Book contents
- Frontmatter
- Contents
- Preface
- 0 Background
- 1 Optimal Quadratic Cost Problem Over a Preassigned Finite Time Interval: Differential Riccati Equation
- 2 Optimal Quadratic Cost Problem over an Infinite Time Interval: Algebraic Riccati Equation
- 3 Illustrations of the Abstract Theory of Chapters 1 and 2 to Partial Differential Equations 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
- Index
Preface
Published online by Cambridge University Press: 05 June 2013
- Frontmatter
- Contents
- Preface
- 0 Background
- 1 Optimal Quadratic Cost Problem Over a Preassigned Finite Time Interval: Differential Riccati Equation
- 2 Optimal Quadratic Cost Problem over an Infinite Time Interval: Algebraic Riccati Equation
- 3 Illustrations of the Abstract Theory of Chapters 1 and 2 to Partial Differential Equations 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
- Index
Summary
This three-volume treatise presents, in a unified framework, a comprehensive, in-depth, and up-to-date treatment of quadratic optimal control theory for (linear) partial differential equations (PDEs) over a finite or infinite time horizon and related differential (integral) and algebraic Riccati equations. Both continuous theory and numerical approximation theory are included. An abstract space, operator theoretic treatment is provided, which is based on semi group methods, and which is unifying across a few basic classes of evolution.
While addressing all three volumes regarding the basic, broad-range theme covered and the philosophy of approach followed, this preface focuses mostly on Volumes I and II for specific details. Indeed, driven also by recent, new PDE models such as they arise in modern technological applications, the treatment of this work has grown far beyond the original intentions and the anticipated plan. As a result, two volumes now appear in print, with a third one in preparation. A justification for the criteria that have dictated the selection of a natural subdivision of the entire work into three volumes is given below.
This treatise is a much expanded outgrowth, at least in the ratio 1 to 10, of the authors' Springer-Verlag Lectures Notes in Control and Information Sciences, Volume 164, entitled: Differential and Algebraic Riccati Equations with Applications to Boundary-Point Control Problems: Continuous and Approximation Theory. These Lecture Notes, published in 1991, contained a comprehensive account of the theories that were available at that time, along with an array of numerous illustrative PDE applications with boundary/point control.
- Type
- Chapter
- Information
- Control Theory for Partial Differential EquationsContinuous and Approximation Theories, pp. xv - xxiiPublisher: Cambridge University PressPrint publication year: 2000