation errors considered, the robustness properties of the ZNN model are investigated for solving these time-varying problems. In addition, linear activation functions and power-sigmoid activation functions could be applied to such a perturbed ZNN model. Both theoretical-analysis and computer-simulation results demonstrate the good ZNN robustness and superior performance for online time-varying QM and QP problem solving, especially when using power-sigmoid activation functions.

Quadratic algebras and noncommutative integration of Klein-Gordon equations in non-steckel Riemann spaces

International Nuclear Information System (INIS)

Varaksin, O.L.; Firstov, V.V.; Shapovalov, A.V.; Shirokov, I.V.

1995-01-01

The method of noncommutative integration of linear partial differential equations is used to solve the Klein-Gordon equations in Riemann space, in the case when the set of noncommutating symmetry operators of this equation for a quadratic algebra consists of one second-order operator and several first-order operators. Solutions that do not permit variable separation are presented

Estimation of stature from sternum - Exploring the quadratic models.

Science.gov (United States)

Saraf, Ashish; Kanchan, Tanuj; Krishan, Kewal; Ateriya, Navneet; Setia, Puneet

2018-04-14

Identification of the dead is significant in examination of unknown, decomposed and mutilated human remains. Establishing the biological profile is the central issue in such a scenario, and stature estimation remains one of the important criteria in this regard. The present study was undertaken to estimate stature from different parts of the sternum. A sample of 100 sterna was obtained from individuals during the medicolegal autopsies. Length of the deceased and various measurements of the sternum were measured. Student's t-test was performed to find the sex differences in stature and sternal measurements included in the study. Correlation between stature and sternal measurements were analysed using Karl Pearson's correlation, and linear and quadratic regression models were derived. All the measurements were found to be significantly larger in males than females. Stature correlated best with the combined length of sternum, among males (R = 0.894), females (R = 0.859), and for the total sample (R = 0.891). The study showed that the models derived for stature estimation from combined length of sternum are likely to give the most accurate estimates of stature in forensic case work when compared to manubrium and mesosternum. Accuracy of stature estimation further increased with quadratic models derived for the mesosternum among males and combined length of sternum among males and females when compared to linear regression models. Future studies in different geographical locations and a larger sample size are proposed to confirm the study observations. Copyright © 2018 Elsevier Ltd and Faculty of Forensic and Legal Medicine. All rights reserved.

Quadratic Boost A-Source Impedance Network

DEFF Research Database (Denmark)

Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii

2016-01-01

A novel quadratic boost A-source impedance network is proposed to realize converters that demand very high voltage gain. To satisfy the requirement, the network uses an autotransformer where the obtained gain is quadratically dependent on the duty ratio and is unmatched by any existing impedance...

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

Science.gov (United States)

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.

LQG Control of Networked Control Systems with Limited Information

Directory of Open Access Journals (Sweden)

Qing-Quan Liu

2014-01-01

Full Text Available This paper addresses linear quadratic Gaussian (LQG control problems for multi-input multioutput (MIMO, linear time-invariant (LTI systems, where the sensors and controllers are geographically separated and connected via a digital communication channel with limited data rates. An observer-based, quantized state feedback control scheme is employed in order to achieve the minimum data rate for mean square stabilization of the unstable plant. An explicit expression is presented to state the tradeoff between the LQ cost and the data rate. Sufficient conditions on the data rate for mean square stabilization are derived. An illustrative example is given to demonstrate the effectiveness of the proposed scheme.

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

Directory of Open Access Journals (Sweden)

Olav Slupphaug

1999-07-01

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

Neural Networks for Non-linear Control

DEFF Research Database (Denmark)

Sørensen, O.

1994-01-01

This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process.......This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process....

Direct Optimal Control of Duffing Dynamics

Science.gov (United States)

Oz, Hayrani; Ramsey, John K.

2002-01-01

The "direct control method" is a novel concept that is an attractive alternative and competitor to the differential-equation-based methods. The direct method is equally well applicable to nonlinear, linear, time-varying, and time-invariant systems. For all such systems, the method yields explicit closed-form control laws based on minimization of a quadratic control performance measure. We present an application of the direct method to the dynamics and optimal control of the Duffing system where the control performance measure is not restricted to a quadratic form and hence may include a quartic energy term. The results we present in this report also constitute further generalizations of our earlier work in "direct optimal control methodology." The approach is demonstrated for the optimal control of the Duffing equation with a softening nonlinear stiffness.

Quadratic Diophantine equations

CERN Document Server

Andreescu, Titu

2015-01-01

This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.

A Wavelet Bicoherence-Based Quadratic Nonlinearity Feature for Translational Axis Condition Monitoring

Directory of Open Access Journals (Sweden)

Yong Li

2014-01-01

Full Text Available The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features.

Linearizing control of continuous anaerobic fermentation processes

Energy Technology Data Exchange (ETDEWEB)

Babary, J.P. [Centre National d`Etudes Spatiales (CNES), 31 - Toulouse (France). Laboratoire d`Analyse et d`Architecture des Systemes; Simeonov, I. [Institute of Microbiology, Bulgarian Academy of Sciences (Bulgaria); Ljubenova, V. [Institute of Control and System Research, BAS (Country unknown/Code not available); Dochain, D. [Universite Catholique de Louvain (UCL), Louvain-la-Neuve (Belgium)

1997-09-01

Biotechnological processes (BTP) involve living organisms. In the anaerobic fermentation (biogas production process) the organic matter is mineralized by microorganisms into biogas (methane and carbon dioxide) in the absence of oxygen. The biogas is an additional energy source. Generally this process is carried out as a continuous BTP. It has been widely used in life process and has been confirmed as a promising method of solving some energy and ecological problems in the agriculture and industry. Because of the very restrictive on-line information the control of this process in continuous mode is often reduced to control of the biogas production rate or the concentration of the polluting organic matter (de-pollution control) at a desired value in the presence of some perturbations. Investigations show that classical linear controllers have good performances only in the linear zone of the strongly non-linear input-output characteristics. More sophisticated robust and with variable structure (VSC) controllers are studied. Due to the strongly non-linear dynamics of the process the performances of the closed loop system may be degrading in this case. The aim of this paper is to investigate different linearizing algorithms for control of a continuous non-linear methane fermentation process using the dilution rate as a control action and taking into account some practical implementation aspects. (authors) 8 refs.

Rational quadratic trigonometric Bézier curve based on new basis with exponential functions

Directory of Open Access Journals (Sweden)

Wu Beibei

2017-06-01

Full Text Available We construct a rational quadratic trigonometric Bézier curve with four shape parameters by introducing two exponential functions into the trigonometric basis functions in this paper. It has the similar properties as the rational quadratic Bézier curve. For given control points, the shape of the curve can be flexibly adjusted by changing the shape parameters and the weight. Some conics can be exactly represented when the control points, the shape parameters and the weight are chosen appropriately. The C0, C1 and C2 continuous conditions for joining two constructed curves are discussed. Some examples are given.

Input/Output linearizing control of a nuclear reactor

International Nuclear Information System (INIS)

Perez C, V.

1994-01-01

The feedback linearization technique is an approach to nonlinear control design. The basic idea is to transform, by means of algebraic methods, the dynamics of a nonlinear control system into a full or partial linear system. As a result of this linearization process, the well known basic linear control techniques can be used to obtain some desired dynamic characteristics. When full linearization is achieved, the method is referred to as input-state linearization, whereas when partial linearization is achieved, the method is referred to as input-output linearization. We will deal with the latter. By means of input-output linearization, the dynamics of a nonlinear system can be decomposed into an external part (input-output), and an internal part (unobservable). Since the external part consists of a linear relationship among the output of the plant and the auxiliary control input mentioned above, it is easy to design such an auxiliary control input so that we get the output to behave in a predetermined way. Since the internal dynamics of the system is known, we can check its dynamics behavior on order of to ensure that the internal states are bounded. The linearization method described here can be applied to systems with one-input/one-output, as well as to systems with multiple-inputs/multiple-outputs. Typical control problems such as stabilization and reference path tracking can be solved using this technique. In this work, the input/output linearization theory is presented, as well as the problem of getting the output variable to track some desired trayectories. Further, the design of an input/output control system applied to the nonlinear model of a research nuclear reactor is included, along with the results obtained by computer simulation. (Author)

Excited-state absorption in tetrapyridyl porphyrins: comparing real-time and quadratic-response time-dependent density functional theory

Energy Technology Data Exchange (ETDEWEB)

Bowman, David N. [Department of Chemistry; Supercomputing Institute and Chemical Theory Center; University of Minnesota; Minneapolis; USA; Asher, Jason C. [Department of Chemistry; Supercomputing Institute and Chemical Theory Center; University of Minnesota; Minneapolis; USA; Fischer, Sean A. [William R. Wiley Environmental Molecular Sciences Laboratory; Pacific Northwest National Laboratory; P.O. Box 999; Richland; USA; Cramer, Christopher J. [Department of Chemistry; Supercomputing Institute and Chemical Theory Center; University of Minnesota; Minneapolis; USA; Govind, Niranjan [William R. Wiley Environmental Molecular Sciences Laboratory; Pacific Northwest National Laboratory; P.O. Box 999; Richland; USA

2017-01-01

Threemeso-substituted tetrapyridyl porphyrins (free base, Ni(ii), and Cu(ii)) were investigated for their optical limiting (OL) capabilities using real-time (RT-), linear-response (LR-), and quadratic-response (QR-) time-dependent density functional theory (TDDFT) methods.

Non normal and non quadratic anisotropic plasticity coupled with ductile damage in sheet metal forming: Application to the hydro bulging test

International Nuclear Information System (INIS)

Badreddine, Houssem; Saanouni, Khemaies; Dogui, Abdelwaheb

2007-01-01

In this work an improved material model is proposed that shows good agreement with experimental data for both hardening curves and plastic strain ratios in uniaxial and equibiaxial proportional loading paths for steel metal until the final fracture. This model is based on non associative and non normal flow rule using two different orthotropic equivalent stresses in both yield criterion and plastic potential functions. For the plastic potential the classical Hill 1948 quadratic equivalent stress is considered while for the yield criterion the Karafillis and Boyce 1993 non quadratic equivalent stress is used taking into account the non linear mixed (kinematic and isotropic) hardening. Applications are made to hydro bulging tests using both circular and elliptical dies. The results obtained with different particular cases of the model such as the normal quadratic and the non normal non quadratic cases are compared and discussed with respect to the experimental results

Introduction to generalized linear models

CERN Document Server

Dobson, Annette J

2008-01-01

Introduction Background Scope Notation Distributions Related to the Normal Distribution Quadratic Forms Estimation Model Fitting Introduction Examples Some Principles of Statistical Modeling Notation and Coding for Explanatory Variables Exponential Family and Generalized Linear Models Introduction Exponential Family of Distributions Properties of Distributions in the Exponential Family Generalized Linear Models Examples Estimation Introduction Example: Failure Times for Pressure Vessels Maximum Likelihood Estimation Poisson Regression Example Inference Introduction Sampling Distribution for Score Statistics Taylor Series Approximations Sampling Distribution for MLEs Log-Likelihood Ratio Statistic Sampling Distribution for the Deviance Hypothesis Testing Normal Linear Models Introduction Basic Results Multiple Linear Regression Analysis of Variance Analysis of Covariance General Linear Models Binary Variables and Logistic Regression Probability Distributions ...

Attitude and Configuration Control of Flexible Multi-Body Spacecraft

Science.gov (United States)

Cho, Sung-Ki; Cochran, John E., Jr.

2002-06-01

Multi-body spacecraft attitude and configuration control formulations based on the use of collaborative control theory are considered. The control formulations are based on two-player, nonzero-sum, differential game theory applied using a Nash strategy. It is desired that the control laws allow different components of the multi-body system to perform different tasks. For example, it may be desired that one body points toward a fixed star while another body in the system slews to track another satellite. Although similar to the linear quadratic regulator formulation, the collaborative control formulation contains a number of additional design parameters because the problem is formulated as two control problems coupled together. The use of the freedom of the partitioning of the total problem into two coupled control problems and the selection of the elements of the cross-coupling matrices are specific problems addressed in this paper. Examples are used to show that significant improvement in performance, as measured by realistic criteria, of collaborative control over conventional linear quadratic regulator control can be achieved by using proposed design guidelines.

Attitude and Configuration Control of Flexible Multi-Body Spacecraft

Directory of Open Access Journals (Sweden)

Sungki Cho

2002-06-01

Full Text Available Multi-body spacecraft attitude and configuration control formulations based on the use of collaborative control theory are considered. The control formulations are based on two-player, nonzero-sum, differential game theory applied using a Nash strategy. It is desired that the control laws allow different components of the multi-body system to perform different tasks. For example, it may be desired that one body points toward a fixed star while another body in the system slews to track another satellite. Although similar to the linear quadratic regulator formulation, the collaborative control formulation contains a number of additional design parameters because the problem is formulated as two control problems coupled together. The use of the freedom of the partitioning of the total problem into two coupled control problems and the selection of the elements of the cross-coupling matrices are specific problems addressed in this paper. Examples are used to show that significant improvement in performance, as measured by realistic criteria, of collaborative control over conventional linear quadratic regulator control can be achieved by using proposed design guidelines.

Feedback linearizing control of a MIMO power system

Science.gov (United States)

Ilyes, Laszlo

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

Linear time relational prototype based learning.

