Composite control for singularly perturbed nonlinear systems via successive Galerkin approximation

Young Joong Kim, Beom S. Kim, Myo Taeg Lim

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This paper presents a new algorithm of the closed-loop composite control for singularly perturbed nonlinear systems with respect to performance criteria, using the successive Galerkin approximation(SGA). The singularly perturbed nonlinear system is decomposed into two subsystems of a slow-time scale and a fast-time scale by the singular perturbation theory, and two optimal control laws are obtained to each subsystem using the SGA method. The composite control law that consists of two optimal control laws of each subsystem is designed. One of the purposes of this paper is to design the closed-loop composite control law for the singularly perturbed nonlinear systems via the SGA method. The other is to reduce the computational complexity when the SGA method is applied to the high order systems.

Original languageEnglish
Pages (from-to)247-258
Number of pages12
JournalDynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms
Volume10
Issue number1-3
Publication statusPublished - 2003 Feb 1

Fingerprint

Galerkin Approximation
Successive Approximation
Perturbed System
Singularly Perturbed
Nonlinear systems
Nonlinear Systems
Composite
Galerkin Method
Approximation Methods
Subsystem
Composite materials
Closed-loop
Optimal Control
Time Scales
Singular Perturbation Theory
Computational Complexity
Higher Order
Computational complexity

Keywords

  • Composite control
  • Near-optimal control
  • Nonlinear system
  • Singular perturbation
  • Successive Galerkin Approximation

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

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N2 - This paper presents a new algorithm of the closed-loop composite control for singularly perturbed nonlinear systems with respect to performance criteria, using the successive Galerkin approximation(SGA). The singularly perturbed nonlinear system is decomposed into two subsystems of a slow-time scale and a fast-time scale by the singular perturbation theory, and two optimal control laws are obtained to each subsystem using the SGA method. The composite control law that consists of two optimal control laws of each subsystem is designed. One of the purposes of this paper is to design the closed-loop composite control law for the singularly perturbed nonlinear systems via the SGA method. The other is to reduce the computational complexity when the SGA method is applied to the high order systems.

AB - This paper presents a new algorithm of the closed-loop composite control for singularly perturbed nonlinear systems with respect to performance criteria, using the successive Galerkin approximation(SGA). The singularly perturbed nonlinear system is decomposed into two subsystems of a slow-time scale and a fast-time scale by the singular perturbation theory, and two optimal control laws are obtained to each subsystem using the SGA method. The composite control law that consists of two optimal control laws of each subsystem is designed. One of the purposes of this paper is to design the closed-loop composite control law for the singularly perturbed nonlinear systems via the SGA method. The other is to reduce the computational complexity when the SGA method is applied to the high order systems.

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