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

Structural stability of optimal control problems

M'hamed Kesri 1,

1. 

Faculté des Mathématiques, Université USTHB Alger, Algérie, Algeria

Received  October 2004 Revised  April 2005 Published  September 2005

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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