MINIMAX CONTROL OF PARABOLIC-SYSTEMS WITH DIRICHLET BOUNDARY-CONDITIONS AND STATE CONSTRAINTS

In this paper we formulate and study a minimax control problem for a c lass of parabolic systems with controlled Dirichlet boundary condition s and un certain distributed perturbations under pointwise control and state constraints. We prove an existence theorem for minimax solution s and develop effective penalized procedures to approximate state cons traints. Based on a careful variational analysis, we establish converg ence results and optimality conditions for approximating problems that allow us to characterize suboptimal solutions to the original minimax problem with hard constraints. Then passing to the limit in approxima tions, we prove necessary optimality conditions for the minimax proble m considered under proper constraint qualification conditions.