Science.gov (United States)

Gisbrecht, Andrej; Mokbel, Bassam; Schleif, Frank-Michael; Zhu, Xibin; Hammer, Barbara

2012-10-01

Prototype based learning offers an intuitive interface to inspect large quantities of electronic data in supervised or unsupervised settings. Recently, many techniques have been extended to data described by general dissimilarities rather than Euclidean vectors, so-called relational data settings. Unlike the Euclidean counterparts, the techniques have quadratic time complexity due to the underlying quadratic dissimilarity matrix. Thus, they are infeasible already for medium sized data sets. The contribution of this article is twofold: On the one hand we propose a novel supervised prototype based classification technique for dissimilarity data based on popular learning vector quantization (LVQ), on the other hand we transfer a linear time approximation technique, the Nyström approximation, to this algorithm and an unsupervised counterpart, the relational generative topographic mapping (GTM). This way, linear time and space methods result. We evaluate the techniques on three examples from the biomedical domain.

Time-optimal feedback control for linear systems

International Nuclear Information System (INIS)

Mirica, S.

1976-01-01

The paper deals with the results of qualitative investigations of the time-optimal feedback control for linear systems with constant coefficients. In the first section, after some definitions and notations, two examples are given and it is shown that even the time-optimal control problem for linear systems with constant coefficients which looked like ''completely solved'' requires a further qualitative investigation of the stability to ''permanent perturbations'' of optimal feedback control. In the second section some basic results of the linear time-optimal control problem are reviewed. The third section deals with the definition of Boltyanskii's ''regular synthesis'' and its connection to Filippov's theory of right-hand side discontinuous differential equations. In the fourth section a theorem is proved concerning the stability to perturbations of time-optimal feedback control for linear systems with scalar control. In the last two sections it is proved that, if the matrix which defines the system has only real eigenvalues or is three-dimensional, the time-optimal feedback control defines a regular synthesis and therefore is stable to perturbations. (author)

Optimal adaptive control for a class of stochastic systems

NARCIS (Netherlands)

Bagchi, Arunabha; Chen, Han-Fu

1995-01-01

We study linear-quadratic adaptive tracking problems for a special class of stochastic systems expressed in the state-space form. This is a long-standing problem in the control of aircraft flying through atmospheric turbulence. Using an ELS-based algorithm and introducing dither in the control law

Quadratic programming with fuzzy parameters: A membership function approach

International Nuclear Information System (INIS)

Liu, S.-T.

2009-01-01

Quadratic programming has been widely applied to solving real world problems. The conventional quadratic programming model requires the parameters to be known constants. In the real world, however, the parameters are seldom known exactly and have to be estimated. This paper discusses the fuzzy quadratic programming problems where the cost coefficients, constraint coefficients, and right-hand sides are represented by convex fuzzy numbers. Since the parameters in the program are fuzzy numbers, the derived objective value is a fuzzy number as well. Using Zadeh's extension principle, a pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. An example illustrates method proposed in this paper.

Modelling and control of a flotation process

International Nuclear Information System (INIS)

Ding, L.; Gustafsson, T.

1999-01-01

A general description of a flotation process is given. The dynamic model of a MIMO nonlinear subprocess in flotation, i. e. the pulp levels in five compartments in series is developed and the model is verified with real data from a production plant. In order to reject constant disturbances five extra states are introduced and the model is modified. An exact linearization has been made for the non-linear model and a linear quadratic gaussian controller is proposed based on the linearized model. The simulation result shows an improved performance of the pulp level control when the set points are changed or a disturbance occur. In future the controller will be tested in production. (author)

Control and Optimization of Network in Networked Control System

Directory of Open Access Journals (Sweden)

Wang Zhiwen

2014-01-01

Full Text Available In order to avoid quality of performance (QoP degradation resulting from quality of service (QoS, the solution to network congestion from the point of control theory, which marks departure of our results from the existing methods, is proposed in this paper. The congestion and bandwidth are regarded as state and control variables, respectively; then, the linear time-invariant (LTI model between congestion state and bandwidth of network is established. Consequently, linear quadratic method is used to eliminate the network congestion by allocating bandwidth dynamically. At last, numerical simulation results are given to illustrate the effectiveness of this modeling approach.

Solution of the Chew-Low equations in the quadratic approximation

International Nuclear Information System (INIS)

Gerdt, V.P.; Zharkov, A.Yu.

1982-01-01

Within the framework of the iteration scheme for constructing the general solution of the Chew-Low equations as suggested earlier the second order power contributions are found. In contrast to the linear approximation obtained before the quadratic approximation includes an infinite number of poles on the complex plane of the uniformizing variable w. It is shown that taking into account the second order corrections in the general solution allows us to select the class of solutions possessing the Born pole at w=0. The most cumbersome part of analytical computations has been carried out by computer using the algebraic system REDUCE-2

A non-self-adjoint quadratic eigenvalue problem describing a fluid-solid interaction Part II : analysis of convergence

NARCIS (Netherlands)

Bourne, D.P.; Elman, H.; Osborn, J.E.

2009-01-01

This paper is the second part of a two-part paper treating a non-self-adjoint quadratic eigenvalue problem for the linear stability of solutions to the Taylor-Couette problem for flow of a viscous liquid in a deformable cylinder, with the cylinder modelled as a membrane. The first part formulated

Stability in quadratic torsion theories

Energy Technology Data Exchange (ETDEWEB)

Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)

2017-11-15

We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)

Stability in quadratic torsion theories

International Nuclear Information System (INIS)

Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado

2017-01-01

We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)

A high-performance Riccati based solver for tree-structured quadratic programs

DEFF Research Database (Denmark)

Frison, Gianluca; Kouzoupis, Dimitris; Diehl, Moritz

2017-01-01

the online solution of such problems challenging and the development of tailored solvers crucial. In this paper, an interior point method is presented that can solve Quadratic Programs (QPs) arising in multi-stage MPC efficiently by means of a tree-structured Riccati recursion and a high-performance linear...... algebra library. A performance comparison with code-generated and general purpose sparse QP solvers shows that the computation times can be significantly reduced for all problem sizes that are practically relevant in embedded MPC applications. The presented implementation is freely available as part...

Controlling attribute effect in linear regression

KAUST Repository

Calders, Toon; Karim, Asim A.; Kamiran, Faisal; Ali, Wasif Mohammad; Zhang, Xiangliang

2013-01-01

In data mining we often have to learn from biased data, because, for instance, data comes from different batches or there was a gender or racial bias in the collection of social data. In some applications it may be necessary to explicitly control this bias in the models we learn from the data. This paper is the first to study learning linear regression models under constraints that control the biasing effect of a given attribute such as gender or batch number. We show how propensity modeling can be used for factoring out the part of the bias that can be justified by externally provided explanatory attributes. Then we analytically derive linear models that minimize squared error while controlling the bias by imposing constraints on the mean outcome or residuals of the models. Experiments with discrimination-aware crime prediction and batch effect normalization tasks show that the proposed techniques are successful in controlling attribute effects in linear regression models. © 2013 IEEE.

Controlling attribute effect in linear regression

KAUST Repository

Calders, Toon

2013-12-01

In data mining we often have to learn from biased data, because, for instance, data comes from different batches or there was a gender or racial bias in the collection of social data. In some applications it may be necessary to explicitly control this bias in the models we learn from the data. This paper is the first to study learning linear regression models under constraints that control the biasing effect of a given attribute such as gender or batch number. We show how propensity modeling can be used for factoring out the part of the bias that can be justified by externally provided explanatory attributes. Then we analytically derive linear models that minimize squared error while controlling the bias by imposing constraints on the mean outcome or residuals of the models. Experiments with discrimination-aware crime prediction and batch effect normalization tasks show that the proposed techniques are successful in controlling attribute effects in linear regression models. © 2013 IEEE.

Biological equivalence between LDR and PDR in cervical cancer: multifactor analysis using the linear-quadratic model

Directory of Open Access Journals (Sweden)

José Guilherme Couto

2011-09-01

Full Text Available Purpose: The purpose of this work was the biological comparison between Low Dose Rate (LDR and Pulsed DoseRate (PDR in cervical cancer regarding the discontinuation of the afterloading system used for the LDR treatments atour Institution since December 2009. Material and methods: In the first phase we studied the influence of the pulse dose and the pulse time in the biologicalequivalence between LDR and PDR treatments using the Linear Quadratic Model (LQM. In the second phase,the equivalent dose in 2 Gy/fraction (EQD2 for the tumor, rectum and bladder in treatments performed with both techniqueswas evaluated and statistically compared. All evaluated patients had stage IIB cervical cancer and were treatedwith External Beam Radiotherapy (EBRT plus two Brachytherapy (BT applications. Data were collected from 48 patients(26 patients treated with LDR and 22 patients with PDR. Results: In the analyses of the influence of PDR parameters in the biological equivalence between LDR and PDRtreatments (Phase 1, it was calculated that if the pulse dose in PDR was kept equal to the LDR dose rate, a small therapeuticloss was expected. If the pulse dose was decreased, the therapeutic window became larger, but a correction inthe prescribed dose was necessary. In PDR schemes with 1 hour interval between pulses, the pulse time did not influencesignificantly the equivalent dose. In the comparison between the groups treated with LDR and PDR (Phase 2 weconcluded that they were not equivalent, because in the PDR group the total EQD2 for the tumor, rectum and bladderwas smaller than in the LDR group; the LQM estimated that a correction in the prescribed dose of 6% to 10% was ne -cessary to avoid therapeutic loss. Conclusions: A correction in the prescribed dose was necessary; this correction should be achieved by calculatingthe PDR dose equivalent to the desired LDR total dose.

Biological equivalence between LDR and PDR in cervical cancer: multifactor analysis using the linear-quadratic model.

Science.gov (United States)

Couto, José Guilherme; Bravo, Isabel; Pirraco, Rui

2011-09-01

The purpose of this work was the biological comparison between Low Dose Rate (LDR) and Pulsed Dose Rate (PDR) in cervical cancer regarding the discontinuation of the afterloading system used for the LDR treatments at our Institution since December 2009. In the first phase we studied the influence of the pulse dose and the pulse time in the biological equivalence between LDR and PDR treatments using the Linear Quadratic Model (LQM). In the second phase, the equivalent dose in 2 Gy/fraction (EQD(2)) for the tumor, rectum and bladder in treatments performed with both techniques was evaluated and statistically compared. All evaluated patients had stage IIB cervical cancer and were treated with External Beam Radiotherapy (EBRT) plus two Brachytherapy (BT) applications. Data were collected from 48 patients (26 patients treated with LDR and 22 patients with PDR). In the analyses of the influence of PDR parameters in the biological equivalence between LDR and PDR treatments (Phase 1), it was calculated that if the pulse dose in PDR was kept equal to the LDR dose rate, a small the-rapeutic loss was expected. If the pulse dose was decreased, the therapeutic window became larger, but a correction in the prescribed dose was necessary. In PDR schemes with 1 hour interval between pulses, the pulse time did not influence significantly the equivalent dose. In the comparison between the groups treated with LDR and PDR (Phase 2) we concluded that they were not equivalent, because in the PDR group the total EQD(2) for the tumor, rectum and bladder was smaller than in the LDR group; the LQM estimated that a correction in the prescribed dose of 6% to 10% was ne-cessary to avoid therapeutic loss. A correction in the prescribed dose was necessary; this correction should be achieved by calculating the PDR dose equivalent to the desired LDR total dose.

Investigation of various growth mechanisms of solid tumour growth within the linear-quadratic model for radiotherapy

International Nuclear Information System (INIS)

McAneney, H; O'Rourke, S F C

2007-01-01

The standard linear-quadratic survival model for radiotherapy is used to investigate different schedules of radiation treatment planning to study how these may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al (1977 Br. J. Radiol. 50 681), which was concerned with the case of exponential re-growth between treatments. Here we also consider the restricted exponential model. This has been successfully used by Panetta and Adam (1995 Math. Comput. Modelling 22 67) in the case of chemotherapy treatment planning.Treatment schedules investigated include standard fractionation of daily treatments, weekday treatments, accelerated fractionation, optimized uniform schedules and variation of the dosage and α/β ratio, where α and β are radiobiological parameters for the tumour tissue concerned. Parameters for these treatment strategies are extracted from the literature on advanced head and neck cancer, prostate cancer, as well as radiosensitive parameters. Standardized treatment protocols are also considered. Calculations based on the present analysis indicate that even with growth laws scaled to mimic initial growth, such that growth mechanisms are comparable, variation in survival fraction to orders of magnitude emerged. Calculations show that the logistic and exponential models yield similar results in tumour eradication. By comparison the Gompertz model calculations indicate that tumours described by this law result in a significantly poorer prognosis for tumour eradication than either the exponential or logistic models. The present study also shows that the faster the tumour growth rate and the higher the repair capacity of the cell line, the greater the variation in outcome of the survival fraction. Gaps in treatment, planned or unplanned, also accentuate the differences of the survival fraction given alternative growth

Optical-response properties in hybrid optomechanical systems with quadratic coupling

Science.gov (United States)

Sun, Xue-Jian; Wang, Xin; Liu, Li-Na; Liu, Wen-Xiao; Fang, Ai-Ping; Li, Hong-Rong

2018-02-01

We theoretically investigate the optical-response properties of the four-mode quadratically coupled optomechanical system (OMS), in which two standard OMSs with quadratic coupling are coupled to each other via a common waveguide. In the presence of a strong control field applied to one cavity and a weak probe field applied to the other, we show that by suitably tuning the system parameters, there appears the normal mode splitting, optomechanically induced absorption, and double or triple electromagnetically induced transparency phenomena in the probe absorption spectrum. In particular, the explicit physical explanations for those fantastic phenomena are detailed discussed. Moreover, we also show that our proposal can be exploited to implement the optical switch as well as the slow and fast light effects.

Robust control technique for nuclear power plants

International Nuclear Information System (INIS)

Murphy, G.V.; Bailey, J.M.

