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$acr 200 10$aAdaptive Systems $eAn Introduction /$fby Iven Mareels, Jan Willem Polderman 205 $a1st ed. 1996. 210 1$aBoston, MA :$cBirkhäuser Boston :$cImprint: Birkhäuser,$d1996. 215 $a1 online resource (XVII, 342 p.) 225 1 $aSystems & Control: Foundations & Applications,$x2324-9757 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a0-8176-3877-6 311 08$a1-4612-6414-6 320 $aIncludes bibliographical references and index. 327 $a1 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. 330 $aLoosely speaking, adaptive systems are designed to deal with, to adapt to, chang­ ing environmental conditions whilst maintaining performance objectives. Over the years, the theory of adaptive systems evolved from relatively simple and intuitive concepts to a complex multifaceted theory dealing with stochastic, nonlinear and infinite dimensional systems. This book provides a first introduction to the theory of adaptive systems. The book grew out of a graduate course that the authors taught several times in Australia, Belgium, and The Netherlands for students with an engineering and/or mathemat­ ics background. When we taught the course for the first time, we felt that there was a need for a textbook that would introduce the reader to the main aspects of adaptation with emphasis on clarity of presentation and precision rather than on comprehensiveness. The present book tries to serve this need. We expect that the reader will have taken a basic course in linear algebra and mul­ tivariable calculus. Apart from the basic concepts borrowed from these areas of mathematics, the book is intended to be self contained. 410 0$aSystems & Control: Foundations & Applications,$x2324-9757 606 $aSystem theory 606 $aControl theory 606 $aMathematical models 606 $aProbabilities 606 $aSystems Theory, Control 606 $aMathematical Modeling and Industrial Mathematics 606 $aProbability Theory 615 0$aSystem theory. 615 0$aControl theory. 615 0$aMathematical models. 615 0$aProbabilities. 615 14$aSystems Theory, Control. 615 24$aMathematical Modeling and Industrial Mathematics. 615 24$aProbability Theory. 676 $a519 700 $aMareels$b Iven$4aut$4http://id.loc.gov/vocabulary/relators/aut$01829744 702 $aPolderman$b Jan Willem$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910960440903321 996 $aAdaptive Systems$94430411 997 $aUNINA