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|---|---|---|---|---|---|
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Summary
Summary
These authors use soft computing techniques and fractal theory in this new approach to mathematical modeling, simulation and control of complexion-linear dynamical systems. First, a new fuzzy-fractal approach to automated mathematical modeling of non-linear dynamical systems is presented. It is illustrated with examples on the PROLOG programming language. Second, a new fuzzy-genetic approach to automated simulation of dynamical systems is presented. It is illustrated with examples in the MATLAB programming language. Third, a new method for model-based adaptive control using a neuro-fussy fractal approach is combined with the methods mentioned above. This method is illustrated with MATLAB. Finally, applications of these new methods are presented, in the areas such as biochemical processes, robotic systems, manufacturing, food industry and chemical processes.
Author Notes
Professor Patricia Melin has been with the Computer Science Department of the Tijuana Institute of Technology, Mexico for the past two years, and is currently Adjunct Professor at San Diego State University, USA. Before these appointments she was at CETYS University for over ten years. Her current research interests are in neural networks, fuzzy logic, control of non-linear dynamical systems and mathematical modelling and simulation of complex engineering systems.
Professor Oscar Castillo has been with the Computer Science Department of the Tijuana Institute of Technology, Mexico for the past several years, and is currently Adjunct Professor at San Diego State University, USA. His research interests lie in fuzzy logic, neural networks, genetic algorithms, robotics and control of dynamical systems.
Table of Contents
| Preface | p. ix |
| 1 Introduction to Modelling, Simulation and Control of Non-Linear Dynamical Systems | p. 1 |
| 1.1 Modelling and Simulation of Non-Linear Dynamical Systems | p. 2 |
| 1.2 Control of Non-Linear Dynamical Systems | p. 5 |
| 2 Fuzzy Logic for Modelling | p. 9 |
| 2.1 Fuzzy Set Theory | p. 10 |
| 2.2 Fuzzy Reasoning | p. 16 |
| 2.3 Fuzzy Inference Systems | p. 20 |
| 2.4 Fuzzy Modelling | p. 26 |
| 2.5 Summary | p. 28 |
| 3 Neural Networks for Control | p. 29 |
| 3.1 Backpropagation for Feedforward Networks | p. 32 |
| 3.1.1 The backpropagation learning algorithm | p. 33 |
| 3.1.2 Backpropagation multilayer perceptrons | p. 36 |
| 3.2 Adaptive Neuro-Fuzzy Inference Systems | p. 40 |
| 3.2.1 ANFIS architecture | p. 40 |
| 3.2.2 Learning algorithm | p. 43 |
| 3.3 Neuro-Fuzzy Control | p. 45 |
| 3.3.1 Inverse learning | p. 46 |
| 3.3.2 Specialized learning | p. 49 |
| 3.4 Adaptive Model-Based Neuro-Control | p. 52 |
| 3.4.1 Indirect neuro-control | p. 53 |
| 3.4.2 Direct neuro-control | p. 58 |
| 3.4.3 Parameterized neuro-control | p. 63 |
| 3.5 Summary | p. 64 |
| 4 Genetic Algorithms and Fractal Theory for Modelling and Simulation | p. 65 |
| 4.1 Genetic Algorithms | p. 67 |
| 4.2 Simulated Annealing | p. 72 |
| 4.3 Basic Concepts of Fractal Theory | p. 75 |
| 4.4 Summary | p. 80 |
| 5 Fuzzy-Fractal Approach for Automated Mathematical Modelling | p. 81 |
| 5.1 The Problem of Automated Mathematical Modelling | p. 83 |
| 5.2 A Fuzzy-Fractal Method for Automated Modelling | p. 86 |
| 5.3 Implementation of the Method for Automated Modelling | p. 88 |
| 5.3.1 Description of the time series analysis module | p. 88 |
| 5.3.2 Description of the expert selection module | p. 90 |
| 5.3.3 Description of the best model selection module | p. 92 |
| 5.4 Comparison with Related Work | p. 94 |
| 5.5 Summary | p. 94 |
| 6 Fuzzy-Genetic Approach for Automated Simulation | p. 97 |
