Classical Control Using H-Infinity Methods: Theory, Optimization, and Design

This text teaches control system design using H-infinity techniques that are simple and compatible with classical control, yet powerful enough to allow the solution of physically meaningful problems. The authors begin by teaching how to formulate control system design problems as mathematical optimization problems and then discuss the theory and numerics for these optimization problems. The book is separated into modules so that the parts on theory can be read independently of the design parts and vice versa. The authors treat control design problems in a physically correct way. They present a small set of specific rules that the reader can apply to convert a particular design problem to the fundamental optimization problem of H-infinity control. This precisely formulated mathematics problem can then be solved on a computer. The book introduces the control software package OPTDesign, which allows the reader to reproduce the calculations done in the solved examples and try variations on them.

Table of Contents:
Preface; Part I. Short Design Course: 1. A Method for Solving System Design Problems; 2. Internal Stability; 3. Frequency Domain Performance Requirements; 4. Optimization; Review of Concepts; 5. A Design Example With OPTDesign; Part II. More on Design: 6. Examples; 7. Internal Stability; Part III. H-Infinity Theory: 8. H^\infty Optimization and Control; 10. Facts About Analytic Functions; 11. Proof of the Main Result; 12. Computer Solutions to OPT; Part IV. H-Infinity Theory. Vector Case. 13. Many Analytic Functions; 14. Coordinate Descent Approaches to OPT; 15. More Numerical Algorithms; 16. More Theory of the Vector OPT Problem; Part V. Semidefinite Programming vs. H-Infinity Optimization. 17. Matrix H-Infinity Optimization; 18. Numerical Algorithms for H-Infinity Optimization; 19. Semidefinite Programming vs. Matrix H-Infinity Optimization; 20. Proofs; Part VI. Appendices: Appendix A. History and Perspective; Appendix B. Pure Mathematics and H-Infinity Optimization; Appendix C. Uncertainty; Appendix D. Computer Code for Examples in 6; Appendix E. Getting OPTDesign and Anopt; Appendix F. Anopt Notebook; Appendix G. NewtonInterpolant Notebook; Appendix H. NewtonFit Notebook..

Review :
'The books by Helton and Merino contain a wealth of material that can be used by students and researchers in a variety of different ways, depending on background and interests. To enhance this modular flexibility, the authors offer two versions ... Both versions contain introductory material, at an elementary level, on what control engineering is all about ...' Joseph A. Ball, SIAM Review 'This book, treating control system design using H-Infinity techniques and H-Infinity theory motivated by control applications, is a very good tool for a large number of people interested in control and in H^\infty theory, from undergraduate students and engineers to research mathematicians. Here the reader can find answers to practical and theoretical problems, even by a partial reading, because the book is written in a highly modular way ...' I. Valusescu, Zentralblatt fur Mathematik ' The authors make clear that a powerful and unified theory of H-Infinity design is beginning to emerge, but that much remains to be done. The present book is a welcome contribution that should help to publicize the important advances that have been made and their potential for solving a difficult class of engineering control design problems.' N. Harris McClamroch, Mathematical Reviews