Structural stability of optimal control problems

Pages: 743 - 756, Volume 4, Issue 4, December 2005

doi:10.3934/cpaa.2005.4.743       Abstract        Full Text (208.9K)       Related Articles

M'hamed Kesri - Faculté des Mathématiques, Université USTHB Alger, Algérie, Algeria (email)

Abstract: 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:  Hamilton-Jacobi-Bellman equation, value function, optimal control problem, superoptimal, suboptimal, structurally stable
Mathematics Subject Classification:  49J15, 49K15

Received: October 2004;      Revised: April 2005;      Published: September 2005.