Optimal Control of Quasilinear Parabolic PDEs with State-Constraints
Fabian Hoppe, Ira Neitzel
Abstract
We discuss state-constrained optimal control of a quasilinear parabolic PDE. Existence of optimal controls and first-order necessary optimality conditions are derived for a rather general setting including pointwise in time and space constraints on the state. Second-order sufficient optimality conditions are obtained for averaged-in-time and pointwise in space state-constraints under general regularity assumptions for the equation, and for pointwise in time and space state-constraints when restricting in return to a more regular setting for the state equation.
Topics & Concepts
PointwiseMathematicsOptimal controlParabolic partial differential equationPartial differential equationNorm (philosophy)State (computer science)Applied mathematicsControl (management)Maximum principleOrder (exchange)Mathematical optimizationMathematical economicsMathematical analysisComputer scienceAlgorithmLawEconomicsArtificial intelligenceFinancePolitical scienceAdvanced Mathematical Modeling in EngineeringNonlinear Partial Differential EquationsAdvanced Numerical Methods in Computational Mathematics