Optimal control problems for nonlinear parabolic boundary control systems: The Dirichlet boundary condition
A boundary control system described by a semilinear partial differential heat equation is considered. The control is applied through the forced Dirichlet boundary condition. The optimal control problem is that of minimizing a cost functional among all determined admissible controls for which the corresponding solutions satisfy a given target condition. The time at which the optimal process terminates may be fixed or free. The final result is a version of Pontryagin's maximum principle. Existence theorems are also obtained.
scientific article; zbMATH DE number 597522