# American Institute of Mathematical Sciences

July  2012, 8(3): 591-609. doi: 10.3934/jimo.2012.8.591

## A neighboring extremal solution for an optimal switched impulsive control problem

 1 Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, China, China 2 Department of Mathematics and Statistics, Curtin University, Perth, W.A. 6845, Australia 3 Department of Mathematics and Statistics, Curtin University, Perth 6845

Received  May 2011 Revised  November 2011 Published  June 2012

This paper presents a neighboring extremal solution for a class of optimal switched impulsive control problems with perturbations in the initial state, terminal condition and system's parameters. The sequence of mode's switching is pre-specified, and the decision variables, i.e. the switching times and parameters of the system involved, have inequality constraints. It is assumed that the active status of these constraints is unchanged with the perturbations. We derive this solution by expanding the necessary conditions for optimality to first-order and then solving the resulting multiple-point boundary-value problem by the backward sweep technique. Numerical simulations are presented to illustrate this solution method.
Citation: Canghua Jiang, Kok Lay Teo, Ryan Loxton, Guang-Ren Duan. A neighboring extremal solution for an optimal switched impulsive control problem. Journal of Industrial & Management Optimization, 2012, 8 (3) : 591-609. doi: 10.3934/jimo.2012.8.591
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