(1) Department of Mathematics, Wayne State University, Detroit, MI 48202, USA;(2) Laboratoire MIP, Université Paul Sabatier, 31062 Toulouse Cedex 4, France
Abstract:
We study optimal control problems for hyperbolic equations(focusing on the multidimensional wave equation) with control functions in the Dirichletboundary conditions under hard/pointwise control and state constraints. Imposingappropriate convexity assumptions on the cost integral functional, we establish theexistence of optimal control and derive new necessary optimality conditions in theintegral form of the Pontryagin Maximum Principle for hyperbolic state-constrained systems.