1989-03-01

This report summarizes the linear quadratic Guassian (LQG) design technique with loop transfer recovery (LQG/LTR) for design of control systems. The concepts of return ratio, return difference, inverse return difference, and singular values are summarized. The LQG/LTR design technique allows the synthesis of a robust control system. To illustrate the LQG/LTR technique, a linearized model of a simple process has been chosen. The process has three state variables, one input, and one output. Three control system design methods are compared: LQG, LQG/LTR, and a proportional plus integral controller (PI). 7 refs., 20 figs., 6 tabs

Power control method for load-frequency control operation in BWRs

International Nuclear Information System (INIS)

Ie, Shin-ichiroo; Ohgo, Yu-kiharu; Itou, Tetsuo; Shida, Tooichi

1991-01-01

The preliminary design of an advanced power control method for fast load-following [load frequency control (LFC)] maneuvers in a boiling water reactor (BWR) is described in this paper. Application of a multivariable control method using an optimal linear quadratic (LQ) regulator theory effectively improves control system performance when system variables have significant interactions such as in BWRs. The control problem, however, demands strict constraints on system variable from the standpoint of plant operation. These constraints require the control system to have a nonlinear property for better improvement. Therefore, the effectiveness of LQ control is limited by these constraints, because it is based on a linear model. A new method is needed to compensate for the nonlinear property. In this study, the authors propose a new method using fuzzy reasoning with LQ control to achieve nonlinear compensation

Quadratic head loss approximations for optimisation problems in water supply networks

NARCIS (Netherlands)

Pecci, Filippo; Abraham, E.; I, Stoianov

2017-01-01

This paper presents a novel analysis of the accuracy of quadratic approximations for the Hazen–Williams (HW) head loss formula, which enables the control of constraint violations in optimisation problems for water supply networks. The two smooth polynomial approximations considered here minimise the

Mean-Variance Portfolio Selection Problem with Stochastic Salary for a Defined Contribution Pension Scheme: A Stochastic Linear-Quadratic-Exponential Framework

Directory of Open Access Journals (Sweden)

Charles Nkeki

2013-11-01

Full Text Available This paper examines a mean-variance portfolio selection problem with stochastic salary and inflation protection strategy in the accumulation phase of a defined contribution (DC pension plan. The utility function is assumed to be quadratic. It was assumed that the flow of contributions made by the PPM are invested into a market that is characterized by a cash account, an inflation-linked bond and a stock. In this paper, inflationlinked bond is traded and used to hedge inflation risks associated with the investment. The aim of this paper is to maximize the expected final wealth and minimize its variance. Efficient frontier for the three classes of assets (under quadratic utility function that will enable pension plan members (PPMs to decide their own wealth and risk in their investment profile at retirement was obtained.

Exact cancellation of quadratic divergences in top condensation models

International Nuclear Information System (INIS)

Blumhofer, A.

1995-01-01

We discuss the hierarchy problem and the corresponding quadratic divergences in the top mode Standard Model. Quadratic divergences appear at each order 1/N c since fermionic and bosonic contributions are of different order 1/N c . It is shown that the full dynamical system to all orders in 1/N c admits a solution, where the sum of all quadratic divergent contributions disappears. ((orig.))

Sibling curves of quadratic polynomials | Wiggins | Quaestiones ...

African Journals Online (AJOL)

Sibling curves were demonstrated in [1, 2] as a novel way to visualize the zeroes of real valued functions. In [3] it was shown that a polynomial of degree n has n sibling curves. This paper focuses on the algebraic and geometric properites of the sibling curves of real and complex quadratic polynomials. Key words: Quadratic ...

Emotion suppression moderates the quadratic association between RSA and executive function.

Science.gov (United States)

Spangler, Derek P; Bell, Martha Ann; Deater-Deckard, Kirby

2015-09-01

There is uncertainty about whether respiratory sinus arrhythmia (RSA), a cardiac marker of adaptive emotion regulation, is involved in relatively low or high executive function performance. In the present study, we investigated (a) whether RSA during rest and tasks predict both relatively low and high executive function within a larger quadratic association among the two variables, and (b) the extent to which this quadratic trend was moderated by individual differences in emotion regulation. To achieve these aims, a sample of ethnically and socioeconomically diverse women self-reported reappraisal and emotion suppression. They next experienced a 2-min resting period during which electrocardiogram (ECG) was continually assessed. In the next phase, the women completed an array of executive function and nonexecutive cognitive tasks while ECG was measured throughout. As anticipated, resting RSA showed a quadratic association with executive function that was strongest for high suppression. These results suggest that relatively high resting RSA may predict poor executive function ability when emotion regulation consumes executive control resources needed for ongoing cognitive performance. © 2015 Society for Psychophysiological Research.

Linear collider: a preview

Energy Technology Data Exchange (ETDEWEB)

Wiedemann, H.

1981-11-01

Since no linear colliders have been built yet it is difficult to know at what energy the linear cost scaling of linear colliders drops below the quadratic scaling of storage rings. There is, however, no doubt that a linear collider facility for a center of mass energy above say 500 GeV is significantly cheaper than an equivalent storage ring. In order to make the linear collider principle feasible at very high energies a number of problems have to be solved. There are two kinds of problems: one which is related to the feasibility of the principle and the other kind of problems is associated with minimizing the cost of constructing and operating such a facility. This lecture series describes the problems and possible solutions. Since the real test of a principle requires the construction of a prototype I will in the last chapter describe the SLC project at the Stanford Linear Accelerator Center.

Linear collider: a preview

International Nuclear Information System (INIS)

Wiedemann, H.

1981-11-01

Since no linear colliders have been built yet it is difficult to know at what energy the linear cost scaling of linear colliders drops below the quadratic scaling of storage rings. There is, however, no doubt that a linear collider facility for a center of mass energy above say 500 GeV is significantly cheaper than an equivalent storage ring. In order to make the linear collider principle feasible at very high energies a number of problems have to be solved. There are two kinds of problems: one which is related to the feasibility of the principle and the other kind of problems is associated with minimizing the cost of constructing and operating such a facility. This lecture series describes the problems and possible solutions. Since the real test of a principle requires the construction of a prototype I will in the last chapter describe the SLC project at the Stanford Linear Accelerator Center

Temperature uniformity control in RTP using multivariable adaptive control

Energy Technology Data Exchange (ETDEWEB)

Morales, S.; Dahhou, B.; Dilhac, J.M. [Centre National de la Recherche Scientifique (CNRS), 31 - Toulouse (France); Morales, S.

1995-12-31

In Rapid Thermal Processing (RTP) control of the wafer temperature during all processing to get good trajectory following, together with spatial temperature uniformity, is essential. It is well know as RTP process is nonlinear, classical control laws are not very efficient. In this work, the authors aim at studying the applicability of MIMO (Multiple Inputs Multiple Outputs) adaptive techniques to solve the temperature control problems in RTP. A multivariable linear discrete time CARIMA (Controlled Auto Regressive Integrating Moving Average) model of the highly non-linear process is identified on-line using a robust identification technique. The identified model is used to compute an infinite time LQ (Linear Quadratic) based control law, with a partial state reference model. This reference model smooths the original setpoint sequence, and at the same time gives a tracking capability to the LQ control law. After an experimental open-loop investigation, the results of the application of the adaptive control law are presented. Finally, some comments on the future difficulties and developments of the application of adaptive control in RTP are given. (author) 13 refs.

Agreement of quadratic and CRE models in predicting the late effects of continuous low dose-rate radiotherapy; and reply

International Nuclear Information System (INIS)

O'Donoghue, J.A.

1986-01-01

These letters discuss the problems associated with the fact that the normal tissue isoeffect formulae based on the Ellis equation (1969) do not correctly account for the late-occurring effects of fractionated radiotherapy, and with the extension of the linear quadratic model to include continuous low dose-rate radiotherapy with constant or decaying sources by R.G. Dale (1985). J.A. O'Donoghue points out that the 'late effects' and CRE curves correspond closely, whilst the 'acute effects; and CRE curves are in obvious disagreement. For continuous low-dose-rate radiotherapy, the CRE and late effects quadratic model are in agreement. Useful bibliography. (U.K.)

Non-cooperative stochastic differential game theory of generalized Markov jump linear systems

CERN Document Server

Zhang, Cheng-ke; Zhou, Hai-ying; Bin, Ning

2017-01-01

This book systematically studies the stochastic non-cooperative differential game theory of generalized linear Markov jump systems and its application in the field of finance and insurance. The book is an in-depth research book of the continuous time and discrete time linear quadratic stochastic differential game, in order to establish a relatively complete framework of dynamic non-cooperative differential game theory. It uses the method of dynamic programming principle and Riccati equation, and derives it into all kinds of existence conditions and calculating method of the equilibrium strategies of dynamic non-cooperative differential game. Based on the game theory method, this book studies the corresponding robust control problem, especially the existence condition and design method of the optimal robust control strategy. The book discusses the theoretical results and its applications in the risk control, option pricing, and the optimal investment problem in the field of finance and insurance, enriching the...

Linear representation of algebras with non-associative operations which are satisfy in the balanced functional equations

International Nuclear Information System (INIS)

Ehsani, Amir

2015-01-01

Algebras with a pair of non-associative binary operations (f, g) which are satisfy in the balanced quadratic functional equations with four object variables considered. First, we obtain a linear representation for the operations, of this kind of binary algebras (A,f,g), over an abelian group (A, +) and then we generalize the linear representation of operations, to an algebra (A,F) with non-associative binary operations which are satisfy in the balanced quadratic functional equations with four object variables. (paper)

Joint shape segmentation with linear programming

KAUST Repository

Huang, Qixing

2011-01-01

We present an approach to segmenting shapes in a heterogenous shape database. Our approach segments the shapes jointly, utilizing features from multiple shapes to improve the segmentation of each. The approach is entirely unsupervised and is based on an integer quadratic programming formulation of the joint segmentation problem. The program optimizes over possible segmentations of individual shapes as well as over possible correspondences between segments from multiple shapes. The integer quadratic program is solved via a linear programming relaxation, using a block coordinate descent procedure that makes the optimization feasible for large databases. We evaluate the presented approach on the Princeton segmentation benchmark and show that joint shape segmentation significantly outperforms single-shape segmentation techniques. © 2011 ACM.

Design of model based LQG control for integrated building systems

NARCIS (Netherlands)

Yahiaoui, A.; Hensen, J.L.M.; Soethout, L.L.; Paassen, van A.H.C.

2006-01-01

The automation of the operation of integrated building systems requires using modern control techniques to enhance the quality of the building indoor environments. This paper describes the theatrical base and practical application of an optimal dynamic regulator using modelbased Linear Quadratic

Experimental determination of the anisotropy function for the Model 200 103Pd 'light seed' and derivation of the anisotropy constant based upon the linear quadratic model

International Nuclear Information System (INIS)

Yue Ning; Nath, Ravinder

2002-01-01

Since the publication of the AAPM Task Group 43 report in 1995, Model 200 103 Pd seed, which has been widely used in prostate seed implants and other brachytherapy procedures, has undergone some changes in its internal geometry resulting from the manufacturer's transition from lower specific activity reactor-produced 103 Pd ('heavy seeds') to higher specific activity accelerator-produced radioactive material ('light seeds'). Based on previously reported theoretical calculations and measurements, the dose rate constants and the radial dose functions of the two types of seeds are nearly the same and have already been reported. In this work, the anisotropy function of the 'light seed' was experimentally measured and an averaging method for the determination of the anisotropy constant from distance-dependent values of anisotropy factors is presented based upon the continuous low dose rate irradiation linear quadratic model for cell killing. The anisotropy function of Model 200 103 Pd 'light seeds' was measured in a Solid Water trade mark sign phantom using 1x1x1 mm micro LiF TLD chips at radial distances of 1, 2, 3, 4, 5, and 6 cm and at angles from 0 to 90 deg. with respect to the longitudinal axis of the seeds. At a radial distance of 1 cm, the measured anisotropy function of the 103 Pd 'light seed' is considerably lower than that of the 103 Pd 'heavy seed' reported in the TG 43 report. Our measured values at all radial distances are in excellent agreement with the results of a Monte Carlo simulation reported by Weaver, except for points along and near the seed longitudinal axis. The anisotropy constant of the 103 Pd 'light seed' was calculated using the linear quadratic biological model for cell killing in 30 clinical implants. For the model 200 ''light seed,'' it has a value of 0.865. However, our biological model calculations lead us to conclude that if the anisotropy factors of an interstitial brachytherapy seed vary significantly over radial distances anisotropy

Direct Torque Control With Feedback Linearization for Induction Motor Drives

DEFF Research Database (Denmark)

Lascu, Cristian; Jafarzadeh, Saeed; Fadali, Sami M.

2017-01-01

This paper describes a direct-torque-controlled (DTC) induction motor (IM) drive that employs feedback linearization and sliding-mode control (SMC). A new feedback linearization approach is proposed, which yields a decoupled linear IM model with two state variables: torque and stator flux magnitude....... This intuitive linear model is used to implement a DTC-type controller that preserves all DTC advantages and eliminates its main drawback, the flux and torque ripple. Robust, fast, and ripple-free control is achieved by using SMC with proportional control in the vicinity of the sliding surface. SMC assures...... in simulations. The sliding controller is compared with a linear DTC scheme with and without feedback linearization. Extensive experimental results for a sensorless IM drive validate the proposed solution....

Extensions of linear-quadratic control, optimization and matrix theory

CERN Document Server

Jacobson, David H

1977-01-01

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat

Direct torque control with feedback linearization for induction motor drives

DEFF Research Database (Denmark)

Lascu, Cristian; Jafarzadeh, Saeed; Fadali, Sami M.

