Systems and Control

Each chapter ends with Notes and Exercises Preface 1. Dynamical Systems and Modeling 1.1: What Is a System? 1.2: Open-Loop Versus Closed-Loop 1.3: Axiomatic Definition of a Dynamical System 1.4: Mathematical Modeling 1.5: Review of Work and Energy Concepts 1.6: The Lagrange Equations of Motion 1.7: Modeling Examples 1.7.1: Centrifugal Governor 1.7.2: Ground Vehicle 1.7.3: Permanent Magnet Stepper Motor 1.7.4: Stick Balancer 1.7.5: Population Dynamics 2. Analysis of Modeling Equations 2.1: State Plane Analysis 2.1.1: Examples of Phase Portraits 2.1.2: The Method of Isoclines 2.2: Numerical Techniques 2.2.1: The Method of Taylor Series 2.2.2: Euler's Methods 2.2.3: Predictor-Corrector Method 2.2.4: Runge's Method 2.2.5: Runge-Kutta Method 2.3: Principles of Linearization 2.4: Linearizing Differential Equations 2.5: Describing Function Method 2.5.1: Scalar Product of Functions 2.5.2: Fourier Series 2.5.3: Describing Function in the Analysis of Nonlinear Systems 3. Linear Systems 3.1: Reachability and Controllability 3.2: Observability and Constructability 3.3: Companion Forms 3.3.1: Controller Form 3.3.2: Observer Form 3.4: Linear State-Feedback Control 3.5: State Estimators 3.5.1: Full-Order Estimator 3.5.2: Reduced-Order Estimator 3.6: Combined Controller-Estimator Compensator 4. Stability 4.1: Informal Introduction to Stability 4.2: Basic Definitions of Stability 4.3: Stability of Linear Systems 4.4: Evaluating Quadratic Indices 4.5: Discrete-Time Lyapunov Equation 4.6: Constructing Robust Linear Controllers 4.7: Hurwitz and Routh Stability Criteria 4.8: Stability of Nonlinear Systems 4.9: Lyapunov's Indirect Method 4.10: Discontinuous Robust Controllers 4.11: Uniform Ultimate Boundedness 4.12: Lyapunov-Like Analysis 4.13: LaSalle's Invariance Principle 5. Optimal Control 5.1: Performance Indices 5.2: A Glimpse at the Calculus of Variations 5.2.1: Variation and Its Properties 5.2.2: Euler-Lagrange Equation 5.3: Linear Quadratic Regulator 5.3.1: Algebraic Riccati Equation (ARE) 5.3.2: Solving the ARE Using the Eigenvector Method 5.3.3: Optimal Systems with Prescribed Poles 5.3.4: Optimal Saturating Controllers 5.3.5: Linear Quadratic Regulator for Discrete Systems on an Infinite Time Interval 5.4: Dynamic Programming 5.4.1: Discrete-Time Systems 5.4.2: Discrete Linear Quadratic Regulator Problem 5.4.3: Continuous Minimum Time Regulator Problem 5.4.4: The Hamilton-Jacobi-Bellman Equation 5.5: Pontryagin's Minimum Principle 5.5.1: Optimal Control With Constraints on Inputs 5.5.2: A Two-Point Boundary-Value Problem 6. Sliding Modes 6.1: Simple Variable Structure Systems 6.2: Sliding Mode 6.3: A Simple Sliding Mode Controller 6.4: Sliding in Multi-Input Systems 6.5: Sliding Mode and System Zeros 6.6: Nonideal Sliding Mode 6.7: Sliding Surface Design 6.8: State Estimation of Uncertain Systems 6.8.1: Discontinuous Estimators 6.8.2: Boundary Layer Estimators 6.9: Sliding Modes in Solving Optimization Problems 6.9.1: Optimization Problem Statement 6.9.2: Penalty Function Method 6.9.3: Dynamical Gradient Circuit Analysis 7. Vector Field Methods 7.1: A Nonlinear Plant Model 7.2: Controller Form 7.3: Linearizing State-Feedback Control 7.4: Observer Form 7.5: Asymptotic State Estimator 7.6: Combined Controller-Estimator Compensator 8. Fuzzy Systems 8.1: Motivation and Basic Definitions 8.2: Fuzzy Arithmetic and Fuzzy Relations 8.2.1: Interval Arithmetic 8.2.2: Manipulating Fuzzy Numbers 8.2.3: Fuzzy Relations 8.2.4: Composition of Fuzzy Relations 8.3: Standard Additive Model 8.4: Fuzzy Logic Control 8.5: Stabilization Using Fuzzy Models 8.5.1: Fuzzy Modeling 8.5.2: Constructing a Fuzzy Design Model Using a Nonlinear Model 8.5.3: Stabilizability of Fuzzy Models 8.5.4: A Lyapunov-Based Stabilizer 8.6: Stability of Discrete Fuzzy Models 8.7: Fuzzy Estimator 8.7.1: The Comparison Method for Linear Systems 8.7.2: Stability Analysis of the Closed-Loop System 8.8: Adaptive Fuzzy Control 8.8.1: Plant Model and Control Objective 8.8.2: Background Results 8.8.3: Controllers 8.8.4: Examples 9. Neural Networks 9.1: Threshold Logic Unit 9.2: Identification Using Adaptive Linear Element 9.3: Backpropagation 9.4: Neural Fuzzy Identifier 9.5: Radial-Basis Function (RBF) Networks 9.5.1: Interpolation Using RBF Networks 9.5.2: Identification of a Single-Input, Single-State System 9.5.3: Learning Algorithm for the RBF Identifier 9.5.4: Growing RBF Network 9.5.5: Identification of Multivariable Systems 9.6: A Self-Organizing Network 9.7: Hopfield Neural Network 9.7.1: Hopfield Neural Network Modeling and Analysis 9.7.2: Analog-to-Digital Converter 9.8: Hopfield Network Stability Analysis 9.8.1: Hopfield Network Model Analysis 9.8.2: Single Neuron Stability Analysis 9.8.3: Stability Analysis of the Network 9.9: Brain-State-in-a-Box (BSB) Models 9.9.1: Associative Memories 9.9.2: Analysis of BSB Models 9.9.3: Synthesis of Neural Associative Memory 9.9.4: Learning 9.9.5: Forgetting 10. Genetic and Evolutionary Algorithms 10.1: Genetics as an Inspiration for an Optimization Approach 10.2: Implementing a Canonical Genetic Algorithm 10.3: Analysis of the Canonical Genetic Algorithm 10.4: Simple Evolutionary Algorithm (EA) 10.5: Evolutionary Fuzzy Logic Controllers 10.5.1: Vehicle Model and Control Objective 10.5.2: Case 1: EA Tunes Fuzzy Rules 10.5.3: Case 2: EA Tunes Fuzzy Membership Functions 10.5.4: Case 3: EA Tunes Fuzzy Rules and Membership Functions 11. Chaotic Systems and Fractals 11.1: Chaotic Systems Are Dynamical Systems with Wild Behavior 11.2: Chaotic Behavior of the Logistic Equation 11.2.1: The Logistic Equation---An Example From Ecology 11.2.2: Stability Analysis of the Logistic Map 11.2.3: Period Doubling to Chaos 11.2.4: The Feigenbaum Numbers 11.3: Fractals 11.3.1: The Mandelbrot Set 11.3.2: Julia Sets 11.3.3: Iterated Function Systems 11.4: Lyapunov Exponents 11.5: Discretization Chaos 11.6: Controlling Chaotic Systems 11.6.1: Ingredients of Chaotic Control Algorithm 11.6.2: Chaotic Control Algorithm Appendix: 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 Bibliography Index