Optimal Control of Distributed Systems

Abstract

In this chapter we continue our study of optimal control problems from the viewpoint of advanced methods of variational analysis and generalized differentiation. In contrast to the preceding chapter where the main attention was paid to control problems governed by ordinary differential equations and inclusions as well as their discrete-time counterparts, we now focus on control systems with distributed parameters governed by functional-differential and partial differential relations. We particularly study optimal control problems for delayed differential-algebraic inclusions that cover several important classes of control systems essentially different from ordinary ones, and for partial differential equations of hyperbolic and parabolic types that involve boundary controls of both Dirichlet and Neumann types as well as pointwise state constraints. All the mentioned problems have not been sufficiently studied in the literature; most of the material presented in this chapter is based on recent results developed by the author and his collaborators.