2015-01-01

This paper describes a Direct Torque Controlled (DTC) Induction Machine (IM) drive that employs feedback linearization and sliding-mode control. A feedback linearization approach is investigated, which yields a decoupled linear IM model with two state variables: torque and stator flux magnitude....... This intuitive linear model is used to implement a DTC type controller that preserves all DTC advantages and eliminates its main drawback, the flux and torque ripple. Robust, fast, and ripple-free control is achieved by using Variable Structure Control (VSC) with proportional control in the vicinity...... robust stability analysis are presented. The sliding controller is compared with a linear DTC scheme, and experimental results for a sensorless IM drive validate the proposed solution....

Actuator Control of Edgewise Vibrations in Wind Turbine Blades

DEFF Research Database (Denmark)

Staino, A.; Basu, B.; Nielsen, Søren R.K.

2012-01-01

) theory. Multi-Blade Coordinate (MBC) transformation is applied to an edgewise reduced order model, leading to a linear time-invariant (LTI) representation of the dynamic model. The LTI description obtained is used for the design of the active control algorithm. Linear Quadratic (LQ) regulator designed...... for the MBC transformed system is compared with the control synthesis performed directly on an assumed nominal representation of the timevarying system. The LQ regulator is also compared against vibration control performance using Direct Velocity Feedback (DVF). Numerical simulations have been carried out...

Neural Network Based Maximum Power Point Tracking Control with Quadratic Boost Converter for PMSG—Wind Energy Conversion System

Directory of Open Access Journals (Sweden)

Ramji Tiwari

2018-02-01

Full Text Available This paper proposes an artificial neural network (ANN based maximum power point tracking (MPPT control strategy for wind energy conversion system (WECS implemented with a DC/DC converter. The proposed topology utilizes a radial basis function network (RBFN based neural network control strategy to extract the maximum available power from the wind velocity. The results are compared with a classical Perturb and Observe (P&O method and Back propagation network (BPN method. In order to achieve a high voltage rating, the system is implemented with a quadratic boost converter and the performance of the converter is validated with a boost and single ended primary inductance converter (SEPIC. The performance of the MPPT technique along with a DC/DC converter is demonstrated using MATLAB/Simulink.

Relative controllability and null controllability of linear delay systems ...

African Journals Online (AJOL)

Necessary and sufficient conditions are established for the relative, absolute controllability and null controllability of the generalized linear delay system and its discrete prototype. The paper presents illuminating examples on previous controllability results by Manitius and Olbrot [7] and carries over the results of Onwuatu [8] ...

Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

Science.gov (United States)

Laine, A. D.

2015-01-01

There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

Medium-dose-rate brachytherapy of cancer of the cervix: preliminary results of a prospectively designed schedule based on the linear-quadratic model

International Nuclear Information System (INIS)

Leborgne, Felix; Fowler, Jack F.; Leborgne, Jose H.; Zubizarreta, Eduardo; Curochquin, Rene

1999-01-01

Purpose: To compare results and complications of our previous low-dose-rate (LDR) brachytherapy schedule for early-stage cancer of the cervix, with a prospectively designed medium-dose-rate (MDR) schedule, based on the linear-quadratic model (LQ). Methods and Materials: A combination of brachytherapy, external beam pelvic and parametrial irradiation was used in 102 consecutive Stage Ib-IIb LDR treated patients (1986-1990) and 42 equally staged MDR treated patients (1994-1996). The planned MDR schedule consisted of three insertions on three treatment days with six 8-Gy brachytherapy fractions to Point A, two on each treatment day with an interfraction interval of 6 hours, plus 18 Gy external whole pelvic dose, and followed by additional parametrial irradiation. The calculated biologically effective dose (BED) for tumor was 90 Gy 10 and for rectum below 125 Gy 3 . Results: In practice the MDR brachytherapy schedule achieved a tumor BED of 86 Gy 10 and a rectal BED of 101 Gy 3 . The latter was better than originally planned due to a reduction from 85% to 77% in the percentage of the mean dose to the rectum in relation to Point A. The mean overall treatment time was 10 days shorter for MDR in comparison with LDR. The 3-year actuarial central control for LDR and MDR was 97% and 98% (p = NS), respectively. The Grades 2 and 3 late complications (scale 0 to 3) were 1% and 2.4%, respectively for LDR (3-year) and MDR (2-year). Conclusions: LQ is a reliable tool for designing new schedules with altered fractionation and dose rates. The MDR schedule has proven to be an equivalent treatment schedule compared with LDR, with an additional advantage of having a shorter overall treatment time. The mean rectal BED Gy 3 was lower than expected

Teaching Tool for a Control Systems Laboratory Using a Quadrotor as a Plant in MATLAB

Science.gov (United States)

Khan, Subhan; Jaffery, Mujtaba Hussain; Hanif, Athar; Asif, Muhammad Rizwan

2017-01-01

This paper presents a MATLAB-based application to teach the guidance, navigation, and control concepts of a quadrotor to undergraduate students, using a graphical user interface (GUI) and 3-D animations. The Simulink quadrotor model is controlled by a proportional integral derivative controller and a linear quadratic regulator controller. The GUI…

Portfolio optimization using fuzzy linear programming

Science.gov (United States)

Pandit, Purnima K.

2013-09-01

Portfolio Optimization (PO) is a problem in Finance, in which investor tries to maximize return and minimize risk by carefully choosing different assets. Expected return and risk are the most important parameters with regard to optimal portfolios. In the simple form PO can be modeled as quadratic programming problem which can be put into equivalent linear form. PO problems with the fuzzy parameters can be solved as multi-objective fuzzy linear programming problem. In this paper we give the solution to such problems with an illustrative example.

Distribution Locational Marginal Pricing through Quadratic Programming for Congestion Management in Distribution Networks

DEFF Research Database (Denmark)

Huang, Shaojun; Wu, Qiuwei; Oren, Shmuel S.

2015-01-01

) calculates dynamic tariffs and publishes them to the aggregators, who make the optimal energy plans for the flexible demands. The DLMP through QP instead of linear programing as studied in previous literatures solves the multiple solution issue of the ag- gregator optimization which may cause......This paper presents the distribution locational mar- ginal pricing (DLMP) method through quadratic programming (QP) designed to alleviate the congestion that might occur in a distribution network with high penetration of flexible demands. In the DLMP method, the distribution system operator (DSO...

Solutions of the Schrödinger equation with inversely quadratic Hellmann plus inversely quadratic potential using Nikiforov-Uvarov method

International Nuclear Information System (INIS)

Ita, B. I.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.

2014-01-01

By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained

Bound constrained quadratic programming via piecewise

DEFF Research Database (Denmark)

Madsen, Kaj; Nielsen, Hans Bruun; Pinar, M. C.

1999-01-01

of a symmetric, positive definite matrix, and is solved by Newton iteration with line search. The paper describes the algorithm and its implementation including estimation of lambda/sub 1/ , how to get a good starting point for the iteration, and up- and downdating of Cholesky factorization. Results of extensive......We consider the strictly convex quadratic programming problem with bounded variables. A dual problem is derived using Lagrange duality. The dual problem is the minimization of an unconstrained, piecewise quadratic function. It involves a lower bound of lambda/sub 1/ , the smallest eigenvalue...

AUTOJOM, Quadratic Equation Coefficient for Conic Volume, Parallelepipeds, Wedges, Pyramids. JOMREAD, Check of 3-D Geometry Structure from Quadratic Surfaces

International Nuclear Information System (INIS)

2005-01-01

Nature of physical problem solved: AUTOJOM is a computer program that will generate the coefficients of any quadratic equation used to define conic volumes and also the coefficients of the planes needed to define parallelepipeds, wedges, and pyramids. JOMREAD is a computer code to check any 3D geometry composed of and constructed with quadratic surfaces

Finite-Time H∞ Filtering for Linear Continuous Time-Varying Systems with Uncertain Observations

Directory of Open Access Journals (Sweden)

Huihong Zhao

2012-01-01

Full Text Available This paper is concerned with the finite-time H∞ filtering problem for linear continuous time-varying systems with uncertain observations and ℒ2-norm bounded noise. The design of finite-time H∞ filter is equivalent to the problem that a certain indefinite quadratic form has a minimum and the filter is such that the minimum is positive. The quadratic form is related to a Krein state-space model according to the Krein space linear estimation theory. By using the projection theory in Krein space, the finite-time H∞ filtering problem is solved. A numerical example is given to illustrate the performance of the H∞ filter.

The stability of quadratic-reciprocal functional equation

Science.gov (United States)

Song, Aimin; Song, Minwei

2018-04-01

A new quadratic-reciprocal functional equation f ((k +1 )x +k y )+f ((k +1 )x -k y )=2/f (x )f (y )[(k+1 ) 2f (y )+k2f (x )] [(k+1)2f (y )-k2f (x )] 2 is introduced. The Hyers-Ulam stability for the quadratic-reciprocal functional equations is proved in Banach spaces using the direct method and the fixed point method, respectively.

Non-Gaussian lineshapes and dynamics of time-resolved linear and nonlinear (correlation) spectra.

Science.gov (United States)

Dinpajooh, Mohammadhasan; Matyushov, Dmitry V

2014-07-17

Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophore's electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.

Implementation of neural network based non-linear predictive control

DEFF Research Database (Denmark)

Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole

1999-01-01

This paper describes a control method for non-linear systems based on generalized predictive control. Generalized predictive control (GPC) was developed to control linear systems, including open-loop unstable and non-minimum phase systems, but has also been proposed to be extended for the control...... of non-linear systems. GPC is model based and in this paper we propose the use of a neural network for the modeling of the system. Based on the neural network model, a controller with extended control horizon is developed and the implementation issues are discussed, with particular emphasis...... on an efficient quasi-Newton algorithm. The performance is demonstrated on a pneumatic servo system....

Low photon count based digital holography for quadratic phase cryptography.

Science.gov (United States)

Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Ryle, James P; Healy, John J; Lee, Byung-Geun; Sheridan, John T

2017-07-15

Recently, the vulnerability of the linear canonical transform-based double random phase encryption system to attack has been demonstrated. To alleviate this, we present for the first time, to the best of our knowledge, a method for securing a two-dimensional scene using a quadratic phase encoding system operating in the photon-counted imaging (PCI) regime. Position-phase-shifting digital holography is applied to record the photon-limited encrypted complex samples. The reconstruction of the complex wavefront involves four sparse (undersampled) dataset intensity measurements (interferograms) at two different positions. Computer simulations validate that the photon-limited sparse-encrypted data has adequate information to authenticate the original data set. Finally, security analysis, employing iterative phase retrieval attacks, has been performed.

Neural Generalized Predictive Control of a non-linear Process

DEFF Research Database (Denmark)

Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole

1998-01-01

The use of neural network in non-linear control is made difficult by the fact the stability and robustness is not guaranteed and that the implementation in real time is non-trivial. In this paper we introduce a predictive controller based on a neural network model which has promising stability qu...... detail and discuss the implementation difficulties. The neural generalized predictive controller is tested on a pneumatic servo sys-tem.......The use of neural network in non-linear control is made difficult by the fact the stability and robustness is not guaranteed and that the implementation in real time is non-trivial. In this paper we introduce a predictive controller based on a neural network model which has promising stability...... qualities. The controller is a non-linear version of the well-known generalized predictive controller developed in linear control theory. It involves minimization of a cost function which in the present case has to be done numerically. Therefore, we develop the numerical algorithms necessary in substantial...

Adaptive PSO for optimal LQR tracking control of 2 DoF laboratory helicopter

NARCIS (Netherlands)

Vinodh Kumar, E.; Ganapathy Subramanian, R.; Jerome, J.

2016-01-01

This paper deals with the attitude tracking control problem for a 2 DoF laboratory helicopter using optimal linear quadratic regulator (LQR). As the performance of the LQR controller greatly depends on the weighting matrices (Q and R), it is important to select them optimally. However, normally the

Memory State Feedback RMPC for Multiple Time-Delayed Uncertain Linear Systems with Input Constraints

Directory of Open Access Journals (Sweden)

Wei-Wei Qin

2014-01-01

Full Text Available This paper focuses on the problem of asymptotic stabilization for a class of discrete-time multiple time-delayed uncertain linear systems with input constraints. Then, based on the predictive control principle of receding horizon optimization, a delayed state dependent quadratic function is considered for incorporating MPC problem formulation. By developing a memory state feedback controller, the information of the delayed plant states can be taken into full consideration. The MPC problem is formulated to minimize the upper bound of infinite horizon cost that satisfies the sufficient conditions. Then, based on the Lyapunov-Krasovskii function, a delay-dependent sufficient condition in terms of linear matrix inequality (LMI can be derived to design a robust MPC algorithm. Finally, the digital simulation results prove availability of the proposed method.

LQR-Based Optimal Distributed Cooperative Design for Linear Discrete-Time Multiagent Systems.

Science.gov (United States)

Zhang, Huaguang; Feng, Tao; Liang, Hongjing; Luo, Yanhong

2017-03-01

In this paper, a novel linear quadratic regulator (LQR)-based optimal distributed cooperative design method is developed for synchronization control of general linear discrete-time multiagent systems on a fixed, directed graph. Sufficient conditions are derived for synchronization, which restrict the graph eigenvalues into a bounded circular region in the complex plane. The synchronizing speed issue is also considered, and it turns out that the synchronizing region reduces as the synchronizing speed becomes faster. To obtain more desirable synchronizing capacity, the weighting matrices are selected by sufficiently utilizing the guaranteed gain margin of the optimal regulators. Based on the developed LQR-based cooperative design framework, an approximate dynamic programming technique is successfully introduced to overcome the (partially or completely) model-free cooperative design for linear multiagent systems. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design methods.

