Application of general orthogonal polynomials to the optimal control of time-varying linear systems

Chang, Yih-Fong; Lee, Tsu‐Tian

doi:10.1080/00207178608933538

Cited by 26 publications

(9 citation statements)

References 9 publications

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“…Finally, as given in the tables, the proposed method shows more accurate results when compared with some of the existing mentioned references. Therefore, we may conclude that the results of Chang and Lee (1986) and Hsiao and Wang (1999) are modified.…”

Section: Introductionmentioning

confidence: 83%

“…Example 1 Consider the time-varying system described by Chang and Lee (1986) x(t) = tx(t) + u(t), x(0) = 1.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…The polynomial approximations of time functions have been taken by many researchers to solve control problems (Chang & Lee, 1986;Hwang & Chen, 1985;Razzaghi, 1990). Optimizations of time-varying systems have been of considerable interest to control engineers in the recent years (Hsiao & Wang, 1999;Wang, 2007).…”

Section: Introductionmentioning

confidence: 99%

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Optimal control of linear time-varying systems using the Chebyshev wavelets (a comparative approach)

Radhoush

Samavat

Vali

2014

Systems Science & Control Engineering

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This paper extends the application of continuous Chebyshev wavelet expansions to find the optimal solution of linear timevarying systems using two different approaches. By using the product of two time functions together with the operational matrix of integration, the system of state equations are changed into a set of algebraic equations which can be solved using a digital computer. In addition, the Chebyshev wavelets are more successful to find the optimal solution of linear time-varying systems when compared with the other existing mentioned algorithms. Finally, the main feature of this paper over similar possible works is that the use of the Lagrange multipliers approach gives more accurate results in comparison with the results of the Riccati approach. The given examples support these claims.

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Section: Introductionmentioning

confidence: 83%

“…Example 1 Consider the time-varying system described by Chang and Lee (1986) x(t) = tx(t) + u(t), x(0) = 1.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Optimal control of linear time-varying systems using the Chebyshev wavelets (a comparative approach)

Radhoush

Samavat

Vali

2014

Systems Science & Control Engineering

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“…The proposed approach is linear, noniterative, nondifferential, nonintegral, and well adapted to computer implementation. Let f s, I be a sequence of orthogonal polynomials in the interval T, such as shifted Chebychev or Legendre polynomials (Chang and Lee, 1986), and let S(t) = [so (t), Sl (t), ..., Sm-1 (t)] be a vector of the first m orthogonal functions of fs, 1. The functions Us can then be approximated in terms of the following orthogonal functions:…”

Section: Determination Of the Optimal Boundary Controlmentioning

confidence: 99%

A Solution Method for Boundary Control of One-Dimensional Multispan Vibrating Systems

Sadek

Jamru

Almohamad

1999

Journal of Vibration and Control

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Many flexible structures consist of a large number of components coupled end to end in the form of a chain. In this study, the authors consider a type of such structures formed by N one-dimensional coupled structures, with (N — 1) controllers at the coupled points. A method of solution for such a special class of optimal control problems is suggested by using an eigenfunction expansion and the maximum principle. This solution involves reducing the original problem to a system of ordinary differential equations. For comparative studies, the special problem is also solved by the variational approach, which leads to a system of integral equations as a necessary and sufficient condition of optimality The effectiveness of these approaches is demonstrated by means of a numerical solution for controlling the vibrations of two strings that are coupled at the connecting point.

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“…These general orthogonal polynomials are ~o( () = 1, ~1 (() = ao ( + bo and (36.2) The values of the recurrence coefficients ai, bi, ci are listed in Table 36.3 (Chang, Y.F., and Lee, T. T., 1986). The variable ( is defined in the interval a ::; ( ::; b, only.…”

Section: General Orthogonal Polynomials 'Pi(()mentioning

confidence: 99%

Uncertain Models and Robust Control

Weinmann¹

1991

310

126

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PrefaceControl system analysis and design are important fields in the engineering sciences. Process identification and optimum design have developed rapidly over the past decades and resulted in great engineering progress. However, many results have suffered from considerable dependence on uncertainties, mainly incorporated in the plant, in actuators and sensors, and released by other internal disturbances.More and more, methods tackling uncertainties form a central and important issue in designing feedback control systems. Choosing appropriate design methods, the influence of uncertainties on the closed-loop behaviour can be reduced to a large extent. Control systems particularly designed to manage uncertainties are called robust control systems. Robust control theory provides a design philosophy with respect to perturbed or uncertain parts of the system. This monograph is devoted to plants and their approximate models and to the discussion of their uncertainties. The thrust of the book is on systematic representation of methods for robust control.Most of the important areas of robust control are covered. The aim is to provide an introduction to the theory and methods of robust control system design, to present a coherent body of knowledge, to clarify and unify presentation, and to streamline derivations and proofs in the field of uncertainties and robust control. The book contains a thorough treatment of important material which is scattered throughout the literature.The primary goal of the text is to present significant derivations and proofs. As far as less significant proofs or lengthy derivations are concerned, only the results are outlined and the reader is referred to the literature relevant to this subject. In a few cases, some topics are set forth only as a suggestion for further reading.Some important problems treated in this book are:• How is uncertainty described and bounded when applying methods of differential equations, transfer functions or transfer matrices, state-space algorithms or some approximating calculus?• Which uncertainty or which perturbation in some special system description forces the system to instability? This question arises both for open-loop and for closed-loop systems.• Which kind of controller is able to tolerate maximum uncertainty?2In most cases stability robustness is applied but performance robustness is also a very important subject, e.g., determining the regions in the parameter space of controllers which place all the closed-loop eigenvalues into a desired region, thus satisfying the design specifications in the face of uncertain but bounded plant parameters.The book is intended specifically for practicing but mathematically inclined engineers, for postgraduate students and engineers on master's level. Moreover, the book is intended for those readers who wish to apply robust design principles and theories to real-life applications and problems.Emphasis is put on practical considerations and on applicability at the expense of extensive proofs and mathematical rigor.The ...

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Application of general orthogonal polynomials to the optimal control of time-varying linear systems

Cited by 26 publications

References 9 publications

Optimal control of linear time-varying systems using the Chebyshev wavelets (a comparative approach)

Optimal control of linear time-varying systems using the Chebyshev wavelets (a comparative approach)

A Solution Method for Boundary Control of One-Dimensional Multispan Vibrating Systems

Uncertain Models and Robust Control

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