Modelling, Simulation and Control of Non-linear Dynamical Systems: An Intelligent Approach Using Soft Computing and Fractal Theory

by Melin; Patricia

• ISBN13: 9780415272360
• ISBN10: 041527236X
• eBook ISBN(s): 9781000611960
• Edition: Disk
• Format: Hardcover
• Copyright: 2001-10-25
• Publisher: CRC Press
• More Book Details

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 Biography

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	ix
Introduction to Modelling, Simulation and Control of Non-Linear Dynamical Systems	1	(8)
Modelling and Simulation of Non-Linear Dynamical Systems	2	(3)
Control of Non-Linear Dynamical Systems	5	(4)
Fuzzy Logic for Modelling	9	(20)
Fuzzy Set Theory	10	(6)
Fuzzy Reasoning	16	(4)
Fuzzy Inference Systems	20	(6)
Fuzzy Modelling	26	(2)
Summary	28	(1)
Neural Networks For Control	29	(36)
Backpropagation for Feedforward Networks	32	(8)
The backpropagation learning algorithm	33	(3)
Backpropagation multilayer perceptrons	36	(4)
Adaptive Neuro-Fuzzy Inference Systems	40	(5)
ANFIS architecture	40	(3)
Learning algorithm	43	(2)
Neuro-Fuzzy Control	45	(7)
Inverse learning	46	(3)
Specialized learning	49	(3)
Adaptive Model-Based Neuro-Control	52	(12)
Indirect neuro-control	53	(5)
Direct neuro-control	58	(5)
Parameterized neuro-control	63	(1)
Summary	64	(1)
Genetic Algorithms and Fractal Theory for Modelling and Simulation	65	(16)
Genetic Algorithms	67	(5)
Simulated Annealing	72	(3)
Basic Concepts of Fractal Theory	75	(5)
Summary	80	(1)
Fuzzy-Fractal Approach for Automated Mathematical Modelling	81	(16)
The Problem of Automated Mathematical Modelling	83	(3)
A Fuzzy-Fractal Method for Automated Modelling	86	(2)
Implementation of the Method for Automated Modelling	88	(6)
Description of the time series analysis module	88	(2)
Description of the expert selection module	90	(2)
Description of the best model selection module	92	(2)
Comparison with Related Work	94	(1)
Summary	94	(3)
Fuzzy-Genetic Approach for Automated Simulation	97	(16)
The Problem of Automated Simulation	97	(9)
Numerical simulation of dynamical systems	98	(1)
Behavior identification for dynamical systems	99	(5)
Automated simulation of dynamical systems	104	(2)
Method for Automated Parameter Selection using Genetic Algorithms	106	(2)
Method for Dynamic Behavior Identification using Fuzzy Logic	108	(4)
Behavior identification based on the analytical properties of the model	108	(3)
Behavior identification based on the fractal dimension and the Lyapunov exponents	111	(1)
Summary	112	(1)
Neuro-Fuzzy Approach For Adaptive Model-Based Control	113	(14)
Modelling the Process of the Plant	114	(2)
Neural Networks for Control	116	(3)
Fuzzy Logic for Model Selection	119	(5)
Neuro-Fuzzy Adaptive Model-Based Control	124	(2)
Summary	126	(1)
Advanced Applications of Automated Mathematical Modelling And Simulation	127	(48)
Modelling and Simulation of Robotic Dynamic Systems	128	(19)
Mathematical modelling of robotic systems	128	(3)
Automated mathematical modelling of robotic dynamic systems	131	(7)
Automated simulation of robotic dynamic systems	138	(9)
Modelling and Simulation of Biochemical Reactors	147	(12)
Modelling biochemical reactors in the food industry	147	(4)
Automated mathematical modelling of biochemical reactors	151	(1)
Simulation results for biochemical reactors	152	(7)
Modelling and Simulation of International Trade Dynamics	159	(6)
Mathematical modelling of international trade	159	(3)
Simulation results of international trade	162	(3)
Modelling and Simulation of Aircraft Dynamic Systems	165	(9)
Mathematical modelling of aircraft systems	165	(2)
Simulation results of aircraft systems	167	(7)
Concluding Remarks and Future Directions	174	(1)
Advanced Applications of Adaptive Model-Based Control	175	(40)
Intelligent Control of Robotic Dynamic Systems	175	(9)
Traditional model-based adaptive control of robotic systems	177	(1)
Adaptive model-based control of robotic systems with a neuro-fuzzy approach	177	(7)
Intelligent Control of Biochemical Reactors	184	(18)
Fuzzy rule base for model selection	184	(6)
Neural networks for identification and control	190	(2)
Intelligent adaptive model-based control for biochemical reactors	192	(10)
Intelligent Control of International Trade	202	(6)
Adaptive model-based control of international trade	202	(2)
Simulation results for control of international trade	204	(4)
Intelligent Control of Aircraft Dynamic Systems	208	(5)
Adaptive model-based control of aircraft systems	208	(2)
Simulation results for control of aircraft systems	210	(3)
Concluding Remarks and Future Directions	213	(2)
References	215	(10)
APPENDIX A PROTOTYPE INTELLIGENT SYSTEMS FOR AUTOMATED MATHEMATICAL MODELLING	225	(10)
A.1 Automated Mathematical Modelling of Dynamical Systems	225	(4)
A.2 Automated Mathematical Modelling of Robotic Dynamic Systems	229	(6)
APPENDIX B PROTOTYPE INTELLIGENT SYSTEMS FOR AUTOMATED SIMULATION	235	(7)
B.1 Automated Simulation of Non-Linear Dynamical Systems	235	(4)
B.2 Numerical Simulation of Non-Linear Dynamical Systems	239	(3)
APPENDIX C PROTOTYPE INTELLIGENT SYSTEMS FOR ADAPTIVE MODEL-BASED CONTROL	242	(5)
C.1 Fuzzy Logic Model Selection	242	(3)
C.2 Neural Networks for Identification and Control	245	(2)
Index	247