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| Preface | |
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| Introduction | |
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| Introduction | |
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| Systems Theory | |
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| Adaptive Systems | |
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| What Is an Adaptive System? | |
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| Parameter Adaptive and Structurally Adaptive Systems | |
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| Direct and Indirect Control | |
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| Parameter Perturbation Method | |
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| Sensitivity Method | |
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| Model Reference Adaptive Systems and Self-Tuning Regulators | |
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| Identification Model | |
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| Reference Model | |
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| Reference Model with Inputs | |
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| Model Reference Adaptive Control | |
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| Self-Tuning Regulators | |
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| Stable Adaptive Systems | |
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| Error Models | |
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| Applications | |
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| Summary | |
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| Scope of the Book | |
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| Problems | |
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| References | |
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| Stability Theory | |
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| Introduction | |
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| Notation | |
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| Linear Systems | |
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| Linear Time-Invariant Systems | |
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| Almost Time-Invariant Systems | |
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| Lyapunov Stability | |
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| Definitions | |
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| Lyapunov's Direct Method | |
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| V(x, t) [greater than] 0, V(x, t) [Less than or equal] 0 | |
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| LTI Systems and Lyapunov Stability | |
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| Linear Time-Varying Systems | |
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| Positive Real Functions | |
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| Positive Real Transfer Matrices | |
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| Kalman-Yakubovich Lemma | |
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| Input-Output Stability | |
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| Stability of Adaptive Systems | |
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| Two Differential Equations That Arise in Adaptive Systems | |
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| Growth Rates of Signals in Dynamical Systems | |
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| Stability in Terms of a Parameter Vector [theta] | |
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| Other Stability Concepts | |
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| Total Stability | |
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| BIBO Stability | |
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| Summary | |
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| Problems | |
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| References | |
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| Simple Adaptive Systems | |
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| Introduction | |
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| Algebraic Systems | |
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| Identification | |
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| Dynamical Systems | |
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| The Identification Problem: Scalar Case | |
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| The Control Problem: Scalar Case (Direct Control) | |
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| The Control Problem: Scalar Case (Indirect Control) | |
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| Indirect Control: Dynamic Adjustment of Control Parameters | |
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| Examples | |
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| State Variables Accessible | |
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| The Identification Problem: Vector Case | |
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| The Control Problem | |
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| Summary | |
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| Problems | |
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| References | |
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| Adaptive Observers | |
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| Introduction | |
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| The Luenberger Observer | |
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| Adaptive Observers | |
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| Statement of the Problem | |
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| Minimal Realization of Adaptive Observers | |
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| Nonminimal Realization of Adaptive Observers | |
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| Modified Adaptive Observer | |
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| Design of Adaptive Observers | |
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| Representation 1 | |
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| Representation 2 | |
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| Hybrid Algorithms | |
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| Time-Varying Adaptive Gains | |
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| Integral Algorithm | |
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| Multiple Models | |
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| Adaptive Algorithms: An Overview | |
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| Summary | |
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| Problems | |
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| References | |
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| The Control Problem | |
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| Introduction | |
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| Statement of the Problem | |
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| Adaptive Control of Plants with Relative Degree Unity | |
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| Case (i) k[superscript p] Unknown | |
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| Case (ii) Unknown Zeros | |
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| Case (iii) Unknown Poles | |
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| General Case (n* = 1) | |
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| Adaptive Control of Plants with Relative Degree [greater than or equal] 2 | |
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| Bezout Identity | |
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| n* [greater than or equal] 2: Algebraic Part | |
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| n* = 2: Analytic Part | |
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| n* [greater than of equal] 2: Analytic Part | |
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| k[subscript p] Known | |
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| k[subscript p] Unknown | |
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| Proof of Global Stability of the Adaptive System | |
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| k[subscript p] Known | |
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| k[subscript p] Unknown | |
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| Comments on the Control Problem | |
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| Some Remarks on the Controller Structure | |
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| Stable Adaptive Control Using the Indirect Approach | |
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| n* = 1 | |
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| n* [greater than or equal] 2 | |
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| Combined Direct and Indirect Approach | |
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| Summary | |
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| Problems | |
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| References | |
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| Persistent Excitation | |
