Document Type

Technical Report


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.

Number in Series



Applied Mathematics | Control Theory | Mathematics | Partial Differential Equations

AMS Subject Classification

49K20, 93C20, 35L20


Research of the first author was partly supported by the National Science Foundation under grants DMS-0072179 and DMS-0304989