Analysis and Synthesis of Fuzzy Control Systems: A Model-Based Approach

Fuzzy logic control (FLC) has proven to be a popular control methodology for many complex systems in industry, and is often used with great success as an alternative to conventional control techniques. However, because it is fundamentally model free, conventional FLC suffers from a lack of tools for systematic stability analysis and controller design. To address this problem, many model-based fuzzy control approaches have been developed, with the fuzzy dynamic model or the Takagi and Sugeno (T–S) fuzzy model-based approaches receiving the greatest attention.
Analysis and Synthesis of Fuzzy Control Systems: A Model-Based Approach offers a unique reference devoted to the systematic analysis and synthesis of model-based fuzzy control systems. After giving a brief review of the varieties of FLC, including the T–S fuzzy model-based control, it fully explains the fundamental concepts of fuzzy sets, fuzzy logic, and fuzzy systems. This enables the book to be self-contained and provides a basis for later chapters, which cover:


T–S fuzzy modeling and identification via nonlinear models or data
Stability analysis of T–S fuzzy systems
Stabilization controller synthesis as well as robust H8 and observer and output feedback controller synthesis
Robust controller synthesis of uncertain T–S fuzzy systems
Time-delay T–S fuzzy systems
Fuzzy model predictive control
Robust fuzzy filtering
Adaptive control of T–S fuzzy systems

A reference for scientists and engineers in systems and control, the book also serves the needs of graduate students exploring fuzzy logic control. It readily demonstrates that conventional control technology and fuzzy logic control can be elegantly combined and further developed so that disadvantages of conventional FLC can be avoided and the horizon of conventional control technology greatly extended. Many chapters feature application simulation examples and practical numerical examples based on MATLAB®.

Gang (Gary) Feng is Associate Provost and Chair Professor of Mechatronic Engineering at the City University of Hong Kong. He is also the Cheung Kong Chair Professor at Nanjing University of Science and Technology conferred by the Education Ministry of China. Dr. Feng has done research work in adaptive control, robot control, intelligent control, and, more recently, control of piecewise linear systems and switched systems. His research work has led to the publication of one edited book, seven invited book chapters, and over 180 international journal papers and numerous international conference papers. He has received the IEEE Transactions on Fuzzy Systems Outstanding Paper Award (2007), an Alexander von Humboldt Research Fellowship of Germany (1997), and a number of best conference paper awards. He has been invited to give plenary/special lectures at a number of international conferences. Dr. Feng is an IEEE Fellow and an associate editor of IEEE Transactions on Automatic Control, IEEE Transactions on Fuzzy Systems, and Mechatronics. He has served as an associate editor of IEEE Transactions on Systems, Man, & Cybernetics, Part C, Control Theory and Applications, and on the Conference Editorial Board, IEEE Control Systems Society.

