Neumann Boundary Control of Hyperbolic Equations with Pointwise State Constraints

We consider optimal control problems for hyperbolic systems with controls in Neumann boundary conditions with pointwise (hard) constraints on control and state functions. Focusing on hyperbolic dynamics governed by the multidimensional wave equation with a nonlinear term, we derive new necessary optimality conditions in the pointwise form of the Pontryagin Maximum Principle for the state-constrained problem under consideration. Our approach is based on modern methods of variational analysis that allows us to obtain refined necessary optimality conditions with no convexity assumptions on integrands in the minimizing cost functional

Optimal Boundary Control of Hyperbolic Equations with Pointwise State Constraints

In this paper we consider dynamic optimization problems for hyperbolic systems with boundary controls and pointwise state constraints. In contrast to parabolic dynamics, such systems have not been sufficiently studied in the literature. The reason is the lack of regularity in the case of hyperbolic dynamics. We present necessary optimality conditions for both Neumann and Dirichlet boundary control problems and discuss differences and relationships between them