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| Introduction | |
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| Persistent Excitation in Adaptive Systems | |
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| Definitions | |
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| Examples | |
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| Properties of Persistently Exciting Functions | |
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| Algebraic Transformations | |
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| Dynamic Transformations | |
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| Almost Time-Invariant Systems | |
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| Persistent Excitation of Unbounded Signals | |
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| Applications to Adaptive systems | |
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| Parameter Convergence in Adaptive Observers | |
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| Parameter Convergence in Adaptive Control | |
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| Design Considerations | |
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| Persistent Excitation and Uniform Asymptotic Stability | |
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| Summary | |
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| Problems | |
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| References | |
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| Error Models | |
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| Introduction | |
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| Error Model 1 | |
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| Error Model 2 | |
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| Error Model 3 | |
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| Error Model 4 | |
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| Further Comments on Error Models 1-4 | |
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| Use of Error Models in Adaptive Systems | |
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| Problems | |
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| References | |
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| Robust Adaptive Control | |
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| Introduction | |
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| Adaptive Observers in the Presence of Disturbances | |
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| Identifier | |
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| Adaptive Observers | |
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| Error Model | |
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| Adaptive Control of a First-Order Plant in the Presence of Bounded Disturbances | |
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| Exact Cancellation of Disturbance | |
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| Bounded Disturbances: Statement of the Problem | |
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| Category 1: Modifications of the Adaptive Law | |
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| Category 2: Persistent Excitation of the Reference Input | |
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| Performance of the Adaptive System | |
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| Adaptive Control of an nth Order Plant | |
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| Robustness without Persistent Excitation | |
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| Robustness with Persistent Excitation | |
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| Comments on Adaptive Algorithms for Bounded Disturbances | |
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| Hybrid Adaptive Control | |
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| Hybrid Error Models | |
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| Hybrid Adaptive Control | |
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| Hybrid Adaptive Control in the Presence of Bounded Disturbances | |
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| Adaptive Control of Time-Varying Plants | |
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| Adaptive Control of a First-Order Plant | |
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| Time-Varying Plants of Higher Order | |
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| Reduced-Order Controllers | |
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| Instability with Reduced Order Controllers: An Example | |
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| Statement of the Problem | |
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| Small Parameter [mu] in P | |
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| Transfer Function W[subscript m](s) | |
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| Summary | |
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| Problems | |
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| References | |
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| The Control Problem: Relaxation of Assumptions | |
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| Introduction | |
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| Assumption (i): Sign of k[subscript p] | |
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| Assumption (iii): Upper Bound on the Order of the Plant | |
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| Regulation of Plant with Relative Degree n* = 1 | |
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| n* = 2 | |
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| Arbitrary n* | |
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| Universal Controller | |
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| Assumption (iv): Zeros of W[subscript p](s) in C[superscript -] | |
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| Direct Control | |
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| Indirect Control | |
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| Command Generator Tracking Method | |
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| Statement of the Problem | |
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| Summary | |
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| Problems | |
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| References | |
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| Multivariable Adaptive Systems | |
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| Introduction | |
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| Mathematical Preliminaries | |
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| Multivariable Adaptive Identification | |
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| Statement of the Problem | |
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| The Adaptive Observer: Minimal Realization | |
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| The Adaptive Observer: Nonminimal Realization | |
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| Adaptive Control Problem | |
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| Adaptive Control of Two Input-Two Output Plants | |
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| Dynamic Precompensator for a General Multivariable Plant | |
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| Design of the Adaptive Controller | |
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| Summary | |
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| Problems | |
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| References | |
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| Applications of Adaptive Control | |
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| Introduction | |
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| Ship Dynamics | |
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| Process Control | |
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| Distillation Columns | |
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| Power Systems | |
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| Robot Manipulators | |
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| Adaptive Control in Bioengineering | |
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| Blood Pressure Control | |
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| Adaptive Control for Ventricular Assist Devices | |
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| Muscular Control | |
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| Comments and Conclusions | |
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| Refernces | |
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| Kalman-Yakubovich Lemma | |
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| Growth Rates of Unbounded Signals | |
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| Properties of the Adaptive System with Bounded Parameters | |
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| Proof of Boundedness in the Presence of Bounded Disturbances | |
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| Some Facts About Transfer Matrices | |
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| Index | |
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| Errata List | |