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A multi-sector analysis for dynamic quantizer synthesis

A multi-sector analysis for dynamic quantizer synthesis

引用

ieee international symposium on computer aided control system design (cacsd)

作者： Kenji Sawada Seiichi Shin Department of System Engineering University of Electro-Communications Chofu Tokyo Japan

This paper considers analysis and synthesis methods of dynamic quantizers for linear feedback systems with discrete-valued signal, which consist of the linear system and the dynamic quantizer. We propose a multi-sector condition such that the quantization error is expressed in terms of the combination of various sector conditions. First, this paper proposes quantizer analysis conditions by using the multi-sector condition and the S-procedure. Second, this paper considers quantizer synthesis conditions based on the multi-sector analysis framework. Our method can design a stable quantizer such that the order of the quantizer is exactly the same as that of the given linear system and the infinite time control performance is always guaranteed. Finally, this paper points out that the proposed methods are helpful compared with the methods based on the invariant set analysis framework through numerical examples.

关键词： Quantization control systems Optimization Linear matrix inequalities Symmetric matrices Ellipsoids design methodology

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control-theoretic analysis of exploitation and exploration of the PSO algorithm

Control-theoretic analysis of exploitation and exploration o...

引用

ieee international symposium on computer aided control system design (cacsd)

作者： Yuji Wakasa Kanya Tanaka Yuki Nishimura Graduate School of Science and Engineering Yamaguchi University Ube Yamaguchi Japan

The behavior of the particle swarm optimization (PSO) algorithm is analyzed by regarding its dynamics as a system with multiplicative noise and applying control-theoretic analysis methods. In order to evaluate the convergence and diversity of the PSO algorithm, two measures related to the decay rate and l 2 gain of the PSO dynamics are used. These measures are characterized by linear matrix inequalities (LMIs) and are therefore efficiently computed by convex optimization tools. As for the measure related to the decay rate, moreover, an alternative condition in terms of nonlinear scalar inequalities is presented which can be checked more shortly and accurately than the LMI. Numerical experiments suggest that the measures are effective enough to evaluate the convergence and diversity of the PSO algorithm, which results in better understanding of the PSO algorithm from the viewpoints of exploitation and exploration abilities.

关键词： Algorithm design and analysis Convergence Random variables Numerical stability Stability analysis Heuristic algorithms Noise

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Markov Chain Monte Carlo method exploiting barrier functions with applications to control and optimization

Markov Chain Monte Carlo method exploiting barrier functions...

引用

ieee international symposium on computer aided control system design (cacsd)

作者： B.T. Polyak E.N. Gryazina Control Sciences RAS Moscow Russia

In previous works the authors proposed to use Hit-and-Run (H&R) versions of Markov Chain Monte Carlo (MCMC) algorithms for various problems of control and optimization. However the results are unsatisfactory for “bad“ sets, such as level sets of ill-posed functions. The idea of the present paper is to exploit the technique developed for interior-point methods of convex optimization, and to combine it with MCMC algorithms. We present a new modification of H&R method exploiting barrier functions and its validation. Such approach is well tailored for sets defined by linear matrix inequalities (LMI), which are widely used in control and optimization. The results of numerical simulation are promising.

关键词： Optimization Ellipsoids Monte Carlo methods Markov processes Convex functions Linear matrix inequalities Correlation

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design of nonlinear feedback systems with inputs and outputs satisfying bounding conditions

Design of nonlinear feedback systems with inputs and outputs...

引用

ieee international symposium on computer aided control system design (cacsd)

作者： Van Sy Mai Suchin Arunsawatwong Eyad H. Abed Department of Electrical Engineering Faculty of Engineering Chulalongkom University Bangkok Thailand Department of Electrical and Computer Engineering University of Maryland College Park MD USA

This paper develops a method for designing a feedback system comprising a static memoryless nonlinearity and linear time-invariant convolution subsystems so as to ensure that the error and the controller output stay within prescribed bounds for all time and for all inputs having bounded magnitude and bounded slope. Since the original design criteria are computationally intractable, we derive practical sufficient conditions for ensuring them. The conditions provide surrogate design criteria that are in keeping with the method of inequalities. Essentially, the nonlinearity is replaced with a fixed gain and an equivalent disturbance; thus, the nominal system used during the design process becomes linear and the associated performance measures are readily obtainable by known methods. To illustrate the usefulness of the method, a design example of a hydraulic force control system is given.

关键词： control systems Stability criteria Numerical stability Nonlinear systems Linear systems Transfer functions Asymptotic stability

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Robust generation of LPV state-space models using a regularized ℌ2-cost

Robust generation of LPV state-space models using a regulari...

引用

ieee international symposium on computer aided control system design (cacsd)

作者： Daniel Petersson Johan Löfberg Division of Automatic Control Department of Electrical Engineering Linköping Universitet Sweden Division of Automatic Control Löinkpings universitet Sweden

In this paper we present a regularization of an H 2 -minimization based LPV-model generation algorithm. Our goal is to take care of uncertainties in the data, and obtain more robust models when we have few data. We give an interpretation of the regularization, which shows that the regularization has connections to robust optimization and worst-case approaches. We present how to effectively calculate the original cost function and its gradient, and extend these ideas to the regularized cost function and its gradient. A few examples, illustrating effects of both uncertain and few data, are finally presented to show the validity of the regularization.

