NONLINEAR AND ADAPTIVE (INTELLIGENT) SYSTEMS MODELING, DESIGN, & CONTROL A Building Block Approach

Transcription

1 NONLINEAR AND ADAPTIVE (INTELLIGENT) SYSTEMS MODELING, DESIGN, & CONTROL A Building Block Approach P.A. (Rama) Ramamoorthy Electrical & Computer Engineering and Comp. Science Dept., M.L. 30, University of Cincinnati, Cincinnati, OH Fax:(513) ; Tel:(513) pramamoo@ececs.uc.edu CHAPTER 1 Introduction 1.1. General Theme A simple example to illustrate the general theme 1.2. Materials Covered: An overview 1.3. Advantages of Nonlinear Dynamics & Some Applications 1.4. Organization of the Book PART I BASIC THEORY CHAPTER 2 Fundamental Concepts in Signals & LTI Systems 2.0. Introduction 2.1. Representation of Signals 2.2. Systems 2.3. State and State Variables of a System 2.4. Analysis, Modeling, and Synthesis (Design) of Systems 2.5. Linear and Time-Invariant Systems LTI Signal Processing or Filtering LTI Control Similarities & Differences between LTI Signal Processing and Control 2.6. Summary CHAPTER 3 Simulation of Analog Systems & Design of Digital 3.0. Introduction Systems from Analog System Prototypes

2 3.1. The Design Cycle for LTI & Nonlinear, Time-Varying Systems 3.2. Transformations for Simulation of Analog Systems Various Analog to Digital Transformations Forward and Backward Euler Transformation: Bilinear or Trapezoidal Transform Higher-Order Rational Transforms Fractional Degree Transformations Modified Euler Method & Runge-Kutta Methods Distortions due to Transformations 3.3 Digital Systems from Analog System Architectures 3.4. Summary CHAPTER 4 Nonlinear Time-Invariant (Autonomous) Systems Analysis: The Classical Approach 4.0. Introduction 4.1. Basic Concepts of Nonlinear Systems LTI Systems Revisited Using Nonlinear Systems Terminology Nonlinear System Models: Autonomous and Non-autonomous Systems Stable, Unstable, Single, and Multiple Equilibrium Points of Autonomous Nonlinear Systems Concepts of Stability in Autonomous Nonlinear Systems 4.2. Autonomous Nonlinear System Analysis Tools Graphical Approach for the Analysis of Nonlinear Systems Lyapunov's Linearization Method Lyapunov's Direct Method 4.3. Forced Response of Nonlinear Autonomous Systems Forcing Functions in Nonlinear Dynamics Is separation into Transient and Forced Response Necessary? BIBO Stability and Total Stability of Nonlinear Autonomous Systems 4.4. Summary CHAPTER 5 Linear and Nonlinear (Time-Invariant) Electrical 5.0. Introduction Elements as Building Blocks for Nonlinear Systems 5.1. Basic Concepts: Electrical Source, Power, and Energy 5.2. Linear and Nonlinear (Time-invariant) Electrical Elements Nonlinear & Self-Learning ii P.A. (Rama) Ramamoorthy

3 Passive (Lossless and Lossy) and Active Elements One-Port Memoryless Devices Passive, Linear and Nonlinear TI resistors Nonpassive, Linear and Nonlinear TI resistors Multi-port Memoryless Devices Transformers with constant turns ratio Nonlinear Transformers Two port, Linear Gyrators Multi-port, Linear Gyrators Circulator: A special three-port Gyrator Nonlinear Gyrators One Port elements with Memory Capacitors Linear Time-Invariant Capacitors Interconnection of LTI Capacitors and Independent & or Controlled Sources Nonlinear Time Invariant Capacitors Charge controlled or voltage controlled NLTI Capacitors? Importance of the Number and Value of relaxation points Inductors Linear Time-Invariant inductors Interconnection of LTI Inductors and Independent & or Controlled Sources Nonlinear Time-Invariant Inductors Multi-port Devices with Memory Two-port LTI Coupled Inductors Stored Energy and the Inductance Matrix Parameters Equivalent Circuit Representation of magnetically coupled multi-port inductors based on Ideal Transformers M-Port (M > 2) LTI Coupled Inductors Nonlinear Time Invariant Coupled Inductors Energy Stored in a NLTI Coupled Inductor 5.3. Summary Chapter 6 Circuits made of Linear and Nonlinear (Time-Invariant) Electrical Elements & their Dynamics. Nonlinear & Self-Learning iii P.A. (Rama) Ramamoorthy

