Set-Theoretic Methods in Control (eBook)

Franco Blanchini, Stefano Miani (Autoren)

eBook Download: PDF

2007 | 2008
XV, 487 Seiten
Birkhäuser Boston (Verlag)
978-0-8176-4606-6 (ISBN)

Infos

This self-contained monograph describes basic set-theoretic methods for control. It 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. 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.

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Many control problems can be naturally formulated, analyzed, and solved in a set-theoretic context. Sets appear naturally when three aspects, which are crucial in control systems design, are considered: constraints, uncertainties, anddesignspeci?cations.Furthermore,setsarethemostappropriatelanguage to specify severalsystem performances, for instance when we areinterested in determining the domain of attraction, in measuring the e?ect of a persistent noise in a feedback loop or in bounding the error of an estimation algorithm. From a conceptual point of view, the peculiarity of the material presented in this book lies in the fact that sets are not only terms of the formulation, but they play an active role in the solution of the problems as well. Generally speaking, in the control theory context, all the techniques which are theore- cally based on some properties of subsets of the state-space could be referred to as set-theoretic methods. The most popular and clear link is that with Lyapunov theory and positive invariance. Lyapunov functions are positi- de?nite energy-type functions of the state variables, which have the property of being decreasing in time and are fundamental tools to guarantee stability. Besides, their sublevel sets are positively invariant and thus their shape is quite meaningful to characterize the system dynamics, a key point which will be enlightened in the present book. The invariance property will be shown to be fundamental in dealing with problems such as saturating control, noise suppression, model-predictive control, and many others.

Inhalt

Preface 7
Contents 11
1 Introduction 16
2 Lyapunov and Lyapunov-like functions 42
3 Convex sets and their representation 88
4 Invariant sets 113
5 Dynamic programming 162
6 Set-theoretic analysis of dynamic systems 203
7 Control of parameter-varying systems 247
8 Control with time-domain constraints 282
9 (Sub-)Optimal control 347
10 Set-theoretic estimation 399
11 Related topics 424
12 Appendix 460
References 468
Index 486

Produkt-Details

• Erscheint lt. Verlag: 5.10.2007
• Reihe/Serie: Systems & Control: Foundations & Applications
• Reihe/Serie: Systems & Control: Foundations & Applications
• Zusatzinfo: XV, 487 p.
• Verlagsort: Boston
• Sprache: englisch
• Themenwelt: Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Schlagworte: algorithm • algorithms • Calculus • control under constraints • Convex sets • invariant sets • Lyapunov stability • optimal control • parameter-varying systems • persistent disturbance rejection • programming • set-theoretic methods • stability • time-domain constraints • uncertain systems analysis and synthesis
• ISBN-10: 0-8176-4606-X / 081764606X
• ISBN-13: 978-0-8176-4606-6 / 9780817646066