关键词： Cost function Mathematical model Bismuth Robustness Polynomials

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Set computations with subpavings in MATLAB: The SCS Toolbox

Set computations with subpavings in MATLAB: The SCS Toolbox

引用

ieee international symposium on computer aided control system design (cacsd)

作者： Sebastian Tornil-Sin Vicenç Puig Teresa Escobet Advanced Control Systems research group Technical University of Catalonia Terrassa Spain

This paper presents a MATLAB Toolbox that allows to represent and manipulate subpavings, i.e. unions of non-overlapped boxes. The main property of subpavings is their ability to approximate compact sets in W1 with arbitrary precision. The functions provided in the SCS Toolbox allow to: create subpavings; calculate the union and the intersection between subpavings; evaluate the image of a subpaving by a function; evaluate the inverse image; visualize subpavings in R2. The algorithms for function evaluation (both image and inverse image), based on interval analysis tools, allow to deal with non-linear functions. The set of provided functions can be easily used to solve a wide spectrum of problems involving uncertainty that are studied in the automatic control literature. Two examples are presented, a parameter estimation problem where the measurements are uncertain and the simulation of a system from an uncertain initial state.

关键词： MATLAB Approximation methods Uncertainty Approximation algorithms Measurement uncertainty Binary trees Programming

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Nonlinear robust optimization of uncertainty affine dynamic systems under the L-infinity norm

Nonlinear robust optimization of uncertainty affine dynamic ...

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ieee international symposium on computer aided control system design (cacsd)

作者： Boris Houska Moritz Diehl Optimization in Engineering Center OPTEC K.U. Leuven Leuven Belgium

In this paper, we discuss robust optimal control techniques for dynamic systems which are affine in the uncertainty. Here, the uncertainty is assumed to be time-dependent but bounded by an L-infinity norm. We are interested in finding a tight upper bound for the worst case excitation of the inequality state constraints requiring to solve a parameterized lower-level maximization problem. In this paper, we suggest to replace this lower level maximization problem by an equivalent minimization problem using a special version of modified Lyapunov equations. This new reformulation offers advantages for robust optimal control problems where the uncertainty is time-dependent, i.e. infinite dimensional, while the inequality state constraints need to be robustly regarded on the whole time horizon.

关键词： Robustness Optimal control Optimization Approximation methods Uncertainty Differential equations Cranes

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Decentralized guaranteed cost PID control for uncertain large-scale deterministic and stochastic discrete-time systems with additive gain

Decentralized guaranteed cost PID control for uncertain larg...

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ieee international symposium on computer aided control system design (cacsd)

作者： Hiroaki Mukaidani Hua Xu Graduate School of Education Hiroshima University Higashihiroshima Japan Graduate School of Business Sciences University of Tsukuba Bunkyo Tokyo Japan

This paper investigates a novel design method for robust proportional-integral-derivative (PID) control that is based on the decentralized guaranteed cost control (DGCC) problem for a class of discrete-time large-scale uncertain deterministic and stochastic systems with additive gain. On the basis of linear matrix inequality (LMI), a class of fixed PID controller parameters is obtained, and some sufficient conditions for the existence of the DGCC are derived. A novel concept is that the fixed PID controller parameters are combined with additive gain such as that in fuzzy control to enhance the transient stability. Although the additive gain is included in the feedback systems, the stability of closed-loop systems and desired transient response are both attained.

关键词： Linear matrix inequalities Additives Stochastic systems Symmetric matrices Uncertain systems Niobium Bismuth

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A numerical evaluation of highly accurate multiple-precision arithmetic version of semidefinite programming solver: SDPA-GMP, -QD and -DD.

A numerical evaluation of highly accurate multiple-precision...

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ieee international symposium on computer aided control system design (cacsd)

作者： Maho Nakata Advanced Center for Computing and Communication RIKEN Saitama Japan

Semidefinite programming (SDP) is an important branch of optimization and has wide range of applications: engineering, industry, chemistry, mathematics, etc. However, obtaining very accurate optimum for a semidefinite programming is difficult in general, especially for ill-posed ones. In this paper, we evaluated numerically highly accurate SDP solvers; SDPA-GMP, -QD and -DD, which employ multiple-precision arithmetic and mainly developed by our group. We applied to some problems from SDPLIB benchmark which contains some ill-posed problems as well. The SDPA-GMP, and -QD solved problems very accurately, whereas SDPA failed or obtained inaccurate optima. The SDPA-DD may be used for compensation for accuracy and speed. We also investigated the convergence behaviors which agreed well what theories indicated.

关键词： Libraries Convergence Accuracy Programming Mathematical model Equations ieee standards

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Sliding mode control for singularly perturbed linear continuous time systems: Composite control approaches

Sliding mode control for singularly perturbed linear continu...

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ieee international symposium on computer aided control system design (cacsd)

作者： Thang Nguyen Wu-Chung Su Zoran Gajic Department of Electrical Engineering Rutgers University Piscataway NJ USA Department of Electrical Engineering National Chung Hsing University Taichung Taiwan

We investigate the problem of sliding mode control for singularly perturbed systems with external disturbances. Although the system can be decoupled into two time-scales in terms of two lower dimensional state vectors, the similar type of decomposition does not hold for the control law and the disturbance. The system decoupling transformation can only decompose the control law and the disturbances into two time-scales but not reduce their dimensions. Therefore, only one subsystem is designed to enter the sliding mode. Two composite control approaches are proposed to handle the stability and disturbance rejection problems: state feedback control used to stabilize slow or fast modes and discontinuous control used to deal with the remaining modes. A numerical example of a longitudinal model of an F8 aircraft is provided to illustrate the efficiency of the proposed methods.

关键词： Sliding mode control State feedback Asymptotic stability Eigenvalues and eigenfunctions Numerical stability Equations

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