American Institute of Mathematical Sciences

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October  2006, 2(4): 435-450. doi: 10.3934/jimo.2006.2.435

Global impulsive optimal control computation

C.Z. Wu 1, and  K. L. Teo 2,

1. 

Department of Mathematics, Chongqing Normal University, Chongqing, China
2. 

Department of Mathematics and Statistics, Curtin University of Technology, Perth

Received  March 2006 Revised  August 2006 Published  October 2006

In this paper, we develop a global computational approach to a class of optimal control problems governed by impulsive dynamical systems and subject to continuous state inequality constraint. We show that this problem is equivalent to an optimal control problem governed by ordinary differential equations with periodic boundary conditions and subject to a set of the continuous state inequality constraints. For this equivalent optimal control problem, a constraint transcription method is used in conjunction with a penalty function to construct an appended new cost functional. This leads to a sequence of approximate optimal control problems only subject to periodic boundary conditions. Each of these approximate problems can be solved as an optimization problem using gradient-based optimization techniques. However, these techniques are designed only to find local optimal solutions. Thus, a filled function method is introduced to supplement the gradient-based optimization method. This leads to a combined method for finding a global optimal solution. A numerical example is solved using the proposed approach.
Keywords: continuous state inequality constraint, Impulsive optimal control problems, penalty function, equivalent optimal control problem with periodic boundary conditions, constraint transcription, filled function method for global optimal solutions., gradient-based optimization technique for local optimal solutions.
Mathematics Subject Classification: 49J9.
Citation: C.Z. Wu, K. L. Teo. Global impulsive optimal control computation. Journal of Industrial & Management Optimization, 2006, 2 (4) : 435-450. doi: 10.3934/jimo.2006.2.435
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