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9780471986317

Fuzzy Control Synthesis and Analysis

by ; ;
  • ISBN13:

    9780471986317

  • ISBN10:

    0471986313

  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2000-06-08
  • Publisher: WILEY
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Summary

Fuzzy Control Synthesis and Analysis Edited by Shehu S. Farinwata Ford Motor Company, Research Laboratory, Dearborn, Michigan, USA Dimitar Filev Ford Motor Company, AMTDC, Redford, Michigan, USA Reza Langari Texas A & M University, College Station, Texas, USA Fuzzy techniques are used to cope with imprecision in the basic elements of a process under control. Written by an international team of researchers this edited volume covers the modeling, analysis and synthesis of fuzzy control systems. Features include: ? Comprehensive coverage of fuzzy dynamical systems, robustness, stability and sensitivity -- giving the reader a good grasp of the fundamentals of fuzzy control ? Focus on the analytical structures of new fuzzy modeling approaches based on the Takagi-Sugeno-Kang (TSK) or Takagi-Sugeno (TS) model ? Applications of fuzzy control to aircraft systems, rocket engines and automotive engines ? Problems and examples illustrating how fuzzy approaches may be applied to the modeling, analysis and synthesis of closed-loop systems Design and control engineers will value the advanced control techniques and new design and analysis tools presented. Postgraduates studying fuzzy control will find this book a useful reference on synthesis, systems analysis and advanced nonlinear control methods.

Author Biography

Shehu S. Farinwata and Dimitar P. Filev are the authors of Fuzzy Control: Synthesis and Analysis, published by Wiley.