Linear-quadratic dose kinetics or dose-dependent repair/misrepair

International Nuclear Information System (INIS)

Braby, L.A.; Nelson, J.M.

1992-01-01

Models for the response of cells exposed to low (LET) linear energy transfer radiation can be grouped into three general types on the basis of assumptions about the nature of the interaction which results in the shoulder of the survival curve. The three forms of interaction are 1) sublethal damage becoming lethal, 2) potentially lethal damage becoming irreparable, and 3) potentially lethal damage ''saturating'' a repair system. The effects that these three forms of interaction would have on the results of specific types of experiments are investigated. Comparisons with experimental results indicate that only the second type is significant in determining the response of typical cultured mammalian cells. (author)

Analysis of explicit model predictive control for path-following control.

Science.gov (United States)

Lee, Junho; Chang, Hyuk-Jun

2018-01-01

In this paper, explicit Model Predictive Control(MPC) is employed for automated lane-keeping systems. MPC has been regarded as the key to handle such constrained systems. However, the massive computational complexity of MPC, which employs online optimization, has been a major drawback that limits the range of its target application to relatively small and/or slow problems. Explicit MPC can reduce this computational burden using a multi-parametric quadratic programming technique(mp-QP). The control objective is to derive an optimal front steering wheel angle at each sampling time so that autonomous vehicles travel along desired paths, including straight, circular, and clothoid parts, at high entry speeds. In terms of the design of the proposed controller, a method of choosing weighting matrices in an optimization problem and the range of horizons for path-following control are described through simulations. For the verification of the proposed controller, simulation results obtained using other control methods such as MPC, Linear-Quadratic Regulator(LQR), and driver model are employed, and CarSim, which reflects the features of a vehicle more realistically than MATLAB/Simulink, is used for reliable demonstration.

Analysis of explicit model predictive control for path-following control

Science.gov (United States)

2018-01-01

In this paper, explicit Model Predictive Control(MPC) is employed for automated lane-keeping systems. MPC has been regarded as the key to handle such constrained systems. However, the massive computational complexity of MPC, which employs online optimization, has been a major drawback that limits the range of its target application to relatively small and/or slow problems. Explicit MPC can reduce this computational burden using a multi-parametric quadratic programming technique(mp-QP). The control objective is to derive an optimal front steering wheel angle at each sampling time so that autonomous vehicles travel along desired paths, including straight, circular, and clothoid parts, at high entry speeds. In terms of the design of the proposed controller, a method of choosing weighting matrices in an optimization problem and the range of horizons for path-following control are described through simulations. For the verification of the proposed controller, simulation results obtained using other control methods such as MPC, Linear-Quadratic Regulator(LQR), and driver model are employed, and CarSim, which reflects the features of a vehicle more realistically than MATLAB/Simulink, is used for reliable demonstration. PMID:29534080

Robustness of Linear Systems towards Multi-Dissipative Pertubations

DEFF Research Database (Denmark)

Thygesen, Uffe Høgsbro; Poulsen, Niels Kjølstad

1997-01-01

We consider the question of robust stability of a linear time invariant plant subject to dynamic perturbations, which are dissipative in the sense of Willems with respect to several quadratic supply rates. For instance, parasitic dynamics are often both small gain and passive. We reduce several...... robustness analysis questions to linear matrix inequalities: robust stability, robust H2 performance and robust performance in presence of disturbances with finite signal-to-noise ratios...

Yaw control for active damping of structural dynamics

Energy Technology Data Exchange (ETDEWEB)

Ekelund, T. [Chalmers Univ. of Technology, Goeteborg (Sweden). Control Engineering Lab.

1996-12-01

Yaw torque control for reduction of structural dynamic loads in a two-bladed wind turbine is investigated. The models are obtained using rigid-body mechanics. Linear quadratic control theory is utilized for design and analysis. The analysis of two simple examples, where the teeter angle and the tower lateral bending motion are regarded, shows that a time-varying controller has some advantages compared with a time-invariant controller. 6 refs, 9 figs

Evaluation of Linear Regression Simultaneous Myoelectric Control Using Intramuscular EMG.

Science.gov (United States)

Smith, Lauren H; Kuiken, Todd A; Hargrove, Levi J

2016-04-01

The objective of this study was to evaluate the ability of linear regression models to decode patterns of muscle coactivation from intramuscular electromyogram (EMG) and provide simultaneous myoelectric control of a virtual 3-DOF wrist/hand system. Performance was compared to the simultaneous control of conventional myoelectric prosthesis methods using intramuscular EMG (parallel dual-site control)-an approach that requires users to independently modulate individual muscles in the residual limb, which can be challenging for amputees. Linear regression control was evaluated in eight able-bodied subjects during a virtual Fitts' law task and was compared to performance of eight subjects using parallel dual-site control. An offline analysis also evaluated how different types of training data affected prediction accuracy of linear regression control. The two control systems demonstrated similar overall performance; however, the linear regression method demonstrated improved performance for targets requiring use of all three DOFs, whereas parallel dual-site control demonstrated improved performance for targets that required use of only one DOF. Subjects using linear regression control could more easily activate multiple DOFs simultaneously, but often experienced unintended movements when trying to isolate individual DOFs. Offline analyses also suggested that the method used to train linear regression systems may influence controllability. Linear regression myoelectric control using intramuscular EMG provided an alternative to parallel dual-site control for 3-DOF simultaneous control at the wrist and hand. The two methods demonstrated different strengths in controllability, highlighting the tradeoff between providing simultaneous control and the ability to isolate individual DOFs when desired.

Evaluating the Wald entropy from two-derivative terms in quadratic actions

International Nuclear Information System (INIS)

Brustein, Ram; Gorbonos, Dan; Hadad, Merav; Medved, A. J. M.

2011-01-01

We evaluate the Wald Noether charge entropy for a black hole in generalized theories of gravity. Expanding the Lagrangian to second order in gravitational perturbations, we show that contributions to the entropy density originate only from the coefficients of two-derivative terms. The same considerations are extended to include matter fields and to show that arbitrary powers of matter fields and their symmetrized covariant derivatives cannot contribute to the entropy density. We also explain how to use the linearized gravitational field equation rather than quadratic actions to obtain the same results. Several explicit examples are presented that allow us to clarify subtle points in the derivation and application of our method.

Orthogonal and Scaling Transformations of Quadratic Functions with ...

African Journals Online (AJOL)

In this paper we present a non-singular transformation that can reduce a given quadratic function defined on Rn to another simpler quadratic function and study the impact of the transformation in relation to the problem of minimization of the function. In particular, we construct a non-singular transformation that can reduce a ...

Quadratic Frequency Modulation Signals Parameter Estimation Based on Two-Dimensional Product Modified Parameterized Chirp Rate-Quadratic Chirp Rate Distribution.

Science.gov (United States)

Qu, Zhiyu; Qu, Fuxin; Hou, Changbo; Jing, Fulong

2018-05-19

In an inverse synthetic aperture radar (ISAR) imaging system for targets with complex motion, the azimuth echo signals of the target are always modeled as multicomponent quadratic frequency modulation (QFM) signals. The chirp rate (CR) and quadratic chirp rate (QCR) estimation of QFM signals is very important to solve the ISAR image defocus problem. For multicomponent QFM (multi-QFM) signals, the conventional QR and QCR estimation algorithms suffer from the cross-term and poor anti-noise ability. This paper proposes a novel estimation algorithm called a two-dimensional product modified parameterized chirp rate-quadratic chirp rate distribution (2D-PMPCRD) for QFM signals parameter estimation. The 2D-PMPCRD employs a multi-scale parametric symmetric self-correlation function and modified nonuniform fast Fourier transform-Fast Fourier transform to transform the signals into the chirp rate-quadratic chirp rate (CR-QCR) domains. It can greatly suppress the cross-terms while strengthening the auto-terms by multiplying different CR-QCR domains with different scale factors. Compared with high order ambiguity function-integrated cubic phase function and modified Lv's distribution, the simulation results verify that the 2D-PMPCRD acquires higher anti-noise performance and obtains better cross-terms suppression performance for multi-QFM signals with reasonable computation cost.

Emittance control in linear colliders

International Nuclear Information System (INIS)

Ruth, R.D.

1991-01-01

Before completing a realistic design of a next-generation linear collider, the authors must first learn the lessons taught by the first generation, the SLC. Given that, they must make designs fault tolerant by including correction and compensation in the basic design. They must also try to eliminate these faults by improved alignment and stability of components. When these two efforts cross, they have a realistic design. The techniques of generation and control of emittance reviewed here provide a foundation for a design which can obtain the necessary luminosity in a next-generation linear collider

A Quadratic Spring Equation

Science.gov (United States)

Fay, Temple H.

2010-01-01

Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…

Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier

DEFF Research Database (Denmark)

Neumeyer, Stefan; Sorokin, Vladislav; Thomsen, Jon Juel

2016-01-01

We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing–Mathieu equation with appended quadratic nonlinearity is considered as the model system......, and approximate analytical steady-state solutions and corresponding stabilities are obtained by the method of varying amplitudes. Some general effects of pure quadratic, and mixed quadratic and cubic nonlinearities on parametric amplification are shown. In particular, the effects of mixed quadratic and cubic...... nonlinearities may generate additional amplitude–frequency solutions. In this case an increased response and a more phase sensitive amplitude (phase between excitation frequencies) is obtained, as compared to the case with either pure quadratic or cubic nonlinearity. Furthermore, jumps and bi...

Model predictive Controller for Mobile Robot

OpenAIRE

Alireza Rezaee

2017-01-01

This paper proposes a Model Predictive Controller (MPC) for control of a P2AT mobile robot. MPC refers to a group of controllers that employ a distinctly identical model of process to predict its future behavior over an extended prediction horizon. The design of a MPC is formulated as an optimal control problem. Then this problem is considered as linear quadratic equation (LQR) and is solved by making use of Ricatti equation. To show the effectiveness of the proposed method this controller is...

Indirect quantum tomography of quadratic Hamiltonians

Energy Technology Data Exchange (ETDEWEB)

Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)

2011-01-15

A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.

Nonlinear dynamics of quadratically cubic systems

International Nuclear Information System (INIS)

Rudenko, O V

2013-01-01

We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)

On orthogonality preserving quadratic stochastic operators

Energy Technology Data Exchange (ETDEWEB)

Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)

2015-05-15

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

On orthogonality preserving quadratic stochastic operators

International Nuclear Information System (INIS)

Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

2015-01-01

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too

Optimal control of the gear shifting process for shift smoothness in dual-clutch transmissions

Science.gov (United States)

Li, Guoqiang; Görges, Daniel

2018-03-01

The control of the transmission system in vehicles is significant for the driving comfort. In order to design a controller for smooth shifting and comfortable driving, a dynamic model of a dual-clutch transmission is presented in this paper. A finite-time linear quadratic regulator is proposed for the optimal control of the two friction clutches in the torque phase for the upshift process. An integral linear quadratic regulator is introduced to regulate the relative speed difference between the engine and the slipping clutch under the optimization of the input torque during the inertia phase. The control objective focuses on smoothing the upshift process so as to improve the driving comfort. Considering the available sensors in vehicles for feedback control, an observer design is presented to track the immeasurable variables. Simulation results show that the jerk can be reduced both in the torque phase and inertia phase, indicating good shift performance. Furthermore, compared with conventional controllers for the upshift process, the proposed control method can reduce shift jerk and improve shift quality.

Quadratic Twists of Rigid Calabi–Yau Threefolds Over

DEFF Research Database (Denmark)

Gouvêa, Fernando Q.; Kiming, Ian; Yui, Noriko

2013-01-01

of weight 4 on some Γ 0(N). We show that quadratic twisting of a threefold corresponds to twisting the attached newform by quadratic characters and illustrate with a number of obvious and not so obvious examples. The question is motivated by the deeper question of which newforms of weight 4 on some Γ 0(N...

Wave propagation in elastic medium with heterogeneous quadratic nonlinearity

International Nuclear Information System (INIS)

Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin

2011-01-01

This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter β when the nonlinearity distribution in the layer is a stochastic process.

Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach

Energy Technology Data Exchange (ETDEWEB)

Pham, Huyên, E-mail: pham@math.univ-paris-diderot.fr; Wei, Xiaoli, E-mail: tyswxl@gmail.com [Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, Université Paris Diderot (France)

2016-12-15

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.

Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach

International Nuclear Information System (INIS)

Pham, Huyên; Wei, Xiaoli

2016-01-01

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.

Perturbation analysis of linear control problems

International Nuclear Information System (INIS)

Petkov, Petko; Konstantinov, Mihail

2017-01-01

The paper presents a brief overview of the technique of splitting operators, proposed by the authors and intended for perturbation analysis of control problems involving unitary and orthogonal matrices. Combined with the technique of Lyapunov majorants and the implementation of the Banach and Schauder fixed point principles, it allows to obtain rigorous non-local perturbation bounds for a set of sensitivity analysis problems. Among them are the reduction of linear systems into orthogonal canonical forms, the feedback synthesis problem and pole assignment problem in particular, as well as other important problems in control theory and linear algebra. Key words: perturbation analysis, canonical forms, feedback synthesis

Optimal control of inverted pendulum system using PID controller, LQR and MPC

Science.gov (United States)

Varghese, Elisa Sara; Vincent, Anju K.; Bagyaveereswaran, V.

2017-11-01

Inverted pendulum is a highly nonlinear system. Here we propose an optimal control technique for the control of an inverted Pendulum - cart system. The system is modeled, linearized and controlled. Here, the control objective is to control the system such that when the cart reaches a desired position the inverted pendulum stabilizes in the upright position. Initially PID controller is used to control the system. Later, Linear Quadratic Regulator (LQR) a well-known optimal control technique which makes use of the states of the dynamical system and control input to frame the optimal control decision is used. Various combinations of both PID and LQR controllers are implemented. To validate the robustness of the controller, the system is simulated with and without disturbance. Finally the system is also controlled using Model Predictive controller (MPC). MPC has well predictive ability to calculate future events and implement necessary control actions. The performance of the system is compared and analyzed.

