Cover image for Modelling, simulation and control of non-linear dynamical systems : an intelligent approach using soft computing and fractal theory
Title:
Modelling, simulation and control of non-linear dynamical systems : an intelligent approach using soft computing and fractal theory
Personal Author:
Series:
Numerical insights ; 2
Publication Information:
London : Taylor and Francis, 2002
Physical Description:
1 computer disk ; 3 1/2 in
ISBN:
9780415272360
General Note:
Accompanies text with the same title : (QA427 M44 2002)
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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

Prefacep. ix
1 Introduction to Modelling, Simulation and Control of Non-Linear Dynamical Systemsp. 1
1.1 Modelling and Simulation of Non-Linear Dynamical Systemsp. 2
1.2 Control of Non-Linear Dynamical Systemsp. 5
2 Fuzzy Logic for Modellingp. 9
2.1 Fuzzy Set Theoryp. 10
2.2 Fuzzy Reasoningp. 16
2.3 Fuzzy Inference Systemsp. 20
2.4 Fuzzy Modellingp. 26
2.5 Summaryp. 28
3 Neural Networks for Controlp. 29
3.1 Backpropagation for Feedforward Networksp. 32
3.1.1 The backpropagation learning algorithmp. 33
3.1.2 Backpropagation multilayer perceptronsp. 36
3.2 Adaptive Neuro-Fuzzy Inference Systemsp. 40
3.2.1 ANFIS architecturep. 40
3.2.2 Learning algorithmp. 43
3.3 Neuro-Fuzzy Controlp. 45
3.3.1 Inverse learningp. 46
3.3.2 Specialized learningp. 49
3.4 Adaptive Model-Based Neuro-Controlp. 52
3.4.1 Indirect neuro-controlp. 53
3.4.2 Direct neuro-controlp. 58
3.4.3 Parameterized neuro-controlp. 63
3.5 Summaryp. 64
4 Genetic Algorithms and Fractal Theory for Modelling and Simulationp. 65
4.1 Genetic Algorithmsp. 67
4.2 Simulated Annealingp. 72
4.3 Basic Concepts of Fractal Theoryp. 75
4.4 Summaryp. 80
5 Fuzzy-Fractal Approach for Automated Mathematical Modellingp. 81
5.1 The Problem of Automated Mathematical Modellingp. 83
5.2 A Fuzzy-Fractal Method for Automated Modellingp. 86
5.3 Implementation of the Method for Automated Modellingp. 88
5.3.1 Description of the time series analysis modulep. 88
5.3.2 Description of the expert selection modulep. 90
5.3.3 Description of the best model selection modulep. 92
5.4 Comparison with Related Workp. 94
5.5 Summaryp. 94
6 Fuzzy-Genetic Approach for Automated Simulationp. 97
6.1 The Problem of Automated Simulationp. 97
6.1.1 Numerical simulation of dynamical systemsp. 98
6.1.2 Behavior identification for dynamical systemsp. 99
6.1.3 Automated simulation of dynamical systemsp. 104
6.2 Method for Automated Parameter Selection using Genetic Algorithmsp. 106
6.3 Method for Dynamic Behavior Identification using Fuzzy Logicp. 108
6.3.1 Behavior identification based on the analytical properties of the modelp. 108
6.3.2 Behavior identification based on the fractal dimension and the Lyapunov exponentsp. 111
6.4 Summaryp. 112
7 Neuro-Fuzzy Approach for Adaptive Model-Based Controlp. 113
7.1 Modelling the Process of the Plantp. 114
7.2 Neural Networks for Controlp. 116
7.3 Fuzzy Logic for Model Selectionp. 119
7.4 Neuro-Fuzzy Adaptive Model-Based Controlp. 124
7.5 Summaryp. 126
8 Advanced Applications of Automated Mathematical Modelling and Simulationp. 127
8.1 Modelling and Simulation of Robotic Dynamic Systemsp. 128
8.1.1 Mathematical modelling of robotic systemsp. 128
8.1.2 Automated mathematical modelling of robotic dynamic systemsp. 131
8.1.3 Automated simulation of robotic dynamic systemsp. 138
8.2 Modelling and Simulation of Biochemical Reactorsp. 147
8.2.1 Modelling biochemical reactors in the food industryp. 147
8.2.2 Automated mathematical modelling of biochemical reactorsp. 151
8.2.3 Simulation results for biochemical reactorsp. 152
8.3 Modelling and Simulation of International Trade Dynamicsp. 159
8.3.1 Mathematical modelling of international tradep. 159
8.3.2 Simulation results of international tradep. 162
8.4 Modelling and Simulation of Aircraft Dynamic Systemsp. 165
8.4.1 Mathematical modelling of aircraft systemsp. 165
8.4.2 Simulation results of aircraft systemsp. 167
8.5 Concluding Remarks and Future Directionsp. 174
9 Advanced Applications of Adaptive Model-Based Controlp. 175
9.1 Intelligent Control of Robotic Dynamic Systemsp. 175
9.1.1 Traditional model-based adaptive control of robotic systemsp. 177
9.1.2 Adaptive model-based control of robotic systems with a neuro-fuzzy approachp. 177
9.2 Intelligent Control of Biochemical Reactorsp. 184
9.2.1 Fuzzy rule base for model selectionp. 184
9.2.2 Neural networks for identification and controlp. 190
9.2.3 Intelligent adaptive model-based control for biochemical reactorsp. 192
9.3 Intelligent Control of International Tradep. 202
9.3.1 Adaptive model-based control of international tradep. 202
9.3.2 Simulation results for control of international tradep. 204
9.4 Intelligent Control of Aircraft Dynamic Systemsp. 208
9.4.1 Adaptive model-based control of aircraft systemsp. 208
9.4.2 Simulation results for control of aircraft systemsp. 210
9.5 Concluding Remarks and Future Directionsp. 213
Referencesp. 215
Appendix A Prototype Intelligent Systems for Automated Mathematical Modellingp. 225
A.1 Automated Mathematical Modelling of Dynamical Systemsp. 225
A.2 Automated Mathematical Modelling of Robotic Dynamic Systemsp. 229
Appendix B Prototype Intelligent Systems for Automated Simulationp. 235
B.1 Automated Simulation of Non-Linear Dynamical Systemsp. 235
B.2 Numerical Simulation of Non-Linear Dynamical Systemsp. 239
Appendix C Prototype Intelligent Systems for Adaptive Model-Based Controlp. 242
C.1 Fuzzy Logic Model Selectionp. 242
C.2 Neural Networks for Identification and Controlp. 245
Indexp. 247