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OPTIMAL CONTROL PROBLEMS FOR GENERAL GLOBAL HYBRID DYNAMICAL SYSTEMS WITH MATRIX COST FUNCTIONAL

Part of: Existence theories

Published online by Cambridge University Press:  04 October 2010

RUI GAO  and
XINZHI LIU
RUI GAO*
Affiliation:
School of Control Science & Engineering, Shandong University, 250061 Ji’nan, PR China (email: gaorui@sdu.edu.cn)
XINZHI LIU
Affiliation:
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 (email: xzliu@waterloo.ca)
*
✉For correspondence; e-mail: gaorui@sdu.edu.cn]
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Abstract

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This paper considers an optimal control problem for a class of controlled hybrid dynamical systems (HDSs) with prescribed switchings. By using Ekeland’s variational principle and a matrix cost functional, a minimum principle for HDSs is derived, which provides a necessary condition of the aforementioned problem. The results given in this paper include both pure continuous systems and pure discrete-time systems as special cases.

Keywords

hybrid dynamical systemoptimal controlminimum principleEkeland’s variational principlerestricted terminal states

MSC classification

Secondary: 49J21: Optimal control problems involving relations other than differential equations
Type
Research Article
Information
The ANZIAM Journal , Volume 51 , Issue 3 , January 2010 , pp. 331 - 349
Copyright
Copyright © Australian Mathematical Society 2010

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