PONTRYAGINS PRINCIPLE FOR STATE-CONSTRAINED BOUNDARY CONTROL PROBLEMS OF SEMILINEAR PARABOLIC EQUATIONS

摘要

This paper deals with state-constrained optimal control problems governed by semilinear parabolic equations. We establish a minimum principle of Pontryagin's type. To deal with the state constraints, we introduce a penalty problem by using Ekeland's principle. The key tool for the proof is the use of a special kind of spike perturbations distributed in the domain where the controls are defined. Conditions for normality of optimality conditions are given. [References: 33]