Dirichlet Boundary Control of Parabolic Systems with Pointwise State Constraints
Boris S. Mordukhovich, Kaixia Zhang · Birkhäuser Basel eBooks · 1998
In this paper we study an optimal control problem for linear parabolic systems with pointwise state constraints and measurable controls acting in the Dirichlet boundary conditions. Using the framework of mild solutions to parabolic systems with nonregular dynamics, we prove a general existence theorem of optimal controls and derive necessary optimality conditions for the state-constrained problem under consideration. Our variational analysis is based on a well-posed penalization procedure to approximate state constraints and then to study a parametric family of approximating problems. The final result estab- lishes necessary optimality conditions for the original state-constrained problem by passing to the limit from approximating problems under a proper constraint qualification.