Journal of Applied Mathematics
Volume 2012 (2012), Article ID 457121, 11 pages
http://dx.doi.org/10.1155/2012/457121
Research Article

Necessary Optimality Conditions for a Class of Impulsive and Switching Systems

Lihua Li,1,2 Yan Gao,1 and Gexia Wang2

1School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China
2School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China

Received 11 July 2012; Accepted 11 September 2012

Academic Editor: Piyapong Niamsup

Copyright © 2012 Lihua Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An optimal control problem for a class of hybrid impulsive and switching systems is considered. By defining switching times as part of extended state, we get the necessary optimality conditions for this problem. It is shown that the adjoint variables satisfy certain jump conditions and the Hamiltonian are continuous at switching instants. In addition, necessary optimality conditions of Fréchet subdifferential form are presented in this paper.