Optimal Control of Linear Nonstandard Singularly Perturbed Discrete Systems

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6 Citations (Scopus)

Abstract

This paper introduces the definition of the nonstandard linear discrete-time singularly perturbed system and then shows how to solve the corresponding linear-quadratic optimal control problem since the methodology that exists in the literature for the solution of the standard singularly perturbed discrete linear-quadratic optimal control problem can not be extended to the corresponding nonstandard counterpart. The solution of the optimal control problem is obtained in terms of the pure-slow and pure-fast, reduced-order, continuous-time, algebraic Riccati equations. An example is included to illustrate the efficiency of the proposed method.

Original languageEnglish
Pages (from-to)163-174
Number of pages12
JournalDynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm
Volume9
Issue number2
Publication statusPublished - 2002 Jun 1

Fingerprint

Perturbed System
Singularly Perturbed
Discrete Systems
Optimal Control Problem
Optimal Control
Singularly Perturbed Systems
Algebraic Riccati Equation
Riccati equations
Continuous Time
Discrete-time
Methodology

Keywords

  • Optimal control
  • Order reduction
  • Parallel computation
  • Riccati equation
  • Singular perturbation

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

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abstract = "This paper introduces the definition of the nonstandard linear discrete-time singularly perturbed system and then shows how to solve the corresponding linear-quadratic optimal control problem since the methodology that exists in the literature for the solution of the standard singularly perturbed discrete linear-quadratic optimal control problem can not be extended to the corresponding nonstandard counterpart. The solution of the optimal control problem is obtained in terms of the pure-slow and pure-fast, reduced-order, continuous-time, algebraic Riccati equations. An example is included to illustrate the efficiency of the proposed method.",
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AU - Kang, Chung Gu

AU - Kim, Beom S.

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N2 - This paper introduces the definition of the nonstandard linear discrete-time singularly perturbed system and then shows how to solve the corresponding linear-quadratic optimal control problem since the methodology that exists in the literature for the solution of the standard singularly perturbed discrete linear-quadratic optimal control problem can not be extended to the corresponding nonstandard counterpart. The solution of the optimal control problem is obtained in terms of the pure-slow and pure-fast, reduced-order, continuous-time, algebraic Riccati equations. An example is included to illustrate the efficiency of the proposed method.

AB - This paper introduces the definition of the nonstandard linear discrete-time singularly perturbed system and then shows how to solve the corresponding linear-quadratic optimal control problem since the methodology that exists in the literature for the solution of the standard singularly perturbed discrete linear-quadratic optimal control problem can not be extended to the corresponding nonstandard counterpart. The solution of the optimal control problem is obtained in terms of the pure-slow and pure-fast, reduced-order, continuous-time, algebraic Riccati equations. An example is included to illustrate the efficiency of the proposed method.

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KW - Order reduction

KW - Parallel computation

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KW - Singular perturbation

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