INVERSE AND OPTIMAL OUTPUT FEEDBACK CONTROL PROBLEMS FOR INFINITE DIMENSIONAL DETERMINISTIC AND STOCHASTIC SYSTEMS WITH UNCERTAIN SEMIGROUP GENERATORS

Abstract

This paper is concerned with inverse problems and optimal output feedback
control problems for semilinear innite dimensional uncertain systems. We present several
interesting typical and nontypical control problems and their solutions. The nontypical
problems are related to control of the evolution of measures. We prove existence of optimal
feedback control laws for these systems in the presence of uncertainty of the principal oper-
ator. We consider both deterministic and stochastic systems. In the last section we present
the necessary conditions of optimality for the uncertain stochastic feedback control problem.