Table of Contents

Editor's Preface xi
List of Contributors
xix
About the Editors xxi
Acknowledgments xxiii
MODELING 1(236)
Information Granularity in the Analysis and Design of Fuzzy Controllers
3(20)
Introduction
3(1)
The Basic Architecture of the Fuzzy Controller and its Non-linear Relationships
4(3)
Set-Based Approximation of Fuzzy Sets
7(3)
Information Granularity of the Rules of the Fuzzy Controller
10(3)
Fuzzy Sets and Information Granularity
11(2)
Robustness Properties of the Fuzzy Controller
13(4)
Linguistic Information as Inputs of the Fuzzy Controller
17(4)
Conclusions
21(2)
Acknowledgment
21(1)
References
21(2)
Fuzzy Modeling for Predictive Control
23(24)
Introduction
23(1)
Fuzzy Modeling
24(2)
Outline of the Modeling Approach
24(2)
Extraction of an Initial Rule Base
26(1)
Simplification and Reduction of the Initial Rule Base
27(3)
Similarity Analysis
28(1)
Simplification and Reduction
28(2)
Model Predictive Control
30(4)
Basic Principles
30(1)
Optimization in MPC
31(1)
The Branch-and-Bound Optimization
32(2)
Modeling and Control of an HVAC Process
34(8)
Initial Modeling of the System
35(1)
Validating the Initial Model
35(4)
Simplifying the HVAC Model
39(1)
Control Results
40(1)
Summary of Results
41(1)
Concluding Remarks
42(5)
The Gustafson--Kessel Clustering Algorithm
43(1)
The Rule Base Simplification Algorithm
44(1)
References
45(2)
Adaptive and Learning Schemes for Fuzzy Modeling
47(26)
Introduction
47(2)
Identification Problems of the TSK Fuzzy Models
49(5)
Criteria and Schemes for Learning and Evaluation of Fuzzy Models
54(2)
The Global Learning Criterion, QG
54(1)
The Local Learning Criterion, QL
55(1)
Evaluation Criteria
56(1)
Algorithms for Global Learning by Fuzzy Models
56(7)
Comparison of the Learning Algorithm Using a Numerical Example
59(4)
Algorithm for Local Learning by Fuzzy Models
63(3)
Reinforced Learning Algorithm
66(1)
Simulation Results for Control Applications
67(3)
Conclusions
70(3)
References
70(3)
Fuzzy System Identification with General Parameter Radial Basis Function Neural Network
73(22)
Introduction
73(2)
Fuzzy Systems through Neural Networks
75(3)
Radial Basis Function Neural Networks
77(1)
General Parameter Radial Basis Function Network (GP RBFN)
78(3)
General Parameter Method for System Identification
79(1)
GP RBFN Training Algorithm
80(1)
GP RBFN Adaptive Fuzzy Systems (AFSs)
81(3)
Basic Algorithm
81(2)
Unbiasedness Criterion for the GP RBFN AFS
83(1)
Simulation Results
84(6)
Conclusion
90(5)
References
91(4)
ANALYSIS
Lyapunov Stability Analysis of Fuzzy Dynamic Systems
95(18)
Introduction
95(1)
Mathematical Preliminaries
96(1)
Construction of Fuzzy Dynamic Models from Discrete-Time Stochastic Models
97(2)
Construction of Fuzzy Dynamic Models via Fuzzy Composition
98(1)
Construction of a Fuzzy Dynamic Model via the Fuzzy Extension Principle
99(1)
Stability Analysis of Fuzzy Dynamic Systems
99(5)
Convergence in Fuzzy Dynamic Systems
100(1)
Stability of Fuzzy Dynamic Systems
100(3)
The Direct Lyapunov Method for Fuzzy Dynamic Systems
103(1)
Application---First-Order Fuzzy Dynamic System
104(6)
Concluding Remarks
110(3)
References
111(2)
Passivity and Stability of Fuzzy Control Systems
113(32)
Introduction
113(1)
Fuzzy Control Systems
114(3)
Mamdani Fuzzy Controllers
114(1)
Takagi -- Sugeno Fuzzy Control Systems
115(2)
Stability and Passivity of Fuzzy Controllers
117(13)
Basic Concepts
117(5)
Passivity of QPI Controllers
122(1)
Passivity of DPS Controllers
123(3)
Passivity of Polytopic Differential Inclusions
126(4)
Stability of Feedback Control with Fuzzy Controllers
130(5)
Feedback Control with QPI Mamdani Controllers
131(1)
Feedback Control with DPS Mamdani Controllers
131(2)
Feedback Control with Linear Takagi-Sugano Controllers
133(2)
Applications
135(3)
Control of LTI Systems by Fuzzy Controllers
136(1)
Fuzzy Control of Euler-Lagrange Systems
137(1)
Conclusions
138(7)
Acknowledgments
139(1)
Appendix
139(3)
References
142(3)
Frequency Domain Analysis of MIMO Fuzzy Control Systems
145(8)
Introduction
145(1)
Multiple Equilibria in MIMO Fuzzy Control Systems
146(2)
Frequency Analysis of Limit Cycles
148(1)
Robust Analysis of Limit Cycles using Singular Values
149(2)
Conclusions
151(2)
Acknowledgments
151(1)
References
151(2)
Analytical Study of Structure of a Mamdani Fuzzy Controller with Three Input Variables
153(12)
Introduction
153(1)
Configuration of the Fuzzy Controller
154(3)
Analytical Study of the Fuzzy Controller Structure
157(5)
Conclusion
162(3)
Acknowledgment
162(1)
References
162(3)
An Approach to the Analysis of Robust Stability of Fuzzy Control Systems
165(38)
Introduction
165(1)
Perspective
166(1)
The Nominal Fuzzy Control Problem
167(1)
Equilibrium Points for Fuzzy Controlled Processes
168(1)
Fuzzy Robustness Analysis
168(6)
Robustness Problem Statement
169(1)
Concepts of Sensitivity and Robustness
170(1)
Formulation of Fuzzy System Robustness
171(2)
The Main Result
173(1)
Derivation of the Main Result
173(1)
Generalization of the Robust Stability Result
174(4)
Virtual Interactions Based on Stability
175(2)
General Result for Robust Stabilization
177(1)
Minimizing dV
177(1)
Fuzzy Extremes of Perturbations
178(4)
A Measure of Fuzzy Robustness
179(1)
Comments
180(2)
Application Example
182(14)
Problem Statement
185(1)
Simulation Studies and Results
