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.

Control Theory for Partial Differential Equations: Volume 2, Abstract Hyperbolic-like Systems over a Finite Time Horizon: Continuous and Approximation ... and its Applications, Series Number 75)

Science & Math

Lasiecka, Irena

Triggiani, Roberto

Mathematics

Cambridge University Press

<p>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 I includes the abstract parabolic theory (continuous theory and numerical approximation theory) for the finite and infinite cases and corresponding PDE illustrations, and presents numerous new 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.</p>

Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems: Continuous and Approximation Theories (Encyclopedia of Mathematics and its Applications, Series Number 74)

Reference

Encyclopedias & Subject Guides

This book is devoted to the study of coupled partial differential equation models, which describe complex dynamical systems occurring in modern scientific applications such as fluid/flow-structure interactions. The first chapter provides a general description of a fluid-structure interaction, which is formulated within a realistic framework, where the structure subject to a frictional damping moves within the fluid. The second chapter then offers a multifaceted description, with often surprising results, of the case of the static interface; a case that is argued in the literature to be a good model for small, rapid oscillations of the structure. The third chapter describes flow-structure interaction where the compressible Navier-Stokes equations are replaced by the linearized Euler equation, while the solid is taken as a nonlinear plate, which oscillates in the surrounding gas flow. The final chapter focuses on a the equations of nonlinear acoustics coupled with linear acoustics or elasticity, as they arise in the context of high intensity ultrasound applications.

Mathematical Theory of Evolutionary Fluid-Flow Structure Interactions (Oberwolfach Seminars, 48)

Kaltenbacher, Barbara

Kukavica, Igor

Tuffaha, Amjad

Webster, Justin T.

Birkhauser

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, exact con- trollability, and uniform feedback stabilization. It covers the main results of the theory - which has reached a consi- derable degree of maturity over the last few years - as well asthe 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. However, in line with the purpose of the manuscript, many technical pro- ofs are referred to in the literature. Thus, the manuscript should prove useful not only to mathematicians and theoreti- cal scientists with expertise in partial differential equa- tions, operator theory, numerical analysis, control theory, etc., but also to those who simple wish to orient themselves with the scope and status of the theory presently available. Both continuous theory and numerical approximation theory thereof are included.

Differential and Algebraic Riccati Equations with Application to Boundary/Point Control Problems: Continuous Theory and Approximation Theory (Lecture Notes in Control and Information Sciences, 164)

Springer

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