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 |