Mathematical Modelling

Theory and Applications

By: R. Lowen (Editor), A. Verschoren (Editor)

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Hardcover | 5 November 2007

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472 Pages

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24.77 x 14.61 x 1.91

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This is a comprehensive overview of the basics of fuzzy control, which also brings together some recent research results in soft computing, in particular fuzzy logic using genetic algorithms and neural networks.

This book offers researchers not only a solid background but also a snapshot of the current state of the art in this field.

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Non-Fiction Computing & I.T.Computer Programming & Software Development Algorithms & Data Structures Mathematics Applied Mathematics Computer Science Calculus & Mathematical Analysis Optimisation Linear Programming Combinatorics & Graph Theory Databases

Data Capture & Analysis Discrete Mathematics

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Published: 13th November 2010

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An Overview of Fuzzy Control Theory	p. 1
Introduction	p. 1
History	p. 1
Structure of a Fuzzy Controller	p. 3
Fuzzy Modelling Requirements	p. 5
The Fuzzy Controller Block	p. 7
Notations	p. 7
Fuzzy Rule Bases	p. 9
Linguistic Variables	p. 9
Linguistic Hedges	p. 10
Fuzzy Rules	p. 12
Linguistic Variables Revisited	p. 19
The Design of a Fuzzy Controller	p. 20
Choice of Rules	p. 20
Design Parameters	p. 24
Aggregation and Implication Operators	p. 26
t-norms and t-conorms	p. 27
Extension of Logic	p. 28
Conjunction and Disjunction Operators	p. 30
Implication Operators	p. 33
Defuzzification Operators	p. 37
Criteria	p. 37
Overview of the Different Defuzzification Operators	p. 43
An Extended Example	p. 49
Simplified Controllers	p. 52
Table-Based Controllers	p. 53
Sugeno Controllers	p. 55
Adaptive Fuzzy Control	p. 57
General Remarks	p. 57
Scaling	p. 59
Membership Function Tuning using Performance Criteria	p. 60
Gradient Descent Method	p. 64
Self-Organizing Controllers	p. 66
Stability Analysis	p. 69
General Remarks	p. 69
The Input-Output Mapping	p. 70
The State Space Approach	p. 76
Lyapunov Stability	p. 78
Input-Output Stability and Related Techniques	p. 87
Other Adaptive Techniques	p. 88
Neural Networks	p. 89
Neuro-fuzzy Hybrid Systems	p. 107
Genetic Algorithms	p. 120
Fuzzy-Genetic Hybrid Systems	p. 129
References	p. 132
Optimal Fuzzy Management of Reservoir based on Genetic Algorithm	p. 139
Introduction	p. 139
Reservoir Water Release Policy	p. 142
Mathematical Model of the Reservoir	p. 142
Volume Balance Equation	p. 142
Hybrid Dynamical Model of the Reservoir	p. 144
Fuzzy Decision System	p. 144
Optimizing the Decision Strategy	p. 147
Genetic Algorithm and Fuzzy Membership Function Parameters	p. 147
Performances Indices	p. 148
Inflow Identification and Montecarlo Simulation	p. 149
Case Study	p. 154
Conclusions	p. 157
References	p. 158
Genetic Fuzzy Modeling of Supervisory Scheduling of Freight Rail Systems	p. 161
Introduction	p. 161
Genetic Fuzzy Algorithm	p. 164
Supervisory Train Schedule	p. 172
Conclusion	p. 178
References	p. 179
Multiobjective Evolutionary Search of Difference Equations-based Models for Understanding Chaotic Systems	p. 181
Introduction	p. 181
Evolutionary Transparent Modeling of Chaotic Systems	p. 183
Operators Used in the Evolutionary Searches	p. 185
Representation of an Individual	p. 185
Random Generation of Genotypes	p. 186
Genetic Crossover and Mutation	p. 186
Fitness Function	p. 187
Detailed Description of the MOSA Algorithm	p. 188
Outline of the Algorithm	p. 188
The Distance Operator	p. 189
The Selection Operator	p. 190
Example of a MOSA Evolution	p. 190
Experiment and Results	p. 190
Dynamic Behavior of Universal Approximators	p. 190
Benchmark Problems	p. 192
Concluding Remarks and Future Work	p. 198
References	p. 199
An Integrated Fuzzy Inference-based Monitoring, Diagnostic, and Prognostic System for Intelligent Control and Maintenance	p. 203
Introduction	p. 203
