Soft Computing for Control of Non-Linear Dynamical Systems

ISBN-13: 9783662003671 / Angielski / Miękka / 2012 / 224 str.

Oscar Castillo; Patricia Melin

Opis

This book presents a unified view of modelling, simulation, and control of non- linear dynamical systems using soft computing techniques and fractal theory. Our particular point of view is that modelling, simulation, and control are problems that cannot be considered apart, because they are intrinsically related in real world applications. Control of non-linear dynamical systems cannot be achieved if we don't have the appropriate model for the system. On the other hand, we know that complex non-linear dynamical systems can exhibit a wide range of dynamic behaviors ( ranging from simple periodic orbits to chaotic strange attractors), so the problem of simulation and behavior identification is a very important one. Also, we want to automate each of these tasks because in this way it is more easy to solve a particular problem. A real world problem may require that we use modelling, simulation, and control, to achieve the desired level of performance needed for the particular application.

Spis treści

1 Introduction to Control of Non-Linear Dynamical Systems.- 2 Fuzzy Logic.- 2.1 Fuzzy Set Theory.- 2.2 Fuzzy Reasoning.- 2.3 Fuzzy Inference Systems.- 2.4 Type-2 Fuzzy Logic Systems.- 2.4.1 Type-2 Fuzzy Sets.- 2.4.2 Type-2 Fuzzy Systems.- 2.5 Fuzzy Modelling.- 2.6 Summary.- 3 Neural Networks for Control.- 3.1 Backpropagation for Feedforward Networks.- 3.1.1 The Backpropagation Learning Algorithm.- 3.1.2 Backpropagation Multilayer Perceptions.- 3.2 Adaptive Neuro-Fuzzy Inference Systems.- 3.2.1 ANFIS Architecture.- 3.2.2 Learning Algorithm.- 3.3 Neuro-Fuzzy Control.- 3.3.1 Inverse Learning.- 3.3.2 Specialized Learning.- 3.4 Adaptive Model-Based Neuro-Control.- 3.4.1 Indirect Neuro-Control.- 3.4.2 Direct Neuro-Control.- 3.4.3 Parameterized Neuro-Control.- 3.5 Summary.- 4 Genetic Algorithms and Simulated Annealing.- 4.1 Genetic Algorithms.- 4.2 Simulated Annealing.- 4.3 Applications of Genetic Algorithms.- 4.3.1 Evolving Neural Networks.- 4.3.1.1 Evolving Weights in a Fixed Network.- 4.3.1.2 Evolving Network Architectures.- 4.3.2 Evolving Fuzzy Systems.- 4.4 Summary.- 5 Dynamical Systems Theory.- 5.1 Basic Concepts of Dynamical Systems.- 5.2 Controlling Chaos.- 5.2.1 Controlling Chaos through Feedback.- 5.2.1.1 Ott-Grebogi-Yorke Method.- 5.2.1.2 Pyragas’s Control Methods.- 5.2.1.3 Controlling Chaos by Chaos.- 5.2.2 Controlling Chaos without Feedback.- 5.2.2.1 Control through Operating Conditions.- 5.2.2.2 Control by System Design.- 5.2.2.3 Taming Chaos.- 5.2.3 Method Selection.- 5.3 Summary.- 6 Hybrid Intelligent Systems for Time Series Prediction.- 6.1 Problem of Time Series Prediction.- 6.2 Fractal Dimesion of an Object.- 6.3 Fuzzy Logic for Object Classification.- 6.4 Fuzzy Estimation of the Fractal Dimension.- 6.5 Fuzzy Fractal Approach for Time Series Analysis and Prediction.- 6.6 Neural Network Approach for Time Series Prediction.- 6.7 Fuzzy Fractal Approach for Pattern Recognition.- 6.8 Summary.- 7 Modelling Complex Dynamical Systems with a Fuzzy Inference System for Differential Equations.- 7.1 The Problem of Modelling Complex Dynamical Systems.- 7.2 Modelling Complex Dynamical Systems with the New Fuzzy Inference System.- 7.3 Modelling Robotic Dynamic Systems with the New Fuzzy Interence System.- 7.3.1 Mathematical Modelling of Robotic Systems.- 7.3.2 Fuzzy Modelling of Robotic Dynamic Systems.- 7.3.3 Experimental Results.- 7.4 Modelling Aircraft Dynamic Systems with the New Fuzzy Inference System.- 7.5 Summary.- 8 A New Theory of Fuzzy Chaos for Simulation of Non-Linear Dynamical Systems.- 8.1 Problem Description.- 8.2 Towards a New Theory of Fuzzy Chaos.- 8.3 Fuzzy Chaos for Behavior Identification in the Simulation of Dynamical Systems.- 8.4 Simulation of Dynamical Systems.- 8.5 Method for Automated Parameter Selection Using Genetic Algorithms.- 8.6 Method for Dynamic Behavior Identification Using Fuzzy Logic.- 8.6.1 Behavior Identification Based on the Analytical Properties of the Model.- 8.6.2 Behavior Identification Based on the Fractal Dimension and the Lyapunov Exponents.- 8.7 Simulation Results for Robotic Systems.- 8.8 Summary.- 9 Intelligent Control of Robotic Dynamic Systems.- 9.1 Problem Description.- 9.2 Mathematical Modelling of Robotic Dynamic Systems.- 9.3 Method for Adaptive Model-Based Control.- 9.3.1 Fuzzy Logic for Dynamic System Modelling.- 9.3.2 Neuro-Fuzzy-Fractal Adaptive Model-Based Control.- 9.4 Adaptive Control of Robotic Dynamic Systems.- 9.5 Simulation Results for Robotic Dynamic Systems.- 9.6 Summary.- 10 Controlling Biochemical Reactors.- 10.1 Introduction.- 10.2 Fuzzy Logic for Modelling.- 10.3 Neural Networks for Control.- 10.4 Adaptive Control of a Non-Linear Plant.- 10.5 Fractal Identification of Bacteria.- 10.6 Experimantal Results.- 10.7 Summary.- 11 Controlling Aircraft Dynamic Systems.- 11.1 Introduction.- 11.2 Fuzzy Modelling of Dynamical Systems.- 11.3 Neural Networks for Control.- 11.4 Adaptive Control of Aircraft Systems.- 11.5 Experimental Results.- 11.6 Summary.- 12 Controlling Electrochemical Processes.- 12.1 Introduction.- 12.2 Problem Description.- 12.3 Fuzzy Method for cControl.- 12.4 Neuro-Fuzzy Methof for Control.- 12.5 Neuro-Fuzzy-Genetic Method for Control.- 12.6 Experimental Results for the Three Hybrid Approaches.- 12.7 Summary.- 13 Controlling International Trade Dynamics.- 13.1 Introduction.- 13.2 Mathematical Modelling of International Trade.- 13.2.1 Oscillations in Autonomous Economies.- 13.2.2 International Trade as a Perturbation of Internal Oscillations.- 13.3 Fuzzy Logic for Model Selection.- 13.4 Adaptive Model-Based Control of International Trade.- 13.5 Simulation Results for Control of International Trade.- 13.6 Summary.- References.

Blurb

The book describes the application of soft computing techniques to modelling, simulation and control of non-linear dynamical systems. Hybrid intelligence systems, which integrate different techniques and mathematical models, are also presented. The book covers the basics of fuzzy logic, neural networks, evolutionary computation, chaos and fractal theory. It also presents in detail different hybrid architectures for developing intelligent control systems for applications in robotics, reactors, manufacturing, aircraft systems and economics.