4 6.0. Introduction 6.1. Circuits made of Linear Time-Invariant Passive Elements Kirchhoff's current and voltage law and Tellegen s theorem Restrictions on the Interconnections I/O Characteristics of Linear Time-Invariant passive Networks Admittance / Impedance Matrices of Multi-port Linear LTI passive nets Impedance Scaling and Frequency Transformations in LTI Passive Nets 6.2. Circuits made of Nonlinear Time -Invariant Passive Elements Transient and forced response of Nonlinear TI Passive circuits Is Separation into transient and forced response really necessary? Absolute Stability Vs. BIBO Stability: Network Interpretation 6.3. Summary CHAPTER 7 The Classical Approach to Time-Variant (Non- Autonomous), Linear & Nonlinear systems Introduction 7.1. Non-autonomous System Models and Examples 7.2. Equilibrium points and Stability Concepts 7.3. Lyapunov's Direct Method for Stability Analysis of Non-autonomous Systems 7.4. Analysis of Non-Autonomous Systems 7.5. Summary Chapter 8 Time-Varying (Linear and Nonlinear) Electrical Elements, Circuits made of such elements & the resulting Dynamics Introduction 8.1. Time-Varying Passive Electrical Elements Time-Varying Resistors Time-Varying Gyrators Time-vVarying Transformers Time-Varying Capacitors Time-Varying Inductors 8.2. Time-Varying Active and Non-passive Elements 8.3. Electrical Circuits with Time-Varying passive Elements 8.4. Summary Nonlinear & Self-Learning iv P.A. (Rama) Ramamoorthy

5 PART II APPLICATION OF NONLINEAR DYNAMICS & THE NEW PARADIGM CHAPTER 9 Modeling Nonlinear Systems - The classical Approach 9.0. Introduction 9.1. Mathematical/Signal Flow-Graph Approaches to Modeling of Nonlinear Autonomous Systems Modeling of Nonlinear Systems with no Memory Modeling using Orthonormal polynomials Convergence Properties of the Models Modeling through measurements Nonlinear time-invariant systems with memory Volterra Series Representation Volterra-Wiener Series Representation Identification of Wiener Kernels by Cross-correlation Restrictions on the use of Volterra Wiener Models Cascade Models Neural Network Models 9.2. Summary CHAPTER Introduction Nonlinear Dynamical Systems Design Using Passive & Non-passive Elements as Building Blocks Stable Nonlinear Dynamics from Passive Elements General Philosophy Precedence Constrained Optimization Problem to Unconstrained Optimization Problem Stability, Sensitivity & Filter Design Problems 1. Combined Frequency and Impedance Scaling in Active RC Networks 2. One-Dimensional Digital Filters from One-dimensional continuous Filter Prototypes and s to z Transformations 3. Stable Two-Dimensional Digital Filters from Two- Dimensional Continuous Filters Complex First-Order and Second-Order Dynamics from Passive Networks Nonlinear & Self-Learning v P.A. (Rama) Ramamoorthy

