Differential and Algebraic Riccati Equations with Application to Boundary/Point Control Problems: Continuous Theory and Approximation Theory

This text provides, in a unified framework, an updated treatment centered on the theory of optimal control with quadratic cost functional for abstract linear systems, with application to boundary/point control problems for partial differential equations (distributed parameter systems). It culminates with the analysis of differential and algebraic Riccati equations which arise in the pointwise feedback synthesis of the optimal pair. It incorporates the critical topics of optimal irregularity of solutions to mixed problems for partial differential equations, exact controlability, and uniform feedback stabilization. It covers the main results of the theory, as well as the authors' basic philosophy behind it. Moreover, it provides numerous illustrative examples of boundary/point control problems for partial differential equations, where the abstract theory applies. Both continuous theory and numerical approximation theory are included.