Use of probabilistic weights to enhance linear regression myoelectric control.

Science.gov (United States)

Smith, Lauren H; Kuiken, Todd A; Hargrove, Levi J

2015-12-01

Clinically available prostheses for transradial amputees do not allow simultaneous myoelectric control of degrees of freedom (DOFs). Linear regression methods can provide simultaneous myoelectric control, but frequently also result in difficulty with isolating individual DOFs when desired. This study evaluated the potential of using probabilistic estimates of categories of gross prosthesis movement, which are commonly used in classification-based myoelectric control, to enhance linear regression myoelectric control. Gaussian models were fit to electromyogram (EMG) feature distributions for three movement classes at each DOF (no movement, or movement in either direction) and used to weight the output of linear regression models by the probability that the user intended the movement. Eight able-bodied and two transradial amputee subjects worked in a virtual Fitts' law task to evaluate differences in controllability between linear regression and probability-weighted regression for an intramuscular EMG-based three-DOF wrist and hand system. Real-time and offline analyses in able-bodied subjects demonstrated that probability weighting improved performance during single-DOF tasks (p linear regression control. Use of probability weights can improve the ability to isolate individual during linear regression myoelectric control, while maintaining the ability to simultaneously control multiple DOFs.

On Convex Quadratic Approximation

NARCIS (Netherlands)

den Hertog, D.; de Klerk, E.; Roos, J.

2000-01-01

In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of

LQG Controller Design for Pitch Regulated Variable Speed Wind Turbine

DEFF Research Database (Denmark)

Imran, Raja Muhammed; Hussain, Dil Muhammad Akbar; Chen, Zhe

2014-01-01

Variable speed wind turbine is a complex and nonlinear system, a sophisticated control is required to meet the challenges posed by these systems. This paper is presenting a pitch regulation strategy based on LQG (Linear Quadratic Gaussian) to regulate turbine at its rated power and to reject...

Adaptive Control for Linear Uncertain Systems with Unmodeled Dynamics Revisited via Optimal Control Modification

Science.gov (United States)

Nguyen, Nhan

2013-01-01

This paper presents the optimal control modification for linear uncertain plants. The Lyapunov analysis shows that the modification parameter has a limiting value depending on the nature of the uncertainty. The optimal control modification exhibits a linear asymptotic property that enables it to be analyzed in a linear time invariant framework for linear uncertain plants. The linear asymptotic property shows that the closed-loop plants in the limit possess a scaled input-output mapping. Using this property, we can derive an analytical closed-loop transfer function in the limit as the adaptive gain tends to infinity. The paper revisits the Rohrs counterexample problem that illustrates the nature of non-robustness of model-reference adaptive control in the presence of unmodeled dynamics. An analytical approach is developed to compute exactly the modification parameter for the optimal control modification that stabilizes the plant in the Rohrs counterexample. The linear asymptotic property is also used to address output feedback adaptive control for non-minimum phase plants with a relative degree 1.

Lambda-Lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, Olivier; Schultz, Ulrik Pagh

2002-01-01

Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

Lambda-Lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, Olivier; Schultz, Ulrik Pagh

2003-01-01

Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

Lambda-Lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, Olivier; Schultz, Ulrik Pagh

2004-01-01

Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

Predictive IP controller for robust position control of linear servo system.

Science.gov (United States)

Lu, Shaowu; Zhou, Fengxing; Ma, Yajie; Tang, Xiaoqi

2016-07-01

Position control is a typical application of linear servo system. In this paper, to reduce the system overshoot, an integral plus proportional (IP) controller is used in the position control implementation. To further improve the control performance, a gain-tuning IP controller based on a generalized predictive control (GPC) law is proposed. Firstly, to represent the dynamics of the position loop, a second-order linear model is used and its model parameters are estimated on-line by using a recursive least squares method. Secondly, based on the GPC law, an optimal control sequence is obtained by using receding horizon, then directly supplies the IP controller with the corresponding control parameters in the real operations. Finally, simulation and experimental results are presented to show the efficiency of proposed scheme. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Nearly Quadratic n-Derivations on Non-Archimedean Banach Algebras

Directory of Open Access Journals (Sweden)

Madjid Eshaghi Gordji

2012-01-01

Full Text Available Let n>1 be an integer, let A be an algebra, and X be an A-module. A quadratic function D:A→X is called a quadratic n-derivation if D(∏i=1nai=D(a1a22⋯an2+a12D(a2a32⋯an2+⋯+a12a22⋯an−12D(an for all a1,...,an∈A. We investigate the Hyers-Ulam stability of quadratic n-derivations from non-Archimedean Banach algebras into non-Archimedean Banach modules by using the Banach fixed point theorem.

Algorithms for sparse, symmetric, definite quadratic lambda-matrix eigenproblems

International Nuclear Information System (INIS)

Scott, D.S.; Ward, R.C.

1981-01-01

Methods are presented for computing eigenpairs of the quadratic lambda-matrix, M lambda 2 + C lambda + K, where M, C, and K are large and sparse, and have special symmetry-type properties. These properties are sufficient to insure that all the eigenvalues are real and that theory analogous to the standard symmetric eigenproblem exists. The methods employ some standard techniques such as partial tri-diagonalization via the Lanczos Method and subsequent eigenpair calculation, shift-and- invert strategy and subspace iteration. The methods also employ some new techniques such as Rayleigh-Ritz quadratic roots and the inertia of symmetric, definite, quadratic lambda-matrices

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. ...

Determining the Optimal Solution for Quadratically Constrained Quadratic Programming (QCQP) on Energy-Saving Generation Dispatch Problem

Science.gov (United States)

Lesmana, E.; Chaerani, D.; Khansa, H. N.

2018-03-01

Energy-Saving Generation Dispatch (ESGD) is a scheme made by Chinese Government in attempt to minimize CO2 emission produced by power plant. This scheme is made related to global warming which is primarily caused by too much CO2 in earth’s atmosphere, and while the need of electricity is something absolute, the power plants producing it are mostly thermal-power plant which produced many CO2. Many approach to fulfill this scheme has been made, one of them came through Minimum Cost Flow in which resulted in a Quadratically Constrained Quadratic Programming (QCQP) form. In this paper, ESGD problem with Minimum Cost Flow in QCQP form will be solved using Lagrange’s Multiplier Method

Solution of Large Systems of Linear Equations with Quadratic or Non-Quadratic Matrices and Deconvoiution of Spectra

Energy Technology Data Exchange (ETDEWEB)

Nygaard, K

1967-12-15

The numerical deconvolution of spectra is equivalent to the solution of a (large) system of linear equations with a matrix which is not necessarily a square matrix. The demand that the square sum of the residual errors shall be minimum is not in general sufficient to ensure a unique or 'sound' solution. Therefore other demands which may include the demand for minimum square errors are introduced which lead to 'sound' and 'non-oscillatory' solutions irrespective of the shape of the original matrix and of the determinant of the matrix of the normal equations.

PSQP: Puzzle Solving by Quadratic Programming.

Science.gov (United States)

Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome

2017-02-01

In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.

Visualising the Roots of Quadratic Equations with Complex Coefficients

Science.gov (United States)

Bardell, Nicholas S.

2014-01-01

This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…

Structured Control of Affine Linear Parameter Varying Systems

DEFF Research Database (Denmark)

Adegas, Fabiano Daher; Stoustrup, Jakob

2011-01-01

This paper presents a new procedure to design structured controllers for discrete-time affine linear parametervarying systems (A LPV). The class of control structures includes decentralized of any order, fixed order output feedback, simultaneous plant-control design, among others. A parametervarying...... non-convex condition for an upper bound on the induced L2-norm performance is solved by an iterative linear matrix inequalities (LMI) optimization algorithm. Numerical examples demostrate the effectiveness of the proposed approach....

Differentiated Learning Environment--A Classroom for Quadratic Equation, Function and Graphs

Science.gov (United States)

Dinç, Emre

2017-01-01

This paper will cover the design of a learning environment as a classroom regarding the Quadratic Equations, Functions and Graphs. The goal of the learning environment offered in the paper is to design a classroom where students will enjoy the process, use their skills they already have during the learning process, control and plan their learning…

Scale-Invariant Rotating Black Holes in Quadratic Gravity

Directory of Open Access Journals (Sweden)

Guido Cognola

2015-07-01

Full Text Available Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.

Applying the J-optimal channelized quadratic observer to SPECT myocardial perfusion defect detection

Science.gov (United States)

Kupinski, Meredith K.; Clarkson, Eric; Ghaly, Michael; Frey, Eric C.

2016-03-01

To evaluate performance on a perfusion defect detection task from 540 image pairs of myocardial perfusion SPECT image data we apply the J-optimal channelized quadratic observer (J-CQO). We compare AUC values of the linear Hotelling observer and J-CQO when the defect location is fixed and when it occurs in one of two locations. As expected, when the location is fixed a single channels maximizes AUC; location variability requires multiple channels to maximize the AUC. The AUC is estimated from both the projection data and reconstructed images. J-CQO is quadratic since it uses the first- and second- order statistics of the image data from both classes. The linear data reduction by the channels is described by an L x M channel matrix and in prior work we introduced an iterative gradient-based method for calculating the channel matrix. The dimensionality reduction from M measurements to L channels yields better estimates of these sample statistics from smaller sample sizes, and since the channelized covariance matrix is L x L instead of M x M, the matrix inverse is easier to compute. The novelty of our approach is the use of Jeffrey's divergence (J) as the figure of merit (FOM) for optimizing the channel matrix. We previously showed that the J-optimal channels are also the optimum channels for the AUC and the Bhattacharyya distance when the channel outputs are Gaussian distributed with equal means. This work evaluates the use of J as a surrogate FOM (SFOM) for AUC when these statistical conditions are not satisfied.

Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems

International Nuclear Information System (INIS)

Marquette, Ian

2011-01-01

There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.

Controller for control of pulsed electron linear accelerator

International Nuclear Information System (INIS)

Bryazgin, A.A.; Faktorovich, B.L.

1995-01-01

The controller is based on the K1816VE31 microprocessor and contains 22-channel integrating 10-digital two-wire analog-to-digital converter, 8-channel 12-digit digital-to-analog converter, 24-digit output register, 16-digit input register pulse generator in the range of 0.5 - 50 Hz with the regulation step of 0.05 Hz and delayed pulse generator. The controller is used for pulsed electron linear accelerator control and is reduced to regulation of the electron beam pulse repetition rate and beam energy. 1 ref., 1 fig

Geometric Approaches to Quadratic Equations from Other Times and Places.

Science.gov (United States)

Allaire, Patricia R.; Bradley, Robert E.

2001-01-01

Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

Approximate *-derivations and approximate quadratic *-derivations on C*-algebras

Directory of Open Access Journals (Sweden)

Park Choonkil

2011-01-01

Full Text Available Abstract In this paper, we prove the stability of *-derivations and of quadratic *-derivations on Banach *-algebras. We moreover prove the superstability of *-derivations and of quadratic *-derivations on C*-algebras. 2000 Mathematics Subject Classification: 39B52; 47B47; 46L05; 39B72.

Compressor Surge Control Design Using Linear Matrix Inequality Approach

OpenAIRE

Uddin, Nur; Gravdahl, Jan Tommy

2017-01-01

A novel design for active compressor surge control system (ASCS) using linear matrix inequality (LMI) approach is presented and including a case study on piston-actuated active compressor surge control system (PAASCS). The non-linear system dynamics of the PAASCS is transformed into linear parameter varying (LPV) system dynamics. The system parameters are varying as a function of the compressor performance curve slope. A compressor surge stabilization problem is then formulated as a LMI probl...

Design Robust Controller for Rotary Kiln

Directory of Open Access Journals (Sweden)

Omar D. Hernández-Arboleda

2013-11-01

Full Text Available This paper presents the design of a robust controller for a rotary kiln. The designed controller is a combination of a fractional PID and linear quadratic regulator (LQR, these are not used to control the kiln until now, in addition robustness criteria are evaluated (gain margin, phase margin, strength gain, rejecting high frequency noise and sensitivity applied to the entire model (controller-plant, obtaining good results with a frequency range of 0.020 to 90 rad/s, which contributes to the robustness of the system.

Multivariable control in nuclear power stations

International Nuclear Information System (INIS)

Parent, M.; McMorran, P.D.

1982-11-01

Multivariable methods have the potential to improve the control of large systems such as nuclear power stations. Linear-quadratic optimal control is a multivariable method based on the minimization of a cost function. A related technique leads to the Kalman filter for estimation of plant state from noisy measurements. A design program for optimal control and Kalman filtering has been developed as part of a computer-aided design package for multivariable control systems. The method is demonstrated on a model of a nuclear steam generator, and simulated results are presented

Analysis of Students' Error in Learning of Quadratic Equations

Science.gov (United States)

Zakaria, Effandi; Ibrahim; Maat, Siti Mistima

2010-01-01

The purpose of the study was to determine the students' error in learning quadratic equation. The samples were 30 form three students from a secondary school in Jambi, Indonesia. Diagnostic test was used as the instrument of this study that included three components: factorization, completing the square and quadratic formula. Diagnostic interview…

Quadratic hamiltonians and relativistic quantum mechanics

International Nuclear Information System (INIS)

Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.

1981-01-01

For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru

Relative null controllability of linear systems with multiple delays in ...

