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Stable Adaptive Systems

ISBN-10: 0486442268
ISBN-13: 9780486442266
Edition: 2005
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Book details

List price: $29.95
Copyright year: 2005
Publisher: Dover Publications, Incorporated
Publication date: 5/31/2005
Binding: Paperback
Pages: 512
Size: 6.57" wide x 9.21" long x 0.98" tall
Weight: 1.496
Language: English

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

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