A unified theory of maximumprinciple for continuous and discrete time optimal control problems

Zaidong Zhan; Shuping Chen; Wei Wei

doi:10.3934/mcrf.2012.2.195

Article Contents

2012, Volume 2, Issue 2: 195-215. Doi: 10.3934/mcrf.2012.2.195

This issue Previous Article Finite element method for constrained optimal control problems governed by nonlinear elliptic PDEs Next Article

A unified theory of maximum principle for continuous and discrete time optimal control problems

1.
Department of Mathematics, Zhejiang University, Zhejiang, Hangzhou, 310027
2.
Department of Mathematics, Guizhou University, Guiyang, Guizhou, 550025

Received: February 2011

Revised: February 2012

Published: June 2012

Abstract / Introduction Related Papers Cited by

Abstract

Traditionally, the time domains that are widely used in mathematical descriptions are limited to real numbers for the case of continuous-time optimal control problems or to integers for the case of discrete-time optimal control problems. In this paper, based on a family of "needle variations", we derive maximum principle for optimal control problem on time scales. The results not only unify the theory of continuous and discrete optimal control problems but also conclude problems involving time domains in partly continuous and partly discrete ingredients. A simple optimal control problem on time scales is discussed in detail. Meanwhile, the results also unify the theory of some hybrid systems, for example, impulsive systems.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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