Structural stability of optimal control problems

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December 2005, 4(4): 743-756. doi: 10.3934/cpaa.2005.4.743

Structural stability of optimal control problems

1.	Faculté des Mathématiques, Université USTHB Alger, Algérie, Algeria

Received October 2004 Revised April 2005 Published September 2005

Abstract
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In this article, we prove that solutions for a class of optimal control problems we study, defined "in a less restrictive sense then usual" a dynamical system such that every state which is optimal is a sink and between every pair of sinks there is a unique source at least generically. The corresponding problem is shown to be structurally stable.

Keywords: superoptimal, suboptimal, optimal control problem, value function, structurally stable, Hamilton-Jacobi-Bellman equation.

Mathematics Subject Classification: 49J15, 49K15.

Citation: M'hamed Kesri. Structural stability of optimal control problems. Communications on Pure & Applied Analysis, 2005, 4 (4) : 743-756. doi: 10.3934/cpaa.2005.4.743

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