Preface
1 Dynamical Systems and Modeling 1
1.1 What Is a System? 1
1.2 Open-Loop Versus Closed-Loop 3
1.3 Axiomatic Definition of a Dynamical System 5
1.4 Mathematical Modeling 8
1.5 Review of Work and Energy Concepts 9
1.6 The Lagrange Equations of Motion 12
1.7 Modeling Examples 21
2 Analysis of Modeling Equations 48
2.1 State-Plane Analysis 48
2.2 Numerical Techniques 59
2.3 Principles of Linearization 71
2.4 Linearizing Differential Equations 74
2.5 Describing Function Method 77
3 Linear Systems 94
3.1 Reachability and Controllability 94
3.2 Observability and Constructability 107
3.3 Companion Forms 111
3.4 Linear State-Feedback Control 120
3.5 State Estimators 126
3.6 Combined Controller-Estimator Compensator 131
4 Stability 149
4.1 Informal Introduction to Stability 149
4.2 Basic Definitions of Stability 150
4.3 Stability of Linear Systems 154
4.4 Evaluating Quadratic Indices 159
4.5 Discrete-Time Lyapunov Equation 165
4.6 Constructing Robust Linear Controllers 168
4.7 Hurwitz and Routh Stability Criteria 171
4.8 Stability of Nonlinear Systems 176
4.9 Lyapunov's Indirect Method 188
4.10 Discontinuous Robust Controllers 194
4.11 Uniform Ultimate Boundedness 201
4.12 Lyapunov-Like Analysis 210
4.13 LaSalle's Invariance Principle 213
5 Optimal Control 225
5.1 Performance Indices 225
5.2 A Glimpse at the Calculus of Variations 227
5.3 Linear Quadratic Regulator 244
5.4 Dynamic Programming 273
5.5 Pontryagin's Minimum Principle 292
6 Sliding Modes 315
6.1 Simple Variable Structure Systems 315
6.2 Sliding Mode Definition 320
6.3 A Simple Sliding Mode Controller 324
6.4 Sliding in Multi-Input Systems 327
6.5 Sliding Mode and System Zeros 328
6.6 Nonideal Sliding Mode 329
6.7 Sliding Surface Design 333
6.8 State Estimation of Uncertain Systems 336
6.9 Sliding Modes in Solving Optimization Problems 340
7 Vector Field Methods 367
7.1 A Nonlinear Plant Model 368
7.2 Controller Form 369
7.3 Linearizing State-Feedback Control 380
7.4 Observer Form 382
7.5 Asymptotic State Estimator 387
7.6 Combined Controller-Estimator Compensator 388
8 Fuzzy Systems 393
8.1 Motivation and Basic Definitions 393
8.2 Fuzzy Arithmetic and Fuzzy Relations 396
8.3 Standard Additive Model 407
8.4 Fuzzy Logic Control 410
8.5 Stabilization Using Fuzzy Models 420
8.6 Stability of Discrete Fuzzy Models 437
8.7 Fuzzy Estimator 440
8.8 Adaptive Fuzzy Control 447
9 Neural Networks 469
9.1 Threshold logic Unit 470
9.2 Identification Using Adaptive Linear Element 478
9.3 Backpropagation 484
9.4 Neural Fuzzy Identifier 489
9.5 Radial-Basis Function (RBF) Networks 494
9.6 A Self-Organizing Network 506
9.7 Hopfield Neural Network 508
9.8 Hopfield Network Stability Analysis 517
9.9 Brain-State-in-a-Box (BSB) Models 529
10 Genetic and Evolutionary Algorithms 553
10.1 Genetics as an Inspiration for an Optimization Approach 553
10.2 Implementing a Canonical Genetic Algorithm 555
10.3 Analysis of the Canonical Genetic Algorithm 559
10.4 Simple Evolutionary Algorithm (EA) 561
10.5 Evolutionary Fuzzy Logic Controllers 563
11 Chaotic Systems and Fractals 578
11.1 Chaotic Systems Are Dynamical Systems with Wild Behavior 578
11.2 Chaotic Behavior of the Logistic Equation 579
11.3 Fractals 593
11.4 Lyapunov Exponents 599
11.5 Discretization Chaos 605
11.6 Controlling Chaotic Systems 607
App.: Math Review 624
Bibliography 679
Index 693