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On some robust control problems for nonlinear parabolic equations. (English) Zbl 1041.49022

Summary: We study a robust control problem for a class of systems governed by nonlinear parabolic equations. First, the control is the forcing. We formulate the robust control problem, we prove the existence and the uniqueness of the solution and we give the necessary conditions for optimality. Second, an initial perturbation problem is considered. A robust control problem is reformulated and the existence and the conditions of the uniqueness of the optimal solution are derived. First order necessary conditions for optimality are obtained.

MSC:

49K20 Optimality conditions for problems involving partial differential equations
93B35 Sensitivity (robustness)
49J20 Existence theories for optimal control problems involving partial differential equations
49J50 Fréchet and Gateaux differentiability in optimization
35K55 Nonlinear parabolic equations
49K35 Optimality conditions for minimax problems
35K57 Reaction-diffusion equations