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Existence theory of optimal controls for distributed parameter systems. (English) Zbl 0770.49005
An existence theory for optimal control problems related with systems described by nonlinear distributed parameter systems are considered. The results are established in the framework of mild solutions for the investigated equations. The Cesari’s property and the theory of compact semigroups are used for the proof of the existence of the optimal pair. Optimal control problems for systems described by nonlinear evolutional equations of first and second order and elliptic variational inequalities are investigated. The results can be used for the analysis of many optimal control problems, for example, in singular optimal control systems.
MSC:
49J27Optimal control problems in abstract spaces (existence)
49J20Optimal control problems with PDE (existence)