Reliability Engineering Methods	p. 204
Integrated Framework	p. 204
Nonparametric Fuzzy Inference System	p. 206
Embodiments of the NFIS	p. 208
Prediction	p. 209
Detection	p. 210
Diagnosis	p. 210
Prognosis	p. 212
Methodology	p. 215
Results	p. 217
Monitoring	p. 217
Diagnosis	p. 218
Prognosis	p. 219
Conclusions	p. 220
References	p. 220
Stable Anti-Swing Control for an Overhead Crane with Velocity Estimation and Fuzzy Compensation	p. 223
Introduction	p. 223
Preliminaries	p. 225
Anti-Swing Control for the Overhead Crane	p. 227
Position Control with Fuzzy Compensation	p. 228
PD Control with a Velocity Observer	p. 229
Stability Analysis	p. 231
Experimental Comparisons	p. 232
Conclusion	p. 235
Appendix	p. 237
References	p. 239
Intelligent Fuzzy PID Controller	p. 241
Introduction	p. 242
The Development of Self-Organizing Fuzzy PID Controller	p. 243
Kinematics and Dynamics of the Robot-Arm	p. 248
Computer Simulation Results	p. 249
Conclusion	p. 258
References	p. 259
Stability Analysis and Performance Design for Fuzzy Model-based Control Systems using a BMI-based Approach	p. 261
Introduction	p. 262
Fuzzy Model and Fuzzy Controller	p. 263
Fuzzy Model	p. 264
Fuzzy Controller	p. 264
Stability Analysis	p. 265
Design of G[subscript j] and a[subscript j] for the Fuzzy Controller	p. 269
Design of Feedback Gains	p. 269
Solution Solving	p. 270
BMI-Based Performance Design of Fuzzy Model-Based Control System	p. 271
Simulation Examples	p. 274
Simulation Example 1	p. 274
Simulation Example 2	p. 275
Conclusion	p. 280
References	p. 281
Two-Level Tuning of Fuzzy PID Controllers for Multivariable Process Systems	p. 283
Introduction	p. 284
System Description	p. 286
Two-Level Tuning	p. 287
Low-Level Tuning: Linear PID Controller Tuning	p. 288
Tuning First Loop	p. 289
Tuning ith loop	p. 291
High-Level Tuning: Nonlinearity Tuning	p. 291
Standard Additive Model (SAM)	p. 292
SAM Theorem	p. 294
Fuzzy PID (FPID) Configurations	p. 295
High-Level Nonlinear Tuning Variables	p. 296
Design of SAM	p. 297
Stability Analysis	p. 298
Direct Nyquist Array (DNA) Stability Theorem	p. 298
Maximum Values of PID Parameters	p. 299
Control Simulation	p. 302
Example 1	p. 303
Example 2	p. 303
Performance Analysis	p. 306
Conclusions	p. 310
References	p. 310
Evaluation of Fuzzy Implications and Intuitive Criteria of GMP and GMT using MATLAB GUI	p. 313
Introduction	p. 313
Intuitive Criteria of GMP and GMT	p. 314
Fuzzy Implication Methods	p. 316
Properties of Interpretations of Fuzzy IF-THEN Rules	p. 319
Study of Satisfaction of Criteria using MATLAB/Graphics	p. 320
Discussions	p. 385
Conclusions	p. 385
References	p. 385
FzController: A Development Environment for Fuzzy Controllers	p. 387
Introduction	p. 387
General Conception of the FzController System	p. 388
Exact method	p. 388
Approximated Method	p. 389
Modules in FzController	p. 390
Identification Module	p. 390
Design of Fuzzy Controllers Module	p. 391
Real-Time Control Module	p. 396
Automatic Generation of Codes Module	p. 397
Conclusions	p. 400
References	p. 401
A Consistency Criterion for Optimizing Defuzzification in Fuzzy Control	p. 403
Introduction	p. 403
MOM- and COG-defuzzification	p. 409
Single Controller	p. 409
Two Single Disjoint Controllers	p. 411
Two Subcentrally Overlapping Controllers	p. 412
Two Supercentrally Overlapping Controllers	p. 416
Overlapping Controllers with Border Conditions	p. 420
The Consistency Criterion	p. 422
Example	p. 423
BADD-defuzzification	p. 427
Results with No Border Constraints	p. 428
Results with Border Constraints	p. 429
Conclusions	p. 430
References	p. 431
An Asymptotic Consistency Criterion for Optimizing Defuzzification in Fuzzy Control	p. 433
Introduction	p. 433
Rule Antecedent Bases	p. 434
Rule Base Sequences	p. 437
The Asymptotic Consistency Criterion	p. 440
MOM-defuzzification	p. 441
COG-defuzzification	p. 444
BADD-defuzzification	p. 447
Defuzzification Fitness Comparison	p. 448
Conclusions	p. 455
References	p. 455
Table of Contents provided by Ingram. All Rights Reserved.

Mathematical Modelling

Theory and Applications

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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