Systems and Control

Hardcover | December 15, 2002

byStanislaw H. Zak

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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 intopractical 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 fordifferent 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 alsoanalyzed 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 reviewof the necessary mathematical techniques and terminology is provided.

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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 intopractical applications. Classical methods and ...

Stanislaw H. Zak is Professor of Electrical and Computer Engineering at Purdue. He has worked in various areas of control, optimization, and neural networks. He is coauthor of Selected Methods of Analysis of Linear Dynamical Systems (1984, in Polish) and An Introduction to Optimization, 2/e (2001). Dr. Zak has also contributed to the...

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Format:HardcoverDimensions:720 pages, 7.72 × 9.21 × 1.5 inPublished:December 15, 2002Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0195150112

ISBN - 13:9780195150117

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Table of Contents

Each chapter ends with Notes and ExercisesPreface1. Dynamical Systems and Modeling1.1. What Is a System?1.2. Open-Loop Versus Closed-Loop1.3. Axiomatic Definition of a Dynamical System1.4. Mathematical Modeling1.5. Review of Work and Energy Concepts1.6. The Lagrange Equations of Motion1.7. Modeling Examples1.7.1. Centrifugal Governor1.7.2. Ground Vehicle1.7.3. Permanent Magnet Stepper Motor1.7.4. Stick Balancer1.7.5. Population Dynamics2. Analysis of Modeling Equations2.1. State Plane Analysis2.1.1. Examples of Phase Portraits2.1.2. The Method of Isoclines2.2. Numerical Techniques2.2.1. The Method of Taylor Series2.2.2. Euler's Methods2.2.3. Predictor-Corrector Method2.2.4. Runge's Method2.2.5. Runge-Kutta Method2.3. Principles of Linearization2.4. Linearizing Differential Equations2.5. Describing Function Method2.5.1. Scalar Product of Functions2.5.2. Fourier Series2.5.3. Describing Function in the Analysis of Nonlinear Systems3. Linear Systems3.1. Reachability and Controllability3.2. Observability and Constructability3.3. Companion Forms3.3.1. Controller Form3.3.2. Observer Form3.4. Linear State-Feedback Control3.5. State Estimators3.5.1. Full-Order Estimator3.5.2. Reduced-Order Estimator3.6. Combined Controller-Estimator Compensator4. Stability4.1. Informal Introduction to Stability4.2. Basic Definitions of Stability4.3. Stability of Linear Systems4.4. Evaluating Quadratic Indices4.5. Discrete-Time Lyapunov Equation4.6. Constructing Robust Linear Controllers4.7. Hurwitz and Routh Stability Criteria4.8. Stability of Nonlinear Systems4.9. Lyapunov's Indirect Method4.10. Discontinuous Robust Controllers4.11. Uniform Ultimate Boundedness4.12. Lyapunov-Like Analysis4.13. LaSalle's Invariance Principle5. Optimal Control5.1. Performance Indices5.2. A Glimpse at the Calculus of Variations5.2.1. Variation and Its Properties5.2.2. Euler-Lagrange Equation5.3. Linear Quadratic Regulator5.3.1. Algebraic Riccati Equation (ARE)5.3.2. Solving the ARE Using the Eigenvector Method5.3.3. Optimal Systems with Prescribed Poles5.3.4. Optimal Saturating Controllers5.3.5. Linear Quadratic Regulator for Discrete Systems on an Infinite Time Interval5.4. Dynamic Programming5.4.1. Discrete-Time Systems5.4.2. Discrete Linear Quadratic Regulator Problem5.4.3. Continuous Minimum Time Regulator Problem5.4.4. The Hamilton-Jacobi-Bellman Equation5.5. Pontryagin's Minimum Principle5.5.1. Optimal Control With Constraints on Inputs5.5.2. A Two-Point Boundary-Value Problem6. Sliding Modes6.1. Simple Variable Structure Systems6.2. Sliding Mode6.3. A Simple Sliding Mode Controller6.4. Sliding in