Optimal feedback control depending only on the system state is constructed for a control problem by the non-causal descriptor system for which optimal feedback control depending on state derivatives was considered in the paper (Meuller, 1998). To this end, a non-symmetric solution of the algebraic operator Riccati equation is used.
In this paper we consider stochastic differential equations on Banach spaces (not Hilbert). The system is semilinear and the principal operator generating a C₀-semigroup is perturbed by a class of bounded linear operators considered as feedback operators from an admissible set. We consider the corresponding family of measure valued functions and present sufficient conditions for weak compactness. Then we consider applications of this result to several interesting optimal feedback control problems. We present results on existence of optimal feedback operators.
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