Chapter 1. Introduction to Fuzzy Logic Control 1.1 Introduction 1.2 Brief Review of Fuzzy Logic Control 1.2.1 Conventional Fuzzy Control (Mamdani-Type Fuzzy Control) 1.2.2 Fuzzy PID Control 1.2.3 Neuro–Fuzzy Control or Fuzzy–Neuro Control 1.2.4 Fuzzy Sliding Mode Control 1.2.5 Adaptive Fuzzy Control 1.2.6 Takagi–Sugeno Model-Based Fuzzy Control 1.3 Summary Chapter 2. Fuzzy Sets and Fuzzy Systems 2.1 Introduction 2.2 Fuzzy Sets and Related Concepts 2.3 Fuzzy Relations and Fuzzy IF–THEN Rules 2.4 Fuzzy Reasoning 2.5 Fuzzy Models and Fuzzy Systems 2.5.1 Mamdani Fuzzy Systems 2.5.2 Takagi–Sugeno Fuzzy Systems 2.5.3 Fuzzy Dynamic Systems 2.6 Conclusions Chapter 3. T–S Fuzzy Modeling and Identification 3.1 Introduction 3.2 T–S Fuzzy Models 3.3 Universal Function Approximators 3.4 T–S Fuzzy Model Identification from Nonlinear Models 3.5 T–S Fuzzy Model Identification from Data 3.5.1 Identification of Membership Functions 3.5.2 Identification of Local Models 3.6 Approximation Error Analysis 3.7 Conclusions Chapter 4. Stability Analysis of T–S Fuzzy Systems 4.1 Introduction 4.2 Stability Analysis Based on Common Quadratic Lyapunov Functions 4.3 Stability Analysis Based on Piecewise Quadratic Lyapunov Functions 4.4 Stability Analysis Based on Fuzzy Quadratic Lyapunov Functions 4.5 Stability Analysis of T–S Fuzzy Affine Systems Based on Piecewise Quadratic Lyapunov Functions 4.6 Comparison of Stability Results via Numerical Examples 4.7 Conclusions Chapter 5. Stabilization Controller Synthesis of T–S Fuzzy Systems 5.1 Introduction 5.2 Stabilization Based on Common Quadratic Lyapunov Functions 5.3 Stabilization Based on Piecewise Quadratic Lyapunov Functions 5.4 Stabilization Based on Fuzzy Quadratic Lyapunov Functions 5.5 Comparison of Stabilization Results via Numerical Examples 5.6 Conclusions Chapter 6. Robust H∞ Controller Synthesis of T–S Fuzzy Systems 6.1 Introduction 6.2 Robust H∞ Control Based on Common Quadratic Lyapunov Functions 6.3 Robust H∞ Control Based on Piecewise Quadratic Lyapunov Functions 6.4 Robust H∞ Control Based on Fuzzy Quadratic Lyapunov Functions 6.5 Comparison of Robust H∞ Control Results via Numerical Examples 6.6 Conclusions Chapter 7. Observer and Output Feedback Controller Synthesis of T–S Fuzzy Systems 7.1 Introduction 7.2 Observer and Output Feedback Controller Synthesis Based on Common Quadratic Lyapunov Functions 7.3 Observer and Output Feedback Controller Synthesis Based on Piecewise Quadratic Lyapunov Functions 7.4 Observer and Output Feedback Controller Synthesis Based on Fuzzy Quadratic Lyapunov Functions 7.5 Comparison of Observer Design Results via Numerical Examples 7.6 Conclusions Chapter 8. Robust Controller Synthesis of Uncertain T–S Fuzzy Systems 8.1 Introduction 8.2 Model of Uncertain T–S Fuzzy Systems 8.3 Controller Synthesis Based on Piecewise Quadratic Lyapunov Functions 8.3.1 Robust H∞ Performance Analysis 8.3.2 Piecewise State Feedback Controller Design 8.3.3 Piecewise Output Feedback Controller Design 8.4 Controller Synthesis Based on Fuzzy Quadratic Lyapunov Functions 8.4.1 Robust H∞ Performance Analysis 8.4.2 State Feedback Controller Design 8.4.3 Output Feedback Controller Design 8.5 An Example 8.6 Conclusions Chapter 9. Controller Synthesis of T–S Fuzzy Systems with Time-Delay 9.1 Introduction 9.2 Model of T–S Fuzzy Systems with Time-Delay 9.3 Controller Synthesis Based on Piecewise Quadratic Lyapunov Functionals 9.3.1 Delay-Independent H∞ Controller Design 9.3.2 Delay-Dependent H∞ Controller Design 9.4 Controller Synthesis Based on Fuzzy Quadratic Lyapunov Functionals 9.4.1 Delay-Independent H∞ Controller Design 9.4.2 Delay-Dependent H∞ Controller Design 9.5 An Example 9.6 Conclusions Chapter 10. Fuzzy Model Predictive Control 10.1 Introduction 10.2 Problem Formulation 10.3 Fuzzy Model Predictive Control Approaches 10.3.1 Fuzzy Min–Max MPC Based on Common Quadratic Lyapunov Functions 10.3.2 Fuzzy Min–Max MPC Based on Piecewise Quadratic Lyapunov Functions 10.3.3 Constrained Fuzzy MPC 10.4 Simulation Examples 10.5 Conclusions Chapter 11. Robust Filtering of T–S Fuzzy Systems 11.1 Introduction 11.2 Problem Formulation 11.3 Filter Design Based on Common Quadratic Lyapunov Functions 11.3.1 H∞ Filter Design 11.3.2 Generalized H2 Filter Design 11.4 Filter Design Based on Piecewise Quadratic Lyapunov Functions 11.4.1 H∞ Filter Design 11.4.2 Generalized H2 Filter Design 11.5 Filter Design Based on Fuzzy Quadratic Lyapunov Functions 11.5.1 H∞ Filter Design 11.5.2 Generalized H2 Filter Design 11.6 Simulation Examples 11.7 Conclusions Chapter 12. Adaptive Control of T–S Fuzzy Systems 12.1 Introduction 12.2 Problem Formulation 12.3 Adaptive Control System Design 12.3.1 Adaptation Algorithm 12.3.2 Controller Design with Known Parameters 12.3.3 Adaptive Control System Design 12.3.4 Robust Adaptive Control 12.4 A Simulation Example 12.5 Conclusions Appendix Several Useful Lemmas References Index