Design of optimal controller for interval plant from signal energy point of view via evolutionary approaches

Chen-Chien James Hsu, Chih Yung Yu

Research output: Contribution to journalLetter

18 Citations (Scopus)

Abstract

Design of an optimal controller minimizing the integral of squared error (ISE) of the closed-loop system for an interval plant via evolutionary approaches is proposed in this paper. Based on a worst-case design philosophy, the design problem is formulated as a minimax optimization problem from the signal energy point of view, and subsequently solved by two interactive genetic algorithms. To ensure robust stability of the closed-loop system, root locations of the Kharitonov polynomials associated with the characteristic polynomial are used to establish a constraint handling mechanism for incorporation into the fitness function to effectively evaluate chromosomes in the current population. To accelerate the derivation process to obtain the optimal controller, alternative approaches based on the two-phase evolutionary scheme are also proposed, in which the worst-case ISE is suitably estimated via information provided by the Kharitonov plants. Thus, the derived controller not only stabilizes the interval plant, but also minimizes the ISE criterion of the closed-loop system. Constraints on higher order plants and controller order commonly encountered by conventional design methods are therefore removed by using the proposed approach.

Original languageEnglish
Pages (from-to)1609-1617
Number of pages9
JournalIEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Volume34
Issue number3
DOIs
Publication statusPublished - 2004 Jun 1

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Closed loop systems
Controllers
Polynomials
Chromosomes
Genetic algorithms
Population

Keywords

  • Genetic algorithms
  • Integral of squared error (ISE)
  • Interval plants
  • Minimax optimization
  • Robust controllers
  • Signal energy

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Medicine(all)
  • Information Systems
  • Human-Computer Interaction
  • Computer Science Applications
  • Electrical and Electronic Engineering

Cite this

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abstract = "Design of an optimal controller minimizing the integral of squared error (ISE) of the closed-loop system for an interval plant via evolutionary approaches is proposed in this paper. Based on a worst-case design philosophy, the design problem is formulated as a minimax optimization problem from the signal energy point of view, and subsequently solved by two interactive genetic algorithms. To ensure robust stability of the closed-loop system, root locations of the Kharitonov polynomials associated with the characteristic polynomial are used to establish a constraint handling mechanism for incorporation into the fitness function to effectively evaluate chromosomes in the current population. To accelerate the derivation process to obtain the optimal controller, alternative approaches based on the two-phase evolutionary scheme are also proposed, in which the worst-case ISE is suitably estimated via information provided by the Kharitonov plants. Thus, the derived controller not only stabilizes the interval plant, but also minimizes the ISE criterion of the closed-loop system. Constraints on higher order plants and controller order commonly encountered by conventional design methods are therefore removed by using the proposed approach.",
keywords = "Genetic algorithms, Integral of squared error (ISE), Interval plants, Minimax optimization, Robust controllers, Signal energy",
author = "Hsu, {Chen-Chien James} and Yu, {Chih Yung}",
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AU - Yu, Chih Yung

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N2 - Design of an optimal controller minimizing the integral of squared error (ISE) of the closed-loop system for an interval plant via evolutionary approaches is proposed in this paper. Based on a worst-case design philosophy, the design problem is formulated as a minimax optimization problem from the signal energy point of view, and subsequently solved by two interactive genetic algorithms. To ensure robust stability of the closed-loop system, root locations of the Kharitonov polynomials associated with the characteristic polynomial are used to establish a constraint handling mechanism for incorporation into the fitness function to effectively evaluate chromosomes in the current population. To accelerate the derivation process to obtain the optimal controller, alternative approaches based on the two-phase evolutionary scheme are also proposed, in which the worst-case ISE is suitably estimated via information provided by the Kharitonov plants. Thus, the derived controller not only stabilizes the interval plant, but also minimizes the ISE criterion of the closed-loop system. Constraints on higher order plants and controller order commonly encountered by conventional design methods are therefore removed by using the proposed approach.

AB - Design of an optimal controller minimizing the integral of squared error (ISE) of the closed-loop system for an interval plant via evolutionary approaches is proposed in this paper. Based on a worst-case design philosophy, the design problem is formulated as a minimax optimization problem from the signal energy point of view, and subsequently solved by two interactive genetic algorithms. To ensure robust stability of the closed-loop system, root locations of the Kharitonov polynomials associated with the characteristic polynomial are used to establish a constraint handling mechanism for incorporation into the fitness function to effectively evaluate chromosomes in the current population. To accelerate the derivation process to obtain the optimal controller, alternative approaches based on the two-phase evolutionary scheme are also proposed, in which the worst-case ISE is suitably estimated via information provided by the Kharitonov plants. Thus, the derived controller not only stabilizes the interval plant, but also minimizes the ISE criterion of the closed-loop system. Constraints on higher order plants and controller order commonly encountered by conventional design methods are therefore removed by using the proposed approach.

KW - Genetic algorithms

KW - Integral of squared error (ISE)

KW - Interval plants

KW - Minimax optimization

KW - Robust controllers

KW - Signal energy

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