African Journals Online (AJOL)

varying multiple delays in state and control are developed. If the uncontrolled system is uniformly asymptotically stable, and if the linear system is controllable, then the linear system is null controllable. Journal of the Nigerian Association of ...

Linear-constraint wavefront control for exoplanet coronagraphic imaging systems

Science.gov (United States)

Sun, He; Eldorado Riggs, A. J.; Kasdin, N. Jeremy; Vanderbei, Robert J.; Groff, Tyler Dean

2017-01-01

A coronagraph is a leading technology for achieving high-contrast imaging of exoplanets in a space telescope. It uses a system of several masks to modify the diffraction and achieve extremely high contrast in the image plane around target stars. However, coronagraphic imaging systems are very sensitive to optical aberrations, so wavefront correction using deformable mirrors (DMs) is necessary to avoid contrast degradation in the image plane. Electric field conjugation (EFC) and Stroke minimization (SM) are two primary high-contrast wavefront controllers explored in the past decade. EFC minimizes the average contrast in the search areas while regularizing the strength of the control inputs. Stroke minimization calculates the minimum DM commands under the constraint that a target average contrast is achieved. Recently in the High Contrast Imaging Lab at Princeton University (HCIL), a new linear-constraint wavefront controller based on stroke minimization was developed and demonstrated using numerical simulation. Instead of only constraining the average contrast over the entire search area, the new controller constrains the electric field of each single pixel using linear programming, which could led to significant increases in speed of the wavefront correction and also create more uniform dark holes. As a follow-up of this work, another linear-constraint controller modified from EFC is demonstrated theoretically and numerically and the lab verification of the linear-constraint controllers is reported. Based on the simulation and lab results, the pros and cons of linear-constraint controllers are carefully compared with EFC and stroke minimization.

Minimization of the root of a quadratic functional under a system of affine equality constraints with application to portfolio management

Science.gov (United States)

Landsman, Zinoviy

2008-10-01

We present an explicit closed form solution of the problem of minimizing the root of a quadratic functional subject to a system of affine constraints. The result generalizes Z. Landsman, Minimization of the root of a quadratic functional under an affine equality constraint, J. Comput. Appl. Math. 2007, to appear, see sciencedirect.com/science/journal/03770427>, articles in press, where the optimization problem was solved under only one linear constraint. This is of interest for solving significant problems pertaining to financial economics as well as some classes of feasibility and optimization problems which frequently occur in tomography and other fields. The results are illustrated in the problem of optimal portfolio selection and the particular case when the expected return of finance portfolio is certain is discussed.

Multivariable controller for discrete stochastic amplitude-constrained systems

Directory of Open Access Journals (Sweden)

Hannu T. Toivonen

1983-04-01

Full Text Available A sub-optimal multivariable controller for discrete stochastic amplitude-constrained systems is presented. In the approach the regulator structure is restricted to the class of linear saturated feedback laws. The stationary covariances of the controlled system are evaluated by approximating the stationary probability distribution of the state by a gaussian distribution. An algorithm for minimizing a quadratic loss function is given, and examples are presented to illustrate the performance of the sub-optimal controller.

A mathematical perspective on flight dynamics and control

CERN Document Server

L'Afflitto, Andrea

2017-01-01

This brief presents several aspects of flight dynamics, which are usually omitted or briefly mentioned in textbooks, in a concise, self-contained, and rigorous manner. The kinematic and dynamic equations of an aircraft are derived starting from the notion of the derivative of a vector and then thoroughly analysed, interpreting their deep meaning from a mathematical standpoint and without relying on physical intuition. Moreover, some classic and advanced control design techniques are presented and illustrated with meaningful examples. Distinguishing features that characterize this brief include a definition of angular velocity, which leaves no room for ambiguities, an improvement on traditional definitions based on infinitesimal variations. Quaternion algebra, Euler parameters, and their role in capturing the dynamics of an aircraft are discussed in great detail. After having analyzed the longitudinal- and lateral-directional modes of an aircraft, the linear-quadratic regulator, the linear-quadratic Gaussian r...

Turnpike theory of continuous-time linear optimal control problems

CERN Document Server

Zaslavski, Alexander J

2015-01-01

Individual turnpike results are of great interest due to their numerous applications in engineering and in economic theory; in this book the study is focused on new results of turnpike phenomenon in linear optimal control problems.  The book is intended for engineers as well as for mathematicians interested in the calculus of variations, optimal control, and in applied functional analysis. Two large classes of problems are studied in more depth. The first class studied in Chapter 2 consists of linear control problems with periodic nonsmooth convex integrands. Chapters 3-5 consist of linear control problems with autonomous nonconvex and nonsmooth integrands.  Chapter 6 discusses a turnpike property for dynamic zero-sum games with linear constraints. Chapter 7 examines genericity results. In Chapter 8, the description of structure of variational problems with extended-valued integrands is obtained. Chapter 9 ends the exposition with a study of turnpike phenomenon for dynamic games with extended value integran...

Berry phases for 3D Hartree-type equations with a quadratic potential and a uniform magnetic field

International Nuclear Information System (INIS)

Litvinets, F N; Shapovalov, A V; Trifonov, A Yu

2007-01-01

A countable set of asymptotic space-localized solutions is constructed for a 3D Hartree-type equation with a quadratic potential by the complex germ method in the adiabatic approximation. The asymptotic parameter is 1/T, where T >> 1 is the adiabatic evolution time. A generalization of the Berry phase of the linear Schroedinger equation is formulated for the Hartree-type equation. For the solutions constructed, the Berry phases are found in an explicit form

Separation and Extension of Cover Inequalities for Conic Quadratic Knapsack Constraints with Generalized Upper Bounds

DEFF Research Database (Denmark)

Atamtürk, Alper; Muller, Laurent Flindt; Pisinger, David

2013-01-01

Motivated by addressing probabilistic 0-1 programs we study the conic quadratic knapsack polytope with generalized upper bound (GUB) constraints. In particular, we investigate separating and extending GUB cover inequalities. We show that, unlike in the linear case, determining whether a cover can...... be extended with a single variable is NP-hard. We describe and compare a number of exact and heuristic separation and extension algorithms which make use of the structure of the constraints. Computational experiments are performed for comparing the proposed separation and extension algorithms...

Observability of linear control systems on Lie groups

International Nuclear Information System (INIS)

Ayala, V.; Hacibekiroglu, A.K.

1995-01-01

In this paper, we study the observability problem for a linear control system Σ on a Lie group G. The drift vector field of Σ is an infinitesimal automorphism of G and the control vectors are elements in the Lie algebra of G. We establish algebraic conditions to characterize locally and globally observability for Σ. As in the linear case on R n , these conditions are independent of the control vector. We give an algorithm on the co-tangent bundle of G to calculate the equivalence class of the neutral element. (author). 6 refs

Practical Implementations of Advanced Process Control for Linear Systems

DEFF Research Database (Denmark)

Knudsen, Jørgen K . H.; Huusom, Jakob Kjøbsted; Jørgensen, John Bagterp

2013-01-01

This paper describes some practical problems encountered, when implementing Advanced Process Control, APC, schemes on linear processes. The implemented APC controllers discussed will be LQR, Riccati MPC and Condensed MPC controllers illustrated by simulation of the Four Tank Process and a lineari......This paper describes some practical problems encountered, when implementing Advanced Process Control, APC, schemes on linear processes. The implemented APC controllers discussed will be LQR, Riccati MPC and Condensed MPC controllers illustrated by simulation of the Four Tank Process...... on pilot plant equipment on the department of Chemical Engineering DTU Lyngby....

Schwarz and multilevel methods for quadratic spline collocation

Energy Technology Data Exchange (ETDEWEB)

Christara, C.C. [Univ. of Toronto, Ontario (Canada); Smith, B. [Univ. of California, Los Angeles, CA (United States)

1994-12-31

Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.

Lambda-lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, O.; Schultz, U.P.

2004-01-01

-lifting transforms a block-structured program into a set of recursive equations, one for each local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters......Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...

Quadratic Polynomial Regression using Serial Observation Processing:Implementation within DART

Science.gov (United States)

Hodyss, D.; Anderson, J. L.; Collins, N.; Campbell, W. F.; Reinecke, P. A.

2017-12-01

Many Ensemble-Based Kalman ltering (EBKF) algorithms process the observations serially. Serial observation processing views the data assimilation process as an iterative sequence of scalar update equations. What is useful about this data assimilation algorithm is that it has very low memory requirements and does not need complex methods to perform the typical high-dimensional inverse calculation of many other algorithms. Recently, the push has been towards the prediction, and therefore the assimilation of observations, for regions and phenomena for which high-resolution is required and/or highly nonlinear physical processes are operating. For these situations, a basic hypothesis is that the use of the EBKF is sub-optimal and performance gains could be achieved by accounting for aspects of the non-Gaussianty. To this end, we develop here a new component of the Data Assimilation Research Testbed [DART] to allow for a wide-variety of users to test this hypothesis. This new version of DART allows one to run several variants of the EBKF as well as several variants of the quadratic polynomial lter using the same forecast model and observations. Dierences between the results of the two systems will then highlight the degree of non-Gaussianity in the system being examined. We will illustrate in this work the differences between the performance of linear versus quadratic polynomial regression in a hierarchy of models from Lorenz-63 to a simple general circulation model.

On-line control models for the Stanford Linear Collider

International Nuclear Information System (INIS)

Sheppard, J.C.; Helm, R.H.; Lee, M.J.; Woodley, M.D.

1983-03-01

Models for computer control of the SLAC three-kilometer linear accelerator and damping rings have been developed as part of the control system for the Stanford Linear Collider. Some of these models have been tested experimentally and implemented in the control program for routine linac operations. This paper will describe the development and implementation of these models, as well as some of the operational results

Sketching the General Quadratic Equation Using Dynamic Geometry Software

Science.gov (United States)

Stols, G. H.

2005-01-01

This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…

Tangent Lines without Derivatives for Quadratic and Cubic Equations

Science.gov (United States)

Carroll, William J.

2009-01-01

In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

Introduction to geometric nonlinear control; Linearization, observability, decoupling

Energy Technology Data Exchange (ETDEWEB)

Respondek, W [Laboratoire de Mathematiques, INSA de Rouen (France)

2002-07-15

These notes are devoted to the problems of linearization, observability, and decoupling of nonlinear control systems. Together with notes of Bronislaw Jakubczyk in the same volume, they form an introduction to geometric methods in nonlinear control theory. In the first part we discuss equivalence of control systems. We consider various aspects of the problem: state-space and feedback equivalence, local and global equivalence, equivalence to linear and partially linear systems. In the second part we present the notion of observability and give a geometric rank condition for local observability and an algebraic characterization of local observability. We discuss unm observability, decompositions of non-observable systems, and properties of generic observable systems. In the third part we introduce the notion of invariant distributions and discuss disturbance decoupling and input-output decoupling. Many concepts and results are illustrated with examples. (author)

Linear and Non-Linear Control Techniques Applied to Actively Lubricated Journal Bearings

DEFF Research Database (Denmark)

Nicoletti, Rodrigo; Santos, Ilmar

2003-01-01

The main objectives of actively lubricated bearings are the simultaneous reduction of wear and vibration between rotating and stationary machinery parts. For reducing wear and dissipating vibration energy until certain limits, one can count with the conventional hydrodynamic lubrication. For furt......The main objectives of actively lubricated bearings are the simultaneous reduction of wear and vibration between rotating and stationary machinery parts. For reducing wear and dissipating vibration energy until certain limits, one can count with the conventional hydrodynamic lubrication....... For further reduction of shaft vibrations one can count with the active lubrication action, which is based on injecting pressurised oil into the bearing gap through orifices machined in the bearing sliding surface. The design and efficiency of some linear (PD, PI and PID) and non-linear controllers, applied...... vibration reduction of unbalance response of a rigid rotor, where the PD and the non-linear P controllers show better performance for the frequency range of study (0 to 80 Hz). The feasibility of eliminating rotor-bearing instabilities (phenomena of whirl) by using active lubrication is also investigated...

Large linear magnetoresistance from neutral defects in Bi$_2$Se$_3$

OpenAIRE

Kumar, Devendra; Lakhani, Archana

2016-01-01

The chalcogenide Bi$_2$Se$_3$ can attain the three dimensional (3D) Dirac semimetal state under the influence of strain and microstrain. Here we report the presnece of large linear magnetoresistance in such a Bi$_2$Se$_3$ crystal. The magnetoresistance has quadratic form at low fields which crossovers to linear above 4 T. The temperature dependence of magnetoresistance scales with carrier mobility and the crossover field scales with inverse of mobility. Our analysis suggest that the linear ma...

Entanglement-assisted quantum feedback control

Science.gov (United States)

Yamamoto, Naoki; Mikami, Tomoaki

2017-07-01

The main advantage of quantum metrology relies on the effective use of entanglement, which indeed allows us to achieve strictly better estimation performance over the standard quantum limit. In this paper, we propose an analogous method utilizing entanglement for the purpose of feedback control. The system considered is a general linear dynamical quantum system, where the control goal can be systematically formulated as a linear quadratic Gaussian control problem based on the quantum Kalman filtering method; in this setting, an entangled input probe field is effectively used to reduce the estimation error and accordingly the control cost function. In particular, we show that, in the problem of cooling an opto-mechanical oscillator, the entanglement-assisted feedback control can lower the stationary occupation number of the oscillator below the limit attainable by the controller with a coherent probe field and furthermore beats the controller with an optimized squeezed probe field.

Impurity solitons with quadratic nonlinearities

DEFF Research Database (Denmark)

Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis

1998-01-01

We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton...