6 st-order Dynamics nd Order Dynamics General Form of Higher-Order Nonlinear Dynamical Equations from Passive Networks Global Asymptotic Stability of NL Dynamics from Passive Networks Global Asymptotic Stability vs. BIB0 stability: A Network Interpretation Network Models of some well-known Nonlinear Systems Example 1. Model of an underwater vehicle Example 2 Van der Pol Equation Example 3 The Pendulum Design of Nonlinear Time-Varying Systems using the Building Block Concept Summary Chapter 11 Nonlinear Dynamical control Design using the Building block & the Reverse Engineering Approach Introduction Modeling of Physical Systems Asymptotic Stabilization Feedback Linearization Set-Point Control or Regulation Problem Tracking Control Non-Minimum Phase Plants - A Reality or An Artifact of Mathematical Approximation Controller Design Using the Building Block Approach Asymptotic Stabilization and Examples Tracking and Examples Discussion and Conclusion CHAPTER 12 Adaptive Control Introduction Basic Concepts in Adaptive Control Adaptive Control - A Nonlinear Passive Network Approach Summary CHAPTER Introduction Nonlinear Filtering of Signals Nonlinear & Self-Learning vi P.A. (Rama) Ramamoorthy

7 13.1. Linear Filtering - Principles and Limitations Design of Nonlinear Filters Basic Concept One-Dimensional Signal Filtering Filtering of Images Problems and Challenges in Nonlinear Filtering Summary CHAPTER 14 Nonlinear Processing Techniques in Signal Estimation Introduction Linear Processing Techniques in Signal Detection and Estimation: (Detection and Estimation; Matched Filtering; Linear Minimum Mean Squared Estimation; Recursive {Kalman} Filtering) Nonlinear Recursive Estimation Summary CHAPTER Introduction Neural Networks Neural Networks: A Primer Basic Terminology and Functions Primitives Neural Architectures & Feed-forward Neural Nets Implementation Issues Techniques for Signal Encoding Application of Neural Nets Redundancy in Coding & Redundancy in Problem Domain Storage capacity & cross talk Approximation or Training or Learning Recurrent Neural Nets Basic Concepts A Simple RNN Response & stability definitions for RNNs Some well known RNNs Continuous Domain Models Hopfield Model Continuous Additive Bi-directional associative Memory (CABAM) Nonlinear & Self-Learning vii P.A. (Rama) Ramamoorthy

8 Grossberg Models Cohen-Grossberg Model Continuous Bi-directional Associative Memories Continuous Bi-directional Associative Memories Discrete RNN Models Proof for RNN Stability --- NN Style Hopfield Network Discrete Bivalent BAM Model RNNs Using Passive and Active Electrical Net Building Blocks General Concept specific RNN architectures Continuous BAM Dynamics from Network Dynamics Function being minimized by Nonlinear Dynamics from Recurrent Neural Networks Storage Capacity of New RNN Architectures Training based on Network Concepts Summary CHAPTER 16 Fuzzy Expert Systems / Fuzzy Controllers Introduction Fuzzy Logic and Fuzzy Expert Systems - A Primer 16.2 Fuzzy Expert Systems as Controllers Systems for Nonlinear Mapping / Transformation Limitations of Classical Fuzzy Controllers Stability of Closed Loop Systems using Fuzzy Controllers Results from Classical Nonlinear Control Theory Sector Condition and Aizerman's Conjecture Popov's Criterion Fuzzy Expert Systems & Neural Networks: Compare, Contrast & Merge Digital Architecture of FESs & FCs for Real-Time Applications Cerebellar Model Articulation Controllers (CMAC) Neural Networks Vs Fuzzy Expert Systems Design of Stable Feedback Fuzzy Expert Systems and Stable closed Loop Systems with Feedback Fuzzy Controllers Design of Stable Feedback Fuzzy Expert Systems Design of Stable closed Loop Systems with Feedback Fuzzy Controllers Nonlinear & Self-Learning viii P.A. (Rama) Ramamoorthy

9 16.5. Summary CHAPTER 17 Nonlinear Circuits, Limit Cycles, Chaos, And Fractals Introduction Circuits made of Nonlinear Elements and Chaos Nonlinear Circuits with only Passive Elements driven by sinusoidal sources Networks with Nonlinear, Nonpassive Elements with continuously differential characteristics Networks with Nonlinear, Nonpassive elements with piece-wise linear linear characteristics Chaos from One-Parameter Nonlinear Discrete Systems and Interpretation from a Network or Continuous Systems Perspective Dynamics of Nonlinear Circuits Vs Fractals Summary Nonlinear & Self-Learning ix P.A. (Rama) Ramamoorthy