Adaptive Systems

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. Language: English