Multi-Input Systems6.5. Sliding Mode and System Zeros6.6. Nonideal Sliding Mode6.7. Sliding Surface Design6.8. State Estimation of Uncertain Systems6.8.1. Discontinuous Estimators6.8.2. Boundary Layer Estimators6.9. Sliding Modes in Solving Optimization Problems6.9.1. Optimization Problem Statement6.9.2. Penalty Function Method6.9.3. Dynamical Gradient Circuit Analysis7. Vector Field Methods7.1. A Nonlinear Plant Model7.2. Controller Form7.3. Linearizing State-Feedback Control7.4. Observer Form7.5. Asymptotic State Estimator7.6. Combined Controller-Estimator Compensator8. Fuzzy Systems8.1. Motivation and Basic Definitions8.2. Fuzzy Arithmetic and Fuzzy Relations8.2.1. Interval Arithmetic8.2.2. Manipulating Fuzzy Numbers8.2.3. Fuzzy Relations8.2.4. Composition of Fuzzy Relations8.3. Standard Additive Model8.4. Fuzzy Logic Control8.5. Stabilization Using Fuzzy Models8.5.1. Fuzzy Modeling8.5.2. Constructing a Fuzzy Design Model Using a Nonlinear Model8.5.3. Stabilizability of Fuzzy Models8.5.4. A Lyapunov-Based Stabilizer8.6. Stability of Discrete Fuzzy Models8.7. Fuzzy Estimator8.7.1. The Comparison Method for Linear Systems8.7.2. Stability Analysis of the Closed-Loop System8.8. Adaptive Fuzzy Control8.8.1. Plant Model and Control Objective8.8.2. Background Results8.8.3. Controllers8.8.4. Examples9. Neural Networks9.1. Threshold Logic Unit9.2. Identification Using Adaptive Linear Element9.3. Backpropagation9.4. Neural Fuzzy Identifier9.5. Radial-Basis Function (RBF) Networks9.5.1. Interpolation Using RBF Networks9.5.2. Identification of a Single-Input, Single-State System9.5.3. Learning Algorithm for the RBF Identifier9.5.4. Growing RBF Network9.5.5. Identification of Multivariable Systems9.6. A Self-Organizing Network9.7. Hopfield Neural Network9.7.1. Hopfield Neural Network Modeling and Analysis9.7.2. Analog-to-Digital Converter9.8. Hopfield Network Stability Analysis9.8.1. Hopfield Network Model Analysis9.8.2. Single Neuron Stability Analysis9.8.3. Stability Analysis of the Network9.9. Brain-State-in-a-Box (BSB) Models9.9.1. Associative Memories9.9.2. Analysis of BSB Models9.9.3. Synthesis of Neural Associative Memory9.9.4. Learning9.9.5. Forgetting10. Genetic and Evolutionary Algorithms10.1. Genetics as an Inspiration for an Optimization Approach10.2. Implementing a Canonical Genetic Algorithm10.3. Analysis of the Canonical Genetic Algorithm10.4. Simple Evolutionary Algorithm (EA)10.5. Evolutionary Fuzzy Logic Controllers10.5.1. Vehicle Model and Control Objective10.5.2. Case 1: EA Tunes Fuzzy Rules10.5.3. Case 2: EA Tunes Fuzzy Membership Functions10.5.4. Case 3: EA Tunes Fuzzy Rules and Membership Functions11. Chaotic Systems and Fractals11.1. Chaotic Systems Are Dynamical Systems with Wild Behavior11.2. Chaotic Behavior of the Logistic Equation11.2.1. The Logistic Equation---An Example From Ecology11.2.2. Stability Analysis of the Logistic Map11.2.3. Period Doubling to Chaos11.2.4. The Feigenbaum Numbers11.3. Fractals11.3.1. The Mandelbrot Set11.3.2. Julia Sets11.3.3. Iterated Function Systems11.4. Lyapunov Exponents11.5. Discretization Chaos11.6. Controlling Chaotic Systems11.6.1. Ingredients of Chaotic Control Algorithm11.6.2. Chaotic Control AlgorithmAppendix: Math ReviewA.1. Notation and Methods of ProofA.2. VectorsA.3. Matrices and DeterminantsA.4. Quadratic FormsA.5. The Kronecker ProductA.6. Upper and Lower BoundsA.7. SequencesA.8. FunctionsA.9. Linear OperatorsA.10. Vector SpacesA.11. Least SquaresA.12. Contraction MapsA.13. First-Order Differential EquationA.14. Integral and Differential InequalitiesA.14.1. The Bellman-Gronwall LemmaA.14.2. A Comparison TheoremA.15. Solving the State EquationsA.15.1. Solution of Uncontrolled SystemA.15.2. Solution of Controlled SystemA.16. Curves and SurfacesA.17. Vector Fields and Curve IntegralsA.18. Matrix Calculus FormulasNotesExercisesBibliographyIndex