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 45221-0030 Fax:(513)556-7326; Tel:(513)556-4757 Email: pramamoo@ececs.uc.edu CHAPTER 1 Introduction 1.1. General Theme 1.1.1. 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 2.5.1. LTI Signal Processing or Filtering 2.5.2. LTI Control 2.5.3. 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
3.1. The Design Cycle for LTI & Nonlinear, Time-Varying Systems 3.2. Transformations for Simulation of Analog Systems 3.2.1. 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 3.2.2. 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 4.1.1. LTI Systems Revisited Using Nonlinear Systems Terminology 4.1.2. Nonlinear System Models: Autonomous and Non-autonomous Systems 4.1.3. Stable, Unstable, Single, and Multiple Equilibrium Points of Autonomous Nonlinear Systems 4.1.4. Concepts of Stability in Autonomous Nonlinear Systems 4.2. Autonomous Nonlinear System Analysis Tools 4.2.1. Graphical Approach for the Analysis of Nonlinear Systems 4.2.2. Lyapunov's Linearization Method 4.2.3. Lyapunov's Direct Method 4.3. Forced Response of Nonlinear Autonomous Systems 4.3.1. Forcing Functions in Nonlinear Dynamics 4.3.2. Is separation into Transient and Forced Response Necessary? 4.3.3. 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
5.2.1. Passive (Lossless and Lossy) and Active Elements 5.2.2. One-Port Memoryless Devices Passive, Linear and Nonlinear TI resistors Nonpassive, Linear and Nonlinear TI resistors 5.2.3. 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 5.2.4. 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 5.2.5. 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
6.0. Introduction 6.1. Circuits made of Linear Time-Invariant Passive Elements 6.1.1. Kirchhoff's current and voltage law and Tellegen s theorem 6.1.2. Restrictions on the Interconnections 6.1.3. I/O Characteristics of Linear Time-Invariant passive Networks 6.1.4. Admittance / Impedance Matrices of Multi-port Linear LTI passive nets 6.1.5. Impedance Scaling and Frequency Transformations in LTI Passive Nets 6.2. Circuits made of Nonlinear Time -Invariant Passive Elements 6.2.1. Transient and forced response of Nonlinear TI Passive circuits 6.2.2. Is Separation into transient and forced response really necessary? 6.2.3. Absolute Stability Vs. BIBO Stability: Network Interpretation 6.3. Summary CHAPTER 7 The Classical Approach to Time-Variant (Non- Autonomous), Linear & Nonlinear systems. 7.0. 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. 8.0. Introduction 8.1. Time-Varying Passive Electrical Elements 8.1.1 Time-Varying Resistors 8.1.2. Time-Varying Gyrators 8.1.3. Time-vVarying Transformers 8.1.4. Time-Varying Capacitors 8.1.5. 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
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 9.1.1. Modeling of Nonlinear Systems with no Memory 9.1.1.1 Modeling using Orthonormal polynomials Convergence Properties of the Models 9.1.1.2 Modeling through measurements 9.1.2 Nonlinear time-invariant systems with memory 9.1.2.1 Volterra Series Representation 9.1.2.2 Volterra-Wiener Series Representation Identification of Wiener Kernels by Cross-correlation Restrictions on the use of Volterra Wiener Models 9.1.2.3 Cascade Models 9.1.2.4 Neural Network Models 9.2. Summary CHAPTER 10 10.0. Introduction Nonlinear Dynamical Systems Design Using Passive & Non-passive Elements as Building Blocks 10.1. Stable Nonlinear Dynamics from Passive Elements 10.1.1. General Philosophy 10.1.2. 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 10.2. Complex First-Order and Second-Order Dynamics from Passive Networks Nonlinear & Self-Learning v P.A. (Rama) Ramamoorthy
