Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems Continuous and Approximation Theories

Originally published in 2000, this is the first volume of a comprehensive two-volume treatment of quadratic optimal control theory for partial differential equations over a finite or infinite time horizon, and related differential (integral) and algebraic Riccati equations. Both continuous theory and numerical approximation theory are included. The authors use an abstract space, operator theoretic approach, which is based on semigroups methods, and which is unifying across a few basic classes of evolution. The various abstract frameworks are motivated by, and ultimately directed to, partial differential equations with boundary/point control. Volume 1 includes the abstract parabolic theory for the finite and infinite cases and corresponding PDE illustrations as well as various abstract hyperbolic settings in the finite case. It presents numerous fascinating results. These volumes will appeal to graduate students and researchers in pure and applied mathematics and theoretical engineering with an interest in optimal control problems.

Introduction; Part I. Analytic Semigroups: 1. The optimal quadratic cost problem over a preassigned finite time interval: the differential Riccati equation; 2. The optimal quadratic cost problem over a preassigned finite time interval: the algebraic Riccati equation; 3. Illustrations of the abstract theory of chapters 1 and 2 to PDEs with boundary/point controls; 4. Numerical approximations of algebraic Riccati equations; 5. Illustrations of the numerical theory of chapter 4 to parabolic-like boundary/point control PDE problems; 6. Min-max game theory over an infinite time interval and algebraic Riccati equations.

Originally published in 2000, this is the first volume of a comprehensive treatise on the mathematical theory of deterministic control systems modeled by multi-dimensional partial differential equations (distributed parameter systems). Volume 1 presents the abstract parabolic and hyperbolic settings, including many fascinating results.