Systems and Control

by Zak, Stanislaw H.

• ISBN13: 9780195150117
• ISBN10: 0195150112
• Format: Hardcover
• Copyright: 2002-12-19
• Publisher: Oxford University Press

Summary

Systems and Control presents modeling, analysis, and control of dynamical systems. Introducing students to the basics of dynamical system theory and supplying them with the tools necessary for control system design, it emphasizes design and demonstrates how dynamical system theory fits into practical applications. Classical methods and the techniques of postmodern control engineering are presented in a unified fashion, demonstrating how the current tools of a control engineer can supplement more classical tools. Broad in scope, Systems and Control shows the multidisciplinary role of dynamics and control; presents neural networks, fuzzy systems, and genetic algorithms; and provides a self-contained introduction to chaotic systems. The text employs Lyapunov's stability theory as a unifying medium for different types of dynamical systems, using it--with its variants--to analyze dynamical system models. Specifically, optimal, fuzzy, sliding mode, and chaotic controllers are all constructed with the aid of the Lyapunov method and its extensions. In addition, a class of neural networks is also analyzed using Lyapunov's method. Ideal for advanced undergraduate and beginning graduate courses in systems and control, this text can also be used for introductory courses in nonlinear systems and modern automatic control. It requires working knowledge of basic differential equations and elements of linear algebra; a review of the necessary mathematical techniques and terminology is provided.

Author Biography

Stanislaw H. Zak is Professor of Electrical and Computer Engineering at Purdue.

Table of Contents

Preface
Dynamical Systems and Modeling	p. 1
What Is a System?	p. 1
Open-Loop Versus Closed-Loop	p. 3
Axiomatic Definition of a Dynamical System	p. 5
Mathematical Modeling	p. 8
Review of Work and Energy Concepts	p. 9
The Lagrange Equations of Motion	p. 12
Modeling Examples	p. 21
Analysis of Modeling Equations	p. 48
State-Plane Analysis	p. 48
Numerical Techniques	p. 59
Principles of Linearization	p. 71
Linearizing Differential Equations	p. 74
Describing Function Method	p. 77
Linear Systems	p. 94
Reachability and Controllability	p. 94
Observability and Constructability	p. 107
Companion Forms	p. 111
Linear State-Feedback Control	p. 120
State Estimators	p. 126
Combined Controller-Estimator Compensator	p. 131
Stability	p. 149
Informal Introduction to Stability	p. 149
Basic Definitions of Stability	p. 150
Stability of Linear Systems	p. 154
Evaluating Quadratic Indices	p. 159
Discrete-Time Lyapunov Equation	p. 165
Constructing Robust Linear Controllers	p. 168
Hurwitz and Routh Stability Criteria	p. 171
Stability of Nonlinear Systems	p. 176
Lyapunov's Indirect Method	p. 188
Discontinuous Robust Controllers	p. 194
Uniform Ultimate Boundedness	p. 201
Lyapunov-Like Analysis	p. 210
LaSalle's Invariance Principle	p. 213
Optimal Control	p. 225
Performance Indices	p. 225
A Glimpse at the Calculus of Variations	p. 227
Linear Quadratic Regulator	p. 244
Dynamic Programming	p. 273
Pontryagin's Minimum Principle	p. 292
Sliding Modes	p. 315
Simple Variable Structure Systems	p. 315
Sliding Mode Definition	p. 320
A Simple Sliding Mode Controller	p. 324
Sliding in Multi-Input Systems	p. 327
Sliding Mode and System Zeros	p. 328
Nonideal Sliding Mode	p. 329
Sliding Surface Design	p. 333
State Estimation of Uncertain Systems	p. 336
Sliding Modes in Solving Optimization Problems	p. 340
Vector Field Methods	p. 367
A Nonlinear Plant Model	p. 368
Controller Form	p. 369
Linearizing State-Feedback Control	p. 380
Observer Form	p. 382
Asymptotic State Estimator	p. 387
Combined Controller-Estimator Compensator	p. 388
Fuzzy Systems	p. 393
Motivation and Basic Definitions	p. 393
Fuzzy Arithmetic and Fuzzy Relations	p. 396
Standard Additive Model	p. 407
Fuzzy Logic Control	p. 410
Stabilization Using Fuzzy Models	p. 420
Stability of Discrete Fuzzy Models	p. 437
Fuzzy Estimator	p. 440
Adaptive Fuzzy Control	p. 447
Neural Networks	p. 469
Threshold logic Unit	p. 470
Identification Using Adaptive Linear Element	p. 478
Backpropagation	p. 484
Neural Fuzzy Identifier	p. 489
Radial-Basis Function (RBF) Networks	p. 494
A Self-Organizing Network	p. 506
Hopfield Neural Network	p. 508
Hopfield Network Stability Analysis	p. 517
Brain-State-in-a-Box (BSB) Models	p. 529
Genetic and Evolutionary Algorithms	p. 553
Genetics as an Inspiration for an Optimization Approach	p. 553
Implementing a Canonical Genetic Algorithm	p. 555
Analysis of the Canonical Genetic Algorithm	p. 559
Simple Evolutionary Algorithm (EA)	p. 561
Evolutionary Fuzzy Logic Controllers	p. 563
Chaotic Systems and Fractals	p. 578
Chaotic Systems Are Dynamical Systems with Wild Behavior	p. 578
Chaotic Behavior of the Logistic Equation	p. 579
Fractals	p. 593
Lyapunov Exponents	p. 599
Discretization Chaos	p. 605
Controlling Chaotic Systems	p. 607
App.: Math Review	p. 624
Bibliography	p. 679
Index	p. 693
Table of Contents provided by Blackwell. All Rights Reserved.