186(10)
Discussion
196(1)
Conclusions
196(7)
Bibliography
197(6)
Fuzzy Control Systems Stability Analysis with Application to Aircraft Systems
203(34)
Introduction
203(11)
Fuzzy Control
204(1)
Lyapunov Stability of Non-linear Fuzzy Control Systems
205(1)
The Fuzzy Control Problem
205(2)
Equilibrium Points for Fuzzy Controlled Processes
207(1)
The Partitioned State Space
208(1)
Dissipative Mapping and Input--Output Stability
208(2)
Dissipative Mapping for the Fuzzy Control System
210(1)
Stability of Linear Fuzzy Control Systems
211(1)
Positive Realness and Dissipativeness
212(2)
Verifying Dissipativeness
214(1)
Linear Continuous-Time Model Application
214(7)
A Missile Autopilot
214(1)
Analysis
215(4)
Simulation Studies and Results
219(1)
Conclusions
220(1)
Linear Discrete-Time Model Application
221(12)
Advanced Technology Wing Aircraft Model
221(1)
Introduction
221(1)
The ATW Problem
222(1)
Control Architecture
223(1)
Control Rule Synthesis
224(3)
Stability Analysis
227(5)
Conclusions
232(1)
Summary
233(4)
Bibliography
233(4)
SYNTHESIS 237(148)
Observer-Based Controller Synthesis for Model-Based Fuzzy Systems via Linear Matrix Inequalities
239(14)
Introduction
239(1)
Takagi--Sugano Models
240(3)
Continuous-Time T--S Models
240(1)
Continuous-Time T--S Controllers and Closed-Loop Stability
241(1)
Discrete-Time T--S Controllers
242(1)
LMI Stability Conditions for T--S Fuzzy Systems
243(1)
The Continuous-Time Case
243(1)
The Discrete-Time Case
243(1)
Fuzzy Observers
244(5)
Why Output Feedback?
244(1)
Continuous-Time T--S Fuzzy Observers
244(2)
Separation Property of the Observer/Controller
246(1)
Discrete-Time T--S Fuzzy Observers
247(2)
Numerical Example
249(3)
Conclusion
252(1)
References
252(1)
LMI-Based Fuzzy Control: Fuzzy Regulator and Fuzzy Observer Design via LMIs
253(14)
Introduction
253(1)
Takagi-Sugano Fuzzy Model
254(1)
Fuzzy Regulator Design via LMIs
255(7)
Parallel Distributed Compensation
255(1)
Control Performance Represented by LMIs
256(6)
Fuzzy Observer Design
262(1)
Conclusions
263(4)
References
264(3)
A framework for the Synthesis of PDC-Type Takagi-Sugano Fuzzy Control Systems: An LMI Approach
267(16)
Introduction
267(1)
Brief Historical Overview
267(1)
Background Materials
268(3)
T--S Fuzzy Model of Non-linear Dynamic Systems and its Stability
268(1)
PDC-Type T--S Fuzzy Control System and its Stability
269(2)
Stability LMIs as a Framework for the Synthesis of PDC-Type T--S Fuzzy Control Systems
271(3)
Pole Placement Constraint LMIs as Performance Specifications for the Synthesis of PDC-Type T--S Fuzzy Control Systems
274(2)
An Extension to PDC-Type T--S Fuzzy Control Systems with Parameter Uncertainties
276(3)
A Simulated Example
279(2)
Concluding Remarks
281(2)
References
282(1)
On Adaptive Fuzzy Logic Control on Non-linear Systems---Synthesis and Analysis
283(26)
Introduction
283(1)
Control Objective
284(1)
DFLS Identifier
285(2)
Control Law of the System
287(1)
Adaptive Law for the Parameter Vector Y
288(2)
Adaptive Law for g
290(1)
Stability Properties of the DFLS Control Algorithm
291(1)
Illustrative Application
292(3)
Concluding Remarks
295(14)
Proof of Theorem 7.1
296(11)
References
307(2)
Stabilization of Direct Adaptive Fuzzy Control Systems: Two Approaches
309(12)
Introduction
309(1)
Integral Sliding-Mode Adaptive FLC: Approach 1
310(4)
Structure of an Integral Sliding-Mode Adaptive FLC
310(1)
Stabilization of the Integral Sliding-mode Adaptive FLC
311(2)
Properties of the Integral Sliding-Mode Adaptive FLC
313(1)
New Fuzzy Logic Based Learning Control: Approach II
314(2)
Structure of the New Fuzzy Logic Based Learning Control
314(1)
Stabilization of the New Fuzzy Logic Based Learning Control
314(2)
Discussion of the New Fuzzy Logic Based Learning Control
316(1)
Simulation
316(3)
Approach I
316(1)
Approach II
317(2)
Concluding Remarks
319(2)
References
320(1)
Gain Scheduling Based Control of a Class of TSR Systems
321(14)
Introduction
321(1)
TSK Model as a Gain Scheduled System
322(2)
Stability Conditions for TSK Fuzzy Systems
324(3)
Synthesis of TSK Compensators
327(3)
Analytic Form of the Polytopic TSK Compensator
330(3)
Parameterization of Non-parametric TSK Compensators
333(1)
Conclusion
334(1)
References
334(1)
Output Tracking Using Fuzzy Neural Networks
335(14)
Introduction
335(2)
Problem Statement---Assumptions
337(2)
The Structure of the Controller
339(1)
The Main Results
340(1)
The Learning Algorithm
341(1)
Illustrative Examples
342(4)
Comprehensive Results and Conclusions
346(3)
References
347(2)
Fuzzy Life-Extending Control of Mechanical Systems
349(36)
Introduction
349(2)
Architecture of Life-Extending Control Systems
351(1)
Life-Extending Control of a Rocket Engine
352(10)
Inner Loop Feedback Controller for LECS-1
353(2)
Outer Loop Fuzzy Controller for LECS-1
355(4)
Results and Discussion for LECS-1
359(3)
Life-Extending Control of a Power Plant
362(17)
Inner Loop Feedback and Gain Scheduling
364(3)
Fuzzy Controller
367(5)
Results and Discussion
372(7)
Summary and Conclusions
379(6)
Control System Stability
380(1)
Acknowledgments
381(1)
Appendix A: Brief Description of the Rocket Engine
381(1)
Appendix B: Brief Description of the Power Plant
382(1)
References
382(3)
Epilogue 385(2)
Index 387

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