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  • Author or Editor: Nikolaos Papageorgiou x
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Abstract  

In this paper we study optimal control problems for systems governed by nonlinear evolution equations. First we develop an existence theory for systems with a priori feedback using the reduction technique and a convexity-type hypothesis involving property Q. In doing this we also establish the nonemptiness of the set of admissible state-control pairs, by solving a nonlinear evolution inclusion. Then we obtain necessary conditions for optimality for a class of problems with terminal cost criterion and initial condition which is not a priori given but is only required to belong to a given set (systems with insufficient data in the terminology of Lions).

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В работе доказываютс я две теоремы типа Радона—Никодима в мн огозначном случае. Первая из них касаетс я просто многозначны х мер, а вторая — многозначны х мер переноса. В ходе доказательств а второй теоремы уста новлен один результат, представл яющий самостоятельный инт ерес о селекторах пер еноса для многозначных мер пер еноса.

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Abstract  

In this paper we study the relaxation of optimal control problems monitored by subdifferential evolution inclusions. First under appropriate convexity conditions, we establish an existence result. Then we introduce the relaxed problem and show that it always has a solution under fairly general hypotheses on the data. Subsequently we examine when the relaxation is admissible. So we show that every relaxed trajectory can be approximated by extremal original ones (i.e. original trajectories generated by bang-bang controls) and that the values of the original and relaxed problems are equal. Some examples are also presented.

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