ISBN-10:
3790824860
ISBN-13:
9783790824865
Pub. Date:
12/15/2010
Publisher:
Physica-Verlag HD
Fuzzy Modeling and Control / Edition 1

Fuzzy Modeling and Control / Edition 1

by Andrzej Piegat

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Product Details

ISBN-13: 9783790824865
Publisher: Physica-Verlag HD
Publication date: 12/15/2010
Series: Studies in Fuzziness and Soft Computing , #69
Edition description: Softcover reprint of hardcover 1st ed. 2001
Pages: 728
Product dimensions: 6.10(w) x 9.25(h) x 0.06(d)

Table of Contents

1. Introduction.- 1.1 Essence of fuzzy set theory.- 1.2 Development of fuzzy set theory.- 2. Basic Notions of Fuzzy Set Theory.- 2.1 Fuzzy sets.- 2.2 Characteristic parameters (indices) of a fuzzy set.- 2.3 Linguistic modifiers of fuzzy sets.- 2.4 Types of membership functions of fuzzy sets.- 2.5 Type 2 fuzzy sets.- 2.6 Fuzziness and probability: two kinds of uncertainty.- 3. Arithmetic of Fuzzy Sets.- 3.1 The extension principle.- 3.2 Addition of fuzzy numbers.- 3.3 Subtraction of fuzzy numbers.- 3.4 Multiplication of fuzzy numbers.- 3.5 Division of fuzzy numbers.- 3.6 Peculiarities of fuzzy numbers.- 3.7 Differences between fuzzy numbers and linguistic values.- 4. Mathematics of Fuzzy Sets.- 4.1 Basic operations on fuzzy sets.- 4.1.1 Intersection operation (logical product) of fuzzy sets.- 4.1.2 Union (logical sum) of fuzzy sets.- 4.1.3 Compensatory operators.- 4.2 Fuzzy relations.- 4.3 Implication.- 5. Fuzzy Models.- 5.1 Structure, main elements and operations in fuzzy models.- 5.1.1 Fuzzification.- 5.1.2 Inference.- 5.1.2.1 Premise evaluation.- 5.1.2.2 Determination of activated membership functions of conclusions in particular rules at given input values of a fuzzy model.- 5.1.2.3 Determination of the resulting membership function of the rule-base conclusion.- 5.1.3 Defuzzification of the resulting membership function of the rule-base conclusion.- 5.1.4 Example of fuzzy modeling.- 5.2 Significant features of rules, rule bases and fuzzy models.- 5.2.1 Local character of rules.- 5.2.2 Dependence of the number of rules on the number of inputs and fuzzy sets.- 5.2.3 Completeness of a fuzzy model.- 5.2.4 Consistency of the rule base.- 5.2.5 Continuity of the rule base.- 5.2.6 Redundancy of the rule base.- 5.3 Advice relating to rule base construction.- 5.4 Reduction of the rule base.- 5.5 Normalization (scaling) of the fuzzy model inputs and output.- 5.6 Extrapolation in fuzzy models.- 5.7 Types of fuzzy models.- 5.7.1 Mamdani models.- 5.7.2 Takagi-Sugeno models.- 5.7.3 Relational models.- 5.7.4 Global and local fuzzy models.- 5.7.5 Fuzzy multimodels.- 5.7.6 Neuro-fuzzy models.- 5.7.7 Alternative models.- 5.7.8 Similarity principles of the system and of the system model.- 5.7.9 Fuzzy classification.- 6. Methods of Fuzzy Modeling.- 6.1 Fuzzy modeling based on the system expert’s knowledge.- 6.2 Creation of fuzzy, self-tuning models based on input/output measurement data of the system.- 6.2.1 Application of neuro-fuzzy networks for fuzzy model parameter tuning.- 6.2.1.1 Structuring and training of neural networks.- 6.2.1.2 Transformation of a Mamdani fuzzy model into a neuro-fuzzy network.- 6.2.1.3 Transformation of a Takagi-Sugeno fuzzy model into a neuro-fuzzy network.- 6.2.2 Tuning of fuzzy model parameters with the genetic algorithm method.- 6.3 Creation of self-organizing and self-tuning fuzzy models based on input/output measurement data of the system.- 6.3.1 Determination of significant and insignificant inputs of the model.- 6.3.2 Determining of fuzzy curves.- 6.3.3 Self-organization and self-tuning tuning of fuzzy model parameters.- 6.3.3.1 Self-organization and tuning of fuzzy models with the geometric method of the maximum absolute error.- 6.3.3.2 Self-organization and self-tuning of fuzzy models with clustering methods.- 6.3.3.3 Self-organization and self-tuning of fuzzy models with the searching method.- 7. Fuzzy Control.- 7.1 Static fuzzy controllers.- 7.2 Dynamic fuzzy controllers.- 7.3 The determination of structures and parameters for fuzzy controllers (organization and tuning).- 7.3.1 The design of fuzzy controllers on the basis of expert knowledge concerning plant under control.- 7.3.2 The design of a fuzzy controller on the basis of a model of the expert controlling the plant.- 7.3.3 The design of a fuzzy controller on the basis of the model of controlled plant.- 7.3.3.1 Remarks concerning identification of models of dynamic plants.- 7.3.3.2 Some remarks concerning the identification of inverted models of dynamical plants.- 7.3.3.3 Tuning a fuzzy controller with an a priori chosen structure.- 7.3.3.4 Fuzzy control based on the Internal Model Control Structure (IMC structure).- 7.3.3.5 Fuzzy control structure with an inverse of a plant model (InvMC structure).- 7.3.3.6 Adaptive fuzzy control.- 7.3.3.7 Multivariable fuzzy control (MIMO).- 8. The Stability of Fuzzy Control Systems.- 8.1 The stability of fuzzy control systems with unknown models of plants.- 8.2 The circle stability criterion.- 8.3 The application of hyperstability theory to analysis of fuzzysystem stability.- 8.3.1 The frequency domain representation of hyperstability conditions for control systems with a time invariant non-linear part.- 8.3.2 The time domain conditions for hyperstability of continuous, non-linear control systems containing a timeinvariant non-linear part.- 8.3.3 The frequency domain conditions for hyperstability of discrete, non-linear control systems containing a timeinvariant non-linear part.- References.

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