An original, systematic-solution approach to uncertain nonlinear systems control and modeling using fuzzy equations and fuzzy differential equations
There are various numerical and analytical approaches to the modeling and control of uncertain nonlinear systems. Fuzzy logic theory is an increasingly popular method used to solve inconvenience problems in nonlinear modeling. Modeling and Control of Uncertain Nonlinear Systems with Fuzzy Equations and Z-Number presents a structured approach to the control and modeling of uncertain nonlinear systems in industry using fuzzy equations and fuzzy differential equations.
The first major work to explore methods based on neural networks and Bernstein neural networks, this innovative volume provides a framework for control and modeling of uncertain nonlinear systems with applications to industry. Readers learn how to use fuzzy techniques to solve scientific and engineering problems and understand intelligent control design and applications. The text assembles the results of four years of research on control of uncertain nonlinear systems with dual fuzzy equations, fuzzy modeling for uncertain nonlinear systems with fuzzy equations, the numerical solution of fuzzy equations with Z-numbers, and the numerical solution of fuzzy differential equations with Z-numbers. Using clear and accessible language to explain concepts and principles applicable to real-world scenarios, this book:
- Presents the modeling and control of uncertain nonlinear systems with fuzzy equations and fuzzy differential equations
- Includes an overview of uncertain nonlinear systems for non-specialists
- Teaches readers to use simulation, modeling and verification skills valuable for scientific research and engineering systems development
- Reinforces comprehension with illustrations, tables, examples, and simulations
Modeling and Control of Uncertain Nonlinear Systems with Fuzzy Equations and Z-Number is suitable as a textbook for advanced students, academic and industrial researchers, and practitioners in fields of systems engineering, learning control systems, neural networks, computational intelligence, and fuzzy logic control.
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xi | |
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xiii | |
| Preface |
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xv | |
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1 | (20) |
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1 | (1) |
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1 | (2) |
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1.3 Algebraic Fuzzy Equations |
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3 | (2) |
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1.4 Numerical Methods for Solving Fuzzy Equations |
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5 | (15) |
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5 | (2) |
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1.4.2 Steepest Descent Method |
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7 | (1) |
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1.4.3 Adomian Decomposition Method |
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8 | (1) |
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9 | (1) |
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1.4.5 Intelligent Methods |
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10 | (1) |
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1.4.5.1 Genetic Algorithm Method |
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10 | (1) |
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1.4.5.2 Neural Network Method |
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11 | (3) |
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1.4.5.3 Fuzzy Linear Regression Model |
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14 | (6) |
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20 | (1) |
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2 Fuzzy Differential Equations |
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21 | (18) |
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21 | (1) |
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2.2 Predictor-Corrector Method |
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21 | (2) |
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2.3 Adomian Decomposition Method |
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23 | (1) |
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23 | (2) |
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25 | (1) |
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25 | (1) |
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2.7 Finite Difference Method |
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26 | (2) |
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2.8 Differential Transform Method |
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28 | (1) |
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2.9 Neural Network Method |
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29 | (7) |
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36 | (3) |
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3 Modeling and Control Using Fuzzy Equations |
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39 | (30) |
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3.1 Fuzzy Modeling with Fuzzy Equations |
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39 | (13) |
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3.1.1 Fuzzy Parameter Estimation with Neural Networks |
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45 | (3) |
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3.1.2 Upper Bounds of the Modeling Errors |
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48 | (4) |
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3.2 Control with Fuzzy Equations |
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52 | (7) |
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59 | (8) |
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67 | (2) |
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4 Modeling and Control Using Fuzzy Differential Equations |
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69 | (32) |
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69 | (1) |
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4.2 Fuzzy Modeling with Fuzzy Differential Equations |
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69 | (3) |
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4.3 Existence of a Solution |
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72 | (7) |
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4.4 Solution Approximation using Bernstein Neural Networks |
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79 | (4) |
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4.5 Solutions Approximation using the Fuzzy Sumudu Transform |
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83 | (2) |
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85 | (14) |
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99 | (2) |
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5 System Modeling with Partial Differential Equations |
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101 | (18) |
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101 | (1) |
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5.2 Solutions using Burgers--Fisher Equations |
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101 | (5) |
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5.3 Solution using Wave Equations |
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106 | (3) |
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109 | (8) |
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117 | (2) |
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6 System Control using Z-numbers |
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119 | (34) |
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119 | (1) |
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6.2 Modeling using Dual Fuzzy Equations and Z-numbers |
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119 | (5) |
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6.3 Controllability using Dual Fuzzy Equations |
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124 | (4) |
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128 | (3) |
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6.5 Nonlinear System Modeling |
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131 | (1) |
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6.6 Controllability using Fuzzy Differential Equations |
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131 | (4) |
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6.7 Fuzzy Controller Design using Fuzzy Differential Equations and Z-number |
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135 | (3) |
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6.8 Approximation using a Fuzzy Sumudu Transform and Z-numbers |
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138 | (1) |
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139 | (12) |
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151 | (2) |
| References |
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153 | (14) |
| Index |
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167 | |
Wen Yu, PhD, is Professor at CINVESTAV-IPN (National Polytechnic Institute), Mexico City, Mexico. He is Associate Editor of IEEE Transactions on Cybernetics, Neurocomputing, and Journal of Intelligent and Fuzzy Systems. Dr. Yu is a member of the Mexican Academy of Sciences.
Raheleh Jafari is a postdoctoral research fellow at Centre for Artificial Intelligence Research (CAIR), University of Agder, Grimstad, Norway. She is on the editorial board of the Journal of Intelligent and Fuzzy Systems, and served as a reviewer in various journals and conferences. Her research interest is in the field of artificial intelligence, fuzzy control, machine learning, nonlinear systems, neural networks, and fuzzy engineering.
Lisainfo e-raamatute kohta