We study optimal control problems for hyperbolic equations (focusing on the multidimensional wave equation) with control functions in the Dirichlet boundary conditions under hard/pointwise control and state constraints. Imposing appropriate convexity assumptions on the cost integral functional, we establish the existence of optimal control and derive new necessary optimality conditions in the integral form of the Pontryagin Maximum Principle for hyperbolic state-constrained systems.
Number in Series
Applied Mathematics | Control Theory | Mathematics
AMS Subject Classification
Primary 49K20, 49J20, Secondary 93C20, 35L20
Mordukhovich, Boris S. and Raymond, Jean-Pierre, "Dirichlet Boundary Control of Hyperbolic Equations in the Presence of State Constraints" (2003). Mathematics Research Reports. 15.