10.2.1. 1st-order Dynamics 10.2.2. 2nd Order Dynamics 10.3. General Form of Higher-Order Nonlinear Dynamical Equations from Passive Networks 10.4. Global Asymptotic Stability of NL Dynamics from Passive Networks 10.5. Global Asymptotic Stability vs. BIB0 stability: A Network Interpretation 10.6. 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 10.7. Design of Nonlinear Time-Varying Systems using the Building Block Concept 10.8. Summary Chapter 11 Nonlinear Dynamical control Design using the Building block & the Reverse Engineering Approach 11.0. Introduction 11.1. Modeling of Physical Systems 11.2. Asymptotic Stabilization 11.2.1. Feedback Linearization 11.3. Set-Point Control or Regulation Problem 11.4. Tracking Control Non-Minimum Phase Plants - A Reality or An Artifact of Mathematical Approximation 11.5. Controller Design Using the Building Block Approach 11.5.1. Asymptotic Stabilization and Examples 11.5.2. Tracking and Examples 11.6. Discussion and Conclusion CHAPTER 12 Adaptive Control 12.0. Introduction 12.1. Basic Concepts in Adaptive Control 12.2. Adaptive Control - A Nonlinear Passive Network Approach 12.3. Summary CHAPTER 13 13.0. Introduction Nonlinear Filtering of Signals Nonlinear & Self-Learning vi P.A. (Rama) Ramamoorthy
13.1. Linear Filtering - Principles and Limitations 13.2. Design of Nonlinear Filters Basic Concept One-Dimensional Signal Filtering Filtering of Images 13.3. Problems and Challenges in Nonlinear Filtering 13.4. Summary CHAPTER 14 Nonlinear Processing Techniques in Signal Estimation 14.0. Introduction 14.1. Linear Processing Techniques in Signal Detection and Estimation: (Detection and Estimation; Matched Filtering; Linear Minimum Mean Squared Estimation; Recursive {Kalman} Filtering) 14.2. Nonlinear Recursive Estimation 14.3. Summary CHAPTER 15 15.0. Introduction Neural Networks 15.1. Neural Networks: A Primer 15.1.1. Basic Terminology and Functions 15.1.2. Primitives Neural Architectures & Feed-forward Neural Nets 15.1.3. Implementation Issues 15.1.4. Techniques for Signal Encoding 15.1.5. Application of Neural Nets 15.1.6. Redundancy in Coding & Redundancy in Problem Domain 15.1.7. Storage capacity & cross talk 15.1.8. Approximation or Training or Learning 15.2. Recurrent Neural Nets 15.2.1. Basic Concepts 15.2.2. A Simple RNN 15.2.3. Response & stability definitions for RNNs 15.2.4. Some well known RNNs 15.2.4.1. Continuous Domain Models Hopfield Model Continuous Additive Bi-directional associative Memory (CABAM) Nonlinear & Self-Learning vii P.A. (Rama) Ramamoorthy
Grossberg Models Cohen-Grossberg Model Continuous Bi-directional Associative Memories Continuous Bi-directional Associative Memories 15.2.4.2. Discrete RNN Models 15.2.5. Proof for RNN Stability --- NN Style Hopfield Network Discrete Bivalent BAM Model 15.3. RNNs Using Passive and Active Electrical Net Building Blocks 15.3.1. General Concept 15.3.2. specific RNN architectures Continuous BAM Dynamics from Network Dynamics 15.3.3. Function being minimized by Nonlinear Dynamics from Recurrent Neural Networks 15.3.4. Storage Capacity of New RNN Architectures 15.3.5. Training based on Network Concepts 15.4. Summary CHAPTER 16 Fuzzy Expert Systems / Fuzzy Controllers 16.0. Introduction 16.1. Fuzzy Logic and Fuzzy Expert Systems - A Primer 16.2 Fuzzy Expert Systems as Controllers. 16.2.1. Systems for Nonlinear Mapping / Transformation 16.2.2. Limitations of Classical Fuzzy Controllers 16.2.3. Stability of Closed Loop Systems using Fuzzy Controllers Results from Classical Nonlinear Control Theory Sector Condition and Aizerman's Conjecture Popov's Criterion 16.3. Fuzzy Expert Systems & Neural Networks: Compare, Contrast & Merge 16.3.1. Digital Architecture of FESs & FCs for Real-Time Applications 16.3.2. Cerebellar Model Articulation Controllers (CMAC) Neural Networks Vs Fuzzy Expert Systems 16.4. Design of Stable Feedback Fuzzy Expert Systems and Stable closed Loop Systems with Feedback Fuzzy Controllers 16.4.1. Design of Stable Feedback Fuzzy Expert Systems 16.4.2. Design of Stable closed Loop Systems with Feedback Fuzzy Controllers Nonlinear & Self-Learning viii P.A. (Rama) Ramamoorthy
16.5. Summary CHAPTER 17 Nonlinear Circuits, Limit Cycles, Chaos, And Fractals 17.0. Introduction 17.1. Circuits made of Nonlinear Elements and Chaos 17.1.1. Nonlinear Circuits with only Passive Elements driven by sinusoidal sources 17.1.2. Networks with Nonlinear, Nonpassive Elements with continuously differential characteristics 17.1.3. Networks with Nonlinear, Nonpassive elements with piece-wise linear linear characteristics 17.2. Chaos from One-Parameter Nonlinear Discrete Systems and Interpretation from a Network or Continuous Systems Perspective 17.3. Dynamics of Nonlinear Circuits Vs Fractals 17.4. Summary Nonlinear & Self-Learning ix P.A. (Rama) Ramamoorthy