This is the first volume of a comprehensive and up-to-date 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. The authors describe both continuous theory and numerical approximation. They use an abstract space, operator theoretic approach, based on semigroups methods and 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 II focuses on the optimal control problem over a finite time interval for hyperbolic dynamical systems. The chapters consider some abstract models, each motivated by a particular canonical hyperbolic dynamics, and present numerous new results.

The field of control theory in PDEs has broadened considerably as more realistic models have been introduced and investigated. This book presents a broad range of recent developments, new discoveries, and mathematical tools in the field. The authors discuss topics such as elasticity, thermo-elasticity, aero-elasticity, interactions between fluids and elastic structures, and fluid dynamics and the new challenges that they present. Other control theoretic problems include parabolic systems, dynamical Lame systems, linear and nonlinear hyperbolic equations, and pseudo-differential operators on a...

This is the first volume of a comprehensive and up-to-date 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. The authors describe both continuous theory and numerical approximation. They use an abstract space, operator theoretic approach, based on semigroups methods and 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 II focuses on the optimal control problem over a finite time interval for hyperbolic dynamical systems. The chapters consider some abstract models, each motivated by a particular canonical hyperbolic dynamics, and present numerous new results.

This book provides, in a unified framework, an updated and rather comprehensive treatment contered on the theory of ot- pimal control with quadratic cost functional for abstract linear systems with application to boundary/point control problems for partial differential equations (distributed pa- rameter systems). The book culminates with the analysisof differential and algebraic Riccati equations which arise in the pointwisefe- edback synthesis of the optimal pair. It incorporates the critical topics of optimal irregularity of solutions to mi- xed problems for partial differential equations,...