ON MODELS AND METHODS OF A DYNAMIC OPTIMAL MANAGEMENT MODEL

Raoul Bilombo (Congo) and Valeri Anastasievich Doliatovski (Congo)

Received December 29, 2008

Abstract

A regular solution of the Problem 17 to  and   can be written in the form:  The second term of the second member is class  if  but only class  in the opposite case. The first term of the second member is always at least absolutely continuous if u is integrable as compared to t, because  is going to smooth irregularities of  (more or less following the regularity of G, analytic or not notably). In this paper, we show that the condition (4.7) defined by    and m are constants  and  is the semi-group of class  plays the fundamental role in the study of the asymptotic behaviour of solutions in problems of dynamic optimal control in the presence of perturbations.

Keywords and phrases: optimal control, semi-groups, behaviour asymptotic, regularity.