Żak S.H. Systems and Control

New York: Oxford University Press, 2003. — 782 p. — ISBN: 9780195150117.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.Dynamical Systems and Modeling
What Is a System?
Open-Loop Versus Closed-Loop
Axiomatic Definition of a Dynamical System
Mathematical Modeling
Review of Work and Energy Concepts
The Lagrange Equations of Motion
Modeling Examples
Notes
Exercises
Analysis of Modeling Equations
State-Plane Analysis
Numerical Techniques
Principles of Linearization
Linearizing Differential Equations
Describing Function Method
Notes
Exercises
Linear Systems
Reachability and Controllability
Observability and Constructability
Companion Forms
Linear State-Feedback Control
State Estimators
Combined Controller-Estimator Compensator
Notes
Exercises
Stability
Informal Introduction to Stability
Basic Definitions of Stability
Stability of Linear Systems
Evaluating Quadratic Indices
Discrete-Time Lyapunov Equation
Constructing Robust Linear Controllers
Hurwitz and Routh Stability Criteria
Stability of Nonlinear Systems
Lyapunov’s Indirect Method
Notes
Exercises
Optimal Control
Performance Indices
A Glimpse at the Calculus of Variations
Linear Quadratic Regulator
Dynamic Programming
Pontryagin’s Minimum Principle
Notes
Exercises
Sliding Modes
Simple Variable Structure Systems
Sliding Mode Definition
A Simple Sliding Mode Controller
Sliding in Multi-Input Systems
Sliding Mode and System Zeros
Nonideal Sliding Mode
Sliding Surface Design
State Estimation of Uncertain Systems
Sliding Modes in Solving Optimization Problems
Notes
Exercises
Vector Field Methods
A Nonlinear Plant Model
Controller Form
Linearizing State-Feedback Control
Observer Form
Asymptotic State Estimator
Combined Controller-Estimator Compensator
Notes
Exercises
Fuzzy Systems
Motivation and Basic Definitions
Fuzzy Arithmetic and Fuzzy Relations
Standard Additive Model
Fuzzy Logic Control
Stabilization Using Fuzzy Models
Stability of Discrete Fuzzy Models
Fuzzy Estimator
Adaptive Fuzzy Control
Notes
Exercises
Neural Networks
Threshold Logic Unit
Identification Using Adaptive Linear Element
Backpropagation
Neural Fuzzy Identifier
Radial-Basis Function (RBF) Networks
A Self-Organizing Network
Hopfield Neural Network
Hopfield Network Stability Analysis
Brain-State-in-a-Box (BSB) Models
Notes
Exercises
Genetic and Evolutionary Algorithms
Genetics as an Inspiration for an Optimization Approach
Implementing a Canonical Genetic Algorithm
Analysis of the Canonical Genetic Algorithm
Simple Evolutionary Algorithm (EA)
Evolutionary Fuzzy Logic Controllers
Notes
Exercises
Chaotic Systems and Fractals
Chaotic Systems Are Dynamical Systems with Wild Behavior
Chaotic Behavior of the Logistic Equation
Fractals
Lyapunov Exponents
Discretization Chaos
Controlling Chaotic Systems
Notes
Exercises
A: Math Review
A.1 Notation and Methods of Proof
A.2 Vectors
A.3 Matrices and Determinants
A.4 Quadratic Forms
A.5 The Kronecker Product
A.6 Upper and Lower Bounds
A.7 Sequences
A.8 Functions
A.9 Linear Operators
A.10 Vector Spaces
A.11 Least Squares
A.12 Contraction Maps
A.13 First-Order Differential Equation
A.14 Integral and Differential Inequalities
A.14.1 The Bellman-Gronwall Lemma
A.14.2 A Comparison Theorem
A.15 Solving the State Equations
A.15.1 Solution of Uncontrolled System
A.15.2 Solution of Controlled System
A.16 Curves and Surfaces
A.17 Vector Fields and Curve Integrals
A.18 Matrix Calculus Formulas
Notes
Exercises