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Pontryagin's Principle for State-Constrained Boundary Control Problems of Semilinear Parabolic Equations

1997; Society for Industrial and Applied Mathematics; Volume: 35; Issue: 4 Linguagem: Inglês

10.1137/s0363012995283637

1095-7138

Eduardo Casas,

Nonlinear Partial Differential Equations

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.