Set-Theoretic Methods in Control: (Systems & Control: Foundations & Applications)

This self-contained monograph describes basic set-theoretic methods for control and provides a discussion of their links to fundamental problems in Lyapunov stability analysis and stabilization, optimal control, control under constraints, persistent disturbance rejection, and uncertain systems analysis and synthesis. New computer technology has catalyzed a resurgence of research in this area, particularly in the development of set-theoretic techniques, many of which are computationally demanding. The work presents several established and potentially new applications, along with numerical examples and case studies. A key theme is the trade-off between exact (but computationally intensive) and approximate (but conservative) solutions to problems. Mathematical language is kept to the minimum necessary for the adequate formulation and statement of main concepts. Efficient numerical algorithms, both in MATLAB and C++, will be available via the Internet to supplement the presentation and solution of problems in the book. "Set-Theoretic Methods in Control" is accessible to readers familiar with the basics of systems and control theory; prerequisites such as convexity theory are included. The text provides a solid foundation of mathematical techniques and applications and also features avenues for further theoretical study. While it is aimed primarily at graduate students and researchers in applied mathematics and engineering, the book will also appeal to practitioners, since it contains extensive references to the literature and supplies many recipes for solving real-world control problems.

Table of Contents:
Lyapunov and Lyapunov-like functions.- Convex sets and their representation.- Invariant sets.- Dynamic programming.- Set-theoretic analysis of dynamic systems.- Control of parameter-varying systems.- Control with time-domain constraints.- (Sub-)Optimal control.- Set-theoretic estimation.- Related topics.

Review :
From the reviews: "The book is an outstanding monograph of a recent research trend in control. It reflects the vast experience of the authors as well as their noticeable contributions to the development of this field...At the conceptual level, the book was meant as a self contained volume for readers with the usual background in systems and control. The text is very accessible (the style is attractive; the theoretical concepts and results are accompanied by relevant examples so as to facilitate the deep understanding of the discussed topics; both analytical and numerical approaches are presented; the final section of each chapter includes exercises). The book is highly recommended to PhD students and researchers working in control engineering or applied mathematics. The material can also be used for graduate courses in these areas." [Octavian Pastravanu, Zentralblatt MATH] "This is an excellent book, full of new ideas and collecting a lot of diverse material related to set-theoretic methods. It can be recommended to a wide control community audience." (B. T. Polyak, Mathematical Reviews, Issue 2009 f)