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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 | |