| 6.1 The Problem of Automated Simulation | p. 97 |
| 6.1.1 Numerical simulation of dynamical systems | p. 98 |
| 6.1.2 Behavior identification for dynamical systems | p. 99 |
| 6.1.3 Automated simulation of dynamical systems | p. 104 |
| 6.2 Method for Automated Parameter Selection using Genetic Algorithms | p. 106 |
| 6.3 Method for Dynamic Behavior Identification using Fuzzy Logic | p. 108 |
| 6.3.1 Behavior identification based on the analytical properties of the model | p. 108 |
| 6.3.2 Behavior identification based on the fractal dimension and the Lyapunov exponents | p. 111 |
| 6.4 Summary | p. 112 |
| 7 Neuro-Fuzzy Approach for Adaptive Model-Based Control | p. 113 |
| 7.1 Modelling the Process of the Plant | p. 114 |
| 7.2 Neural Networks for Control | p. 116 |
| 7.3 Fuzzy Logic for Model Selection | p. 119 |
| 7.4 Neuro-Fuzzy Adaptive Model-Based Control | p. 124 |
| 7.5 Summary | p. 126 |
| 8 Advanced Applications of Automated Mathematical Modelling and Simulation | p. 127 |
| 8.1 Modelling and Simulation of Robotic Dynamic Systems | p. 128 |
| 8.1.1 Mathematical modelling of robotic systems | p. 128 |
| 8.1.2 Automated mathematical modelling of robotic dynamic systems | p. 131 |
| 8.1.3 Automated simulation of robotic dynamic systems | p. 138 |
| 8.2 Modelling and Simulation of Biochemical Reactors | p. 147 |
| 8.2.1 Modelling biochemical reactors in the food industry | p. 147 |
| 8.2.2 Automated mathematical modelling of biochemical reactors | p. 151 |
| 8.2.3 Simulation results for biochemical reactors | p. 152 |
| 8.3 Modelling and Simulation of International Trade Dynamics | p. 159 |
| 8.3.1 Mathematical modelling of international trade | p. 159 |
| 8.3.2 Simulation results of international trade | p. 162 |
| 8.4 Modelling and Simulation of Aircraft Dynamic Systems | p. 165 |
| 8.4.1 Mathematical modelling of aircraft systems | p. 165 |
| 8.4.2 Simulation results of aircraft systems | p. 167 |
| 8.5 Concluding Remarks and Future Directions | p. 174 |
| 9 Advanced Applications of Adaptive Model-Based Control | p. 175 |
| 9.1 Intelligent Control of Robotic Dynamic Systems | p. 175 |
| 9.1.1 Traditional model-based adaptive control of robotic systems | p. 177 |
| 9.1.2 Adaptive model-based control of robotic systems with a neuro-fuzzy approach | p. 177 |
| 9.2 Intelligent Control of Biochemical Reactors | p. 184 |
| 9.2.1 Fuzzy rule base for model selection | p. 184 |
| 9.2.2 Neural networks for identification and control | p. 190 |
| 9.2.3 Intelligent adaptive model-based control for biochemical reactors | p. 192 |
| 9.3 Intelligent Control of International Trade | p. 202 |
| 9.3.1 Adaptive model-based control of international trade | p. 202 |
| 9.3.2 Simulation results for control of international trade | p. 204 |
| 9.4 Intelligent Control of Aircraft Dynamic Systems | p. 208 |
| 9.4.1 Adaptive model-based control of aircraft systems | p. 208 |
| 9.4.2 Simulation results for control of aircraft systems | p. 210 |
| 9.5 Concluding Remarks and Future Directions | p. 213 |
| References | p. 215 |
| Appendix A Prototype Intelligent Systems for Automated Mathematical Modelling | p. 225 |
| A.1 Automated Mathematical Modelling of Dynamical Systems | p. 225 |
| A.2 Automated Mathematical Modelling of Robotic Dynamic Systems | p. 229 |
| Appendix B Prototype Intelligent Systems for Automated Simulation | p. 235 |
| B.1 Automated Simulation of Non-Linear Dynamical Systems | p. 235 |
| B.2 Numerical Simulation of Non-Linear Dynamical Systems | p. 239 |
| Appendix C Prototype Intelligent Systems for Adaptive Model-Based Control | p. 242 |
| C.1 Fuzzy Logic Model Selection | p. 242 |
| C.2 Neural Networks for Identification and Control | p. 245 |
| Index | p. 247 |