Cascaded Quadratic Soliton Compression in Waveguide Structures

DEFF Research Database (Denmark)

Guo, Hairun

between the Kerr nonlinear effects and the dispersive effects in the medium. A Kerr-like nonlinearity is produced through the cascaded phase mismatched quadratic process, e.g. the second harmonic generation process, which can be flexibly tuned in both the sign and the amplitude, making possible a strong......-phase-matching technology is not necessarily needed. In large-RI-changed waveguides, CQSC is extended to the mid-infrared range to generate single-cycle pulses with purely nonlinear interactions, since an all-normal dispersion profile could be achieved within the guidance band. We believe that CQSC in quadratic waveguides...

Linear inflation from quartic potential

Energy Technology Data Exchange (ETDEWEB)

Kannike, Kristjan; Racioppi, Antonio [National Institute of Chemical Physics and Biophysics,Rävala 10, 10143 Tallinn (Estonia); Raidal, Martti [National Institute of Chemical Physics and Biophysics,Rävala 10, 10143 Tallinn (Estonia); Institute of Physics, University of Tartu,Tartu (Estonia)

2016-01-07

We show that if the inflaton has a non-minimal coupling to gravity and the Planck scale is dynamically generated, the results of Coleman-Weinberg inflation are confined in between two attractor solutions: quadratic inflation, which is ruled out by the recent measurements, and linear inflation which, instead, is in the experimental allowed region. The minimal scenario has only one free parameter — the inflaton’s non-minimal coupling to gravity — that determines all physical parameters such as the tensor-to-scalar ratio and the reheating temperature of the Universe. Should the more precise future measurements of inflationary parameters point towards linear inflation, further interest in scale-invariant scenarios would be motivated.

Controlling bistability by linear augmentation

International Nuclear Information System (INIS)

Sharma, Pooja Rani; Shrimali, Manish Dev; Prasad, Awadhesh; Feudel, Ulrike

2013-01-01

In many bistable oscillating systems only one of the attractors is desired to possessing certain system performance. We present a method to drive a bistable system to a desired target attractor by annihilating the other one. This shift from bistability to monostability is achieved by augmentation of the nonlinear oscillator with a linear control system. For a proper choice of the control function one of the attractors disappears at a critical coupling strength in an control-induced boundary crisis. This transition from bistability to monostability is demonstrated with two paradigmatic examples, the autonomous Chua oscillator and a neuronal system with a periodic input signal.

The application of the linear-quadratic model to fractionated radiotherapy when there is incomplete normal tissue recovery between fractions, and possible implications for treatments involving multiple fractions per day

International Nuclear Information System (INIS)

Dale, R.G.

1986-01-01

By extending a previously developed mathematical model based on the linear-quadratic dose-effect relationship, it is possible to examine the consequences of performing fractionated treatments for which there is insufficient time between fractions to allow complete damage repair. Equations are derived which give the relative effectiveness of such treatments in terms of tissue-repair constants (μ values) and α/β ratios, and these are then applied to some examples of treatments involving multiple fractions per day. The interplay of the various mechanisms involved (including repopulation effects) and their possible influence on treatments involving closely spaced fractions are examined. If current indications of the differences in recovery rates between early- and late-reacting normal tissues are representative, then it is shown that such differences may limit the clinical potential of accelerated fractionation regimes, where several fractions per day are given in a relatively short overall time. (author)

The Type-2 Fuzzy Logic Controller-Based Maximum Power Point Tracking Algorithm and the Quadratic Boost Converter for Pv System

Science.gov (United States)

Altin, Necmi

2018-05-01

An interval type-2 fuzzy logic controller-based maximum power point tracking algorithm and direct current-direct current (DC-DC) converter topology are proposed for photovoltaic (PV) systems. The proposed maximum power point tracking algorithm is designed based on an interval type-2 fuzzy logic controller that has an ability to handle uncertainties. The change in PV power and the change in PV voltage are determined as inputs of the proposed controller, while the change in duty cycle is determined as the output of the controller. Seven interval type-2 fuzzy sets are determined and used as membership functions for input and output variables. The quadratic boost converter provides high voltage step-up ability without any reduction in performance and stability of the system. The performance of the proposed system is validated through MATLAB/Simulink simulations. It is seen that the proposed system provides high maximum power point tracking speed and accuracy even for fast changing atmospheric conditions and high voltage step-up requirements.

Multimodal Image Alignment via Linear Mapping between Feature Modalities.

Science.gov (United States)

Jiang, Yanyun; Zheng, Yuanjie; Hou, Sujuan; Chang, Yuchou; Gee, James

2017-01-01

We propose a novel landmark matching based method for aligning multimodal images, which is accomplished uniquely by resolving a linear mapping between different feature modalities. This linear mapping results in a new measurement on similarity of images captured from different modalities. In addition, our method simultaneously solves this linear mapping and the landmark correspondences by minimizing a convex quadratic function. Our method can estimate complex image relationship between different modalities and nonlinear nonrigid spatial transformations even in the presence of heavy noise, as shown in our experiments carried out by using a variety of image modalities.

Use of probabilistic weights to enhance linear regression myoelectric control

Science.gov (United States)

Smith, Lauren H.; Kuiken, Todd A.; Hargrove, Levi J.

2015-12-01

Objective. Clinically available prostheses for transradial amputees do not allow simultaneous myoelectric control of degrees of freedom (DOFs). Linear regression methods can provide simultaneous myoelectric control, but frequently also result in difficulty with isolating individual DOFs when desired. This study evaluated the potential of using probabilistic estimates of categories of gross prosthesis movement, which are commonly used in classification-based myoelectric control, to enhance linear regression myoelectric control. Approach. Gaussian models were fit to electromyogram (EMG) feature distributions for three movement classes at each DOF (no movement, or movement in either direction) and used to weight the output of linear regression models by the probability that the user intended the movement. Eight able-bodied and two transradial amputee subjects worked in a virtual Fitts’ law task to evaluate differences in controllability between linear regression and probability-weighted regression for an intramuscular EMG-based three-DOF wrist and hand system. Main results. Real-time and offline analyses in able-bodied subjects demonstrated that probability weighting improved performance during single-DOF tasks (p < 0.05) by preventing extraneous movement at additional DOFs. Similar results were seen in experiments with two transradial amputees. Though goodness-of-fit evaluations suggested that the EMG feature distributions showed some deviations from the Gaussian, equal-covariance assumptions used in this experiment, the assumptions were sufficiently met to provide improved performance compared to linear regression control. Significance. Use of probability weights can improve the ability to isolate individual during linear regression myoelectric control, while maintaining the ability to simultaneously control multiple DOFs.

Linear programming foundations and extensions

CERN Document Server

Vanderbei, Robert J

2001-01-01

Linear Programming: Foundations and Extensions is an introduction to the field of optimization. The book emphasizes constrained optimization, beginning with a substantial treatment of linear programming, and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. The book is carefully written. Specific examples and concrete algorithms precede more abstract topics. Topics are clearly developed with a large number of numerical examples worked out in detail. Moreover, Linear Programming: Foundations and Extensions underscores the purpose of optimization: to solve practical problems on a computer. Accordingly, the book is coordinated with free efficient C programs that implement the major algorithms studied: -The two-phase simplex method; -The primal-dual simplex method; -The path-following interior-point method; -The homogeneous self-dual methods. In addition, there are online JAVA applets that illustrate various pivot rules and variants of the simplex m...

The quadratic reciprocity law a collection of classical proofs

CERN Document Server

Baumgart, Oswald

2015-01-01

This book is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise”), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart’s comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory.

Graph Modeling for Quadratic Assignment Problems Associated with the Hypercube

International Nuclear Information System (INIS)

Mittelmann, Hans; Peng Jiming; Wu Xiaolin

2009-01-01

In the paper we consider the quadratic assignment problem arising from channel coding in communications where one coefficient matrix is the adjacency matrix of a hypercube in a finite dimensional space. By using the geometric structure of the hypercube, we first show that there exist at least n different optimal solutions to the underlying QAPs. Moreover, the inherent symmetries in the associated hypercube allow us to obtain partial information regarding the optimal solutions and thus shrink the search space and improve all the existing QAP solvers for the underlying QAPs.Secondly, we use graph modeling technique to derive a new integer linear program (ILP) models for the underlying QAPs. The new ILP model has n(n-1) binary variables and O(n 3 log(n)) linear constraints. This yields the smallest known number of binary variables for the ILP reformulation of QAPs. Various relaxations of the new ILP model are obtained based on the graphical characterization of the hypercube, and the lower bounds provided by the LP relaxations of the new model are analyzed and compared with what provided by several classical LP relaxations of QAPs in the literature.

Linear dynamical quantum systems analysis, synthesis, and control

CERN Document Server

Nurdin, Hendra I

2017-01-01

This monograph provides an in-depth treatment of the class of linear-dynamical quantum systems. The monograph presents a detailed account of the mathematical modeling of these systems using linear algebra and quantum stochastic calculus as the main tools for a treatment that emphasizes a system-theoretic point of view and the control-theoretic formulations of quantum versions of familiar problems from the classical (non-quantum) setting, including estimation and filtering, realization theory, and feedback control. Both measurement-based feedback control (i.e., feedback control by a classical system involving a continuous-time measurement process) and coherent feedback control (i.e., feedback control by another quantum system without the intervention of any measurements in the feedback loop) are treated. Researchers and graduates studying systems and control theory, quantum probability and stochastics or stochastic control whether from backgrounds in mechanical or electrical engineering or applied mathematics ...

Synchronization and Control of Linearly Coupled Singular Systems

Directory of Open Access Journals (Sweden)

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.

Innovation in Active Vibration Control Strategy of Intelligent Structures

Directory of Open Access Journals (Sweden)

A. Moutsopoulou

2014-01-01

Full Text Available Large amplitudes and attenuating vibration periods result in fatigue, instability, and poor structural performance. In light of past approaches in this field, this paper intends to discuss some innovative approaches in vibration control of intelligent structures, particularly in the case of structures with embedded piezoelectric materials. Control strategies are presented, such as the linear quadratic control theory, as well as more advanced theories, such as robust control theory. The paper presents sufficiently a recognizable advance in knowledge of active vibration control in intelligent structures.

Minimal representation of matrix valued white stochastic processes and U–D factorisation of algorithms for optimal control

NARCIS (Netherlands)

Willigenburg, van L.G.; Koning, de W.L.

2013-01-01

Two different descriptions are used in the literature to formulate the optimal dynamic output feedback control problem for linear dynamical systems with white stochastic parameters and quadratic criteria, called the optimal compensation problem. One describes the matrix valued white stochastic

Mixed H∞ and passive control for linear switched systems via hybrid control approach

Science.gov (United States)

Zheng, Qunxian; Ling, Youzhu; Wei, Lisheng; Zhang, Hongbin

2018-03-01

This paper investigates the mixed H∞ and passive control problem for linear switched systems based on a hybrid control strategy. To solve this problem, first, a new performance index is proposed. This performance index can be viewed as the mixed weighted H∞ and passivity performance. Then, the hybrid controllers are used to stabilise the switched systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. The design of state updating controllers not only depends on the pre-switching subsystem and the post-switching subsystem, but also depends on the measurable output signal. The hybrid controllers proposed in this paper can include some existing ones as special cases. Combine the multiple Lyapunov functions approach with the average dwell time technique, new sufficient conditions are obtained. Under the new conditions, the closed-loop linear switched systems are globally uniformly asymptotically stable with a mixed H∞ and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities. Finally, a numerical example and a practical example are given.

On quadratic variation of martingales

Indian Academy of Sciences (India)

On quadratic variation of martingales. 459. The proof relied on the theory of stochastic integration. Subsequently, in Karandikar. [4], the formula was derived using only Doob's maximal inequality. Thus this could be the starting point for the development of stochastic calculus for continuous semimartingales without bringing in ...

Model-based dynamic control and optimization of gas networks

Energy Technology Data Exchange (ETDEWEB)

Hofsten, Kai

2001-07-01

This work contributes to the research on control, optimization and simulation of gas transmission systems to support the dispatch personnel at gas control centres for the decision makings in the daily operation of the natural gas transportation systems. Different control and optimization strategies have been studied. The focus is on the operation of long distance natural gas transportation systems. Stationary optimization in conjunction with linear model predictive control using state space models is proposed for supply security, the control of quality parameters and minimization of transportation costs for networks offering transportation services. The result from the stationary optimization together with a reformulation of a simplified fluid flow model formulates a linear dynamic optimization model. This model is used in a finite time control and state constrained linear model predictive controller. The deviation from the control and the state reference determined from the stationary optimization is penalized quadratically. Because of the time varying status of infrastructure, the control space is also generally time varying. When the average load is expected to change considerably, a new stationary optimization is performed, giving a new state and control reference together with a new dynamic model that is used for both optimization and state estimation. Another proposed control strategy is a control and output constrained nonlinear model predictive controller for the operation of gas transmission systems. Here, the objective is also the security of the supply, quality control and minimization of transportation costs. An output vector is defined, which together with a control vector are both penalized quadratically from their respective references in the objective function. The nonlinear model predictive controller can be combined with a stationary optimization. At each sampling instant, a non convex nonlinear programming problem is solved giving a local minimum

Eigenfunctions of quadratic hamiltonians in Wigner representation

International Nuclear Information System (INIS)

Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.

1984-01-01

Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail

Hybrid vehicle optimal control : Linear interpolation and singular control

NARCIS (Netherlands)

Delprat, S.; Hofman, T.

2015-01-01

Hybrid vehicle energy management can be formulated as an optimal control problem. Considering that the fuel consumption is often computed using linear interpolation over lookup table data, a rigorous analysis of the necessary conditions provided by the Pontryagin Minimum Principle is conducted. For

Remarks on second-order quadratic systems in algebras