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

ISBN-13: 9783540543398 / Angielski / Miękka / 1991 / 165 str.

Irena Lasiecka; Roberto Triggiani; I. Lasiecka

Opis

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.

Spis treści

1. Introduction: Two abstract classes; statement of main problems.- 2. Abstract differential Riccati equation for the first class subject to the analyticity assumption (H.1)=(1.5).- 3. Abstract differential Riccati equations for the second class subject to the trace regularity assumption (H.2)=(1.6).- 4. Abstract differential Riccati equations for the second class subject to the regularity assumptions (H.2R)=(1.8).- 5. Abstract algebraic Riccati equations: Existence and uniqueness.- 6. Examples of partial differential equation problems satisfying (H.1).- 7. Examples of partial differential equation problems satisfying (H.2).- 8. Example of a partial differential equation problem satisfying (H.2R).- 9. Numerical approximations of the solution to the abstract differential and algebraic Riccati equations.- 10. Examples of numerical approximation for the classes (H.1) and (H.2).- 11. Conclusions.