Adaptive Systems

Loosely speaking, adaptive systems are designed to deal with, to adapt to, chang ing environmental conditions whilst maintaining performance objectives. Over the years, the theory of adaptive systems evolved from relatively simple and intuitive concepts to a complex multifaceted theory dealing with stochastic, nonlinear and infinite dimensional systems. This book provides a first introduction to the theory of adaptive systems. The book grew out of a graduate course that the authors taught several times in Australia, Belgium, and The Netherlands for students with an engineering and/or mathemat ics background. When we taught the course for the first time, we felt that there was a need for a textbook that would introduce the reader to the main aspects of adaptation with emphasis on clarity of presentation and precision rather than on comprehensiveness. The present book tries to serve this need. We expect that the reader will have taken a basic course in linear algebra and mul tivariable calculus. Apart from the basic concepts borrowed from these areas of mathematics, the book is intended to be self contained.

Texte du rabat

Introducing readers to adaptive systems in a rigorous but elementary fashion, this text emphasizes the mainstream developments in adaptive control and signal processing of linear discrete time systems. A unified framework is developed whereby the reader can analyze and understand any adaptive system in the literature. The so-called equilibrium analysis facilitates an understanding of the limitations and potential of adaptive systems in a transparent fashion; while the behavioural approach to linear systems plays an essential role at some key points in the text. So-called universal controllers are presented in some detail. Each chapter is accompanied by exercises that aim to develop certain aspects of the theory, as well as to give the reader a better understanding of the actual behaviour of adaptive systems.

Résumé
From the reviews:

"This book is intended to be a first introduction to the theory of adaptive systems for graduate students. It treats exclusively deterministic adaptive control in a discrete-time formulation.... The basic course material contained in Chapters 1, 2, 3, 4, 5, and 6 is supplemented with the presentation of more advanced problems and tools such as well-posedness of the control problem during adaptation (Chapter 7), averaging techniques for analysis of adaptive systems (Chapter 8), and global dynamical analysis of adaptive systems operating in a plant-model mismatch situation (Chapter 9)." -Mathematical Reviews

"The book is based on graduate courses taught by both authors and is intended as a text-book. Therefore it is self contained and only basic knowledge of linear algebra and ordinary differential equations is needed. ... cover the basic theory of adaptive systems and can be used for a one trimester course. ... The book is accompanied by many solved and unsolved exercises, two Maple procedures and a large bibliography." (EMS Newsletter, Issue 27, March, 1998)

Contenu
1 Adaptive Systems.- 1.1 Introduction.- 1.2 Adaptive systems: examples.- 1.3 General structure of adaptive control systems.- 1.4 Illustrating the concepts.- 1.5 Summary of chapter.- 1.6 Notes and references.- 1.7 Exercises.- 2 Systems And Their Representations.- 2.1 Introduction.- 2.2 Notation.- 2.3 The behavior.- 2.4 Latent variables.- 2.5 Equivalent representations.- 2.6 Controllability.- 2.7 Observability.- 2.8 Stability.- 2.9 Elimination of Latent variables.- 2.10 The ring ?[?,??1].- 2.11 An example.- 2.12 A word about the notation.- 2.13 Summary of chapter.- 2.14 Notes and references.- 3 Adaptive systems : principles of identification.- 3.1 Introduction.- 3.2 Object of interest and model class.- 3.3 Identification criterion and algorithms.- 3.4 Data model assumptions.- 3.5 Analysis of identification algorithms.- 3.6 Persistency of excitation.- 3.7 Summary of chapter.- 3.8 Notes and references.- 3.9 Exercises.- 4 Adaptive Pole Assignment.- 4.1 Introduction.- 4.2 Preliminaries.- 4.3 The system and its representations.- 4.4 Equilibrium analysis.- 4.5 An algorithm for adaptive pole assignment.- 4.6 Analysis of the algorithm.- 4.7 Filtered signals.- 4.8 Modification of the projection algorithm.- 4.9 Summary of chapter.- 4.10 Notes and references.- 4.11 Exercises.- 5 Direct Adaptive Model Reference Control.- 5.1 Introduction.- 5.2 Basic problem definition.- 5.3 Model reference control: nonadaptive solution.- 5.4 Error model construction.- 5.5 Equilibrium analysis.- 5.6 Adaptive algorithm.- 5.7 Analysis of the adaptive system.- 5.8 Adaptive model reference control with disturbance rejection.- 5.9 Summary of chapter.- 5.10 Notes and references.- 5.11 Exercises.- 6 Universal Controllers.- 6.1 Introduction.- 6.2 Existence of solutions.- 6.3 The first order case.- 6.4Higher order systems.- 6.5 Mårtensson's algorithm.- 6.6 Summary of chapter.- 6.7 Notes and references.- 6.8 Exercises.- 7 The pole/zero cancellation problem.- 7.1 Introduction.- 7.2 The pole/zero cancellation problem in adaptive control.- 7.3 Combining direct and indirect adaptive control.- 7.4 Adaptive Excitation.- 7.5 A more fundamental viewpoint.- 7.6 Conclusions.- 7.7 Summary of chapter.- 7.8 Notes and references.- 7.9 Exercises.- 8 Averaging Analysis For Adaptive Systems.- 8.1 Introduction.- 8.2 Averaging.- 8.3 Transforming an adaptive system into standard form.- 8.4 Averaging approximation.- 8.5 Application: the MIT rule for adaptive control.- 8.6 Application: echo cancellation in telephony.- 8.7 Summary of chapter.- 8.8 Notes and references.- 8.9 Exercises.- 9 Dynamics of adaptive systems: A case study.- 9.1 Introduction.- 9.2 The example.- 9.3 Global analysis and bifurcations.- 9.4 Adaptive system behavior: ideal case.- 9.5 Adaptive system behavior: undermodelled case.- 9.6 Discussion.- 9.7 Summary of chapter.- 9.8 Notes and References.- 9.9 Exercises.- Epilogue.- A Background material.- A.1 A contraction result.- A.2 The Comparison Principle.- A.2.1 Bellman-Gronwall Lemma.- A.2.2 Perturbed linear stable systems.- A.3 Miscellaneous stability results.- A.3.1 Stability Definitions.- A.3.2 Some Lyapunov stability results.- A.4 Detectability.- A.5 An inequality for linear systems.- A.6 Finite horizon averaging result.- A.7 Maple code for solving Lyapunov equations.- A.8 Maple code for fixed points and two periodic solutions.