Some mathematical aspects of fuzzy systems

In this work, three topics which are important for the further development of fuzzy systems are chosen to be investigated. First, the mathematical aspects of fuzzy relational equations (FREs) are explored. Solving FREs is one of the most important problems in fuzzy systems. In order to identify the algebraic information of the fuzzy space, two new tools, called fuzzy multiplicative inversion and additive inversion, are proposed. Based on these tools, the relationship among fuzzy vectors in fuzzy space is studied. Analytical expressions of maximum and mean solutions for FREs, and an optimal algorithm for calculating minimum solutions are developed. Second, the possibility of applying functional analysis theory to Takagi-Sugeno (T-S) fuzzy systems design is investigated. Fuzzy transforms, which are based on the generalised Fourier transform in functional analysis, are proposed. It is demonstrated that, mathematically, a T-S fuzzy model is equivalent to a fuzzy transform. Hence the parameters of a T-S fuzzy system can be identified by solving equations constructed using the inner product between membership functions and a given target function. The functional point of view leads to an insight into the behaviour of a fuzzy system. It provides a theoretical basis for exploring improvements to the efficiency of T-S fuzzy modelling. Third, the mathematical aspects of model-based fuzzy control (MBFC) are investigated. MBFC theory is not suitable for general nonlinear systems, due to an implicit linearity assumption. This assumption limits fuzzy controller design to a special case of linear time-varying systems control. To apply MBFC in general nonlinear control, a new stability criterion for general nonlinear fuzzy system is proposed. The mathematical aspects investigated in this research, provide a systematic guidance on issues such as efficient fuzzy systems modelling, balanced "soft" and "hard" computing in fuzzy system design, and applicability of fuzzy control to general nonlinear systems. They serve as a theoretical basis for further development of fuzzy systems.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Fuzzy Controllers

Trying to meet the requirements in the field, present book treats different fuzzy control architectures both in terms of the theoretical design and in terms of comparative validation studies in various applications, numerically simulated or experimentally developed. Through the subject matter and through the inter and multidisciplinary content, this book is addressed mainly to the researchers, doctoral students and students interested in developing new applications of intelligent control, but also to the people who want to become familiar with the control concepts based on fuzzy techniques. Bibliographic resources used to perform the work includes books and articles of present interest in the field, published in prestigious journals and publishing houses, and websites dedicated to various applications of fuzzy control. Its structure and the presented studies include the book in the category of those who make a direct connection between theoretical developments and practical applications, thereby constituting a real support for the specialists in artificial intelligence, modelling and control fields

Some mathematical aspects of fuzzy systems

In this work, three topics which are important for the further development of fuzzy systems are chosen to be investigated. First, the mathematical aspects of fuzzy relational equations (FREs) are explored. Solving FREs is one of the most important problems in fuzzy systems. In order to identify the algebraic information of the fuzzy space, two new tools, called fuzzy multiplicative inversion and additive inversion, are proposed. Based on these tools, the relationship among fuzzy vectors in fuzzy space is studied. Analytical expressions of maximum and mean solutions for FREs, and an optimal algorithm for calculating minimum solutions are developed. Second, the possibility of applying functional analysis theory to Takagi-Sugeno (T-S) fuzzy systems design is investigated. Fuzzy transforms, which are based on the generalised Fourier transform in functional analysis, are proposed. It is demonstrated that, mathematically, a T-S fuzzy model is equivalent to a fuzzy transform. Hence the parameters of a T-S fuzzy system can be identified by solving equations constructed using the inner product between membership functions and a given target function. The functional point of view leads to an insight into the behaviour of a fuzzy system. It provides a theoretical basis for exploring improvements to the efficiency of T-S fuzzy modelling. Third, the mathematical aspects of model-based fuzzy control (MBFC) are investigated. MBFC theory is not suitable for general nonlinear systems, due to an implicit linearity assumption. This assumption limits fuzzy controller design to a special case of linear time-varying systems control. To apply MBFC in general nonlinear control, a new stability criterion for general nonlinear fuzzy system is proposed. The mathematical aspects investigated in this research, provide a systematic guidance on issues such as efficient fuzzy systems modelling, balanced 'soft' and 'hard' computing in fuzzy system design, and applicability of fuzzy control to general nonlinear systems. They serve as a theoretical basis for further development of fuzzy systems

Design of stable adaptive fuzzy control.

by John Tak Kuen Koo.Thesis (M.Phil.)--Chinese University of Hong Kong, 1994.Includes bibliographical references (leaves 217-[220]).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Introduction --- p.1Chapter 1.2 --- "Robust, Adaptive and Fuzzy Control" --- p.2Chapter 1.3 --- Adaptive Fuzzy Control --- p.4Chapter 1.4 --- Object of Study --- p.10Chapter 1.5 --- Scope of the Thesis --- p.13Chapter 2 --- Background on Adaptive Control and Fuzzy Logic Control --- p.17Chapter 2.1 --- Adaptive control --- p.17Chapter 2.1.1 --- Model reference adaptive systems --- p.20Chapter 2.1.2 --- MIT Rule --- p.23Chapter 2.1.3 --- Model Reference Adaptive Control (MRAC) --- p.24Chapter 2.2 --- Fuzzy Logic Control --- p.33Chapter 2.2.1 --- Fuzzy sets and logic --- p.33Chapter 2.2.2 --- Fuzzy Relation --- p.40Chapter 2.2.3 --- Inference Mechanisms --- p.43Chapter 2.2.4 --- Defuzzification --- p.49Chapter 3 --- Explicit Form of a Class of Fuzzy Logic Controllers --- p.51Chapter 3.1 --- Introduction --- p.51Chapter 3.2 --- Construction of a class of fuzzy controller --- p.53Chapter 3.3 --- Explicit form of the fuzzy controller --- p.57Chapter 3.4 --- Design criteria on the fuzzy controller --- p.65Chapter 3.5 --- B-Spline fuzzy controller --- p.68Chapter 4 --- Model Reference Adaptive Fuzzy Control (MRAFC) --- p.73Chapter 4.1 --- Introduction --- p.73Chapter 4.2 --- "Fuzzy Controller, Plant and Reference Model" --- p.75Chapter 4.3 --- Derivation of the MRAFC adaptive laws --- p.79Chapter 4.4 --- "Extension to the Multi-Input, Multi-Output Case" --- p.84Chapter 4.5 --- Simulation --- p.90Chapter 5 --- MRAFC on a Class of Nonlinear Systems: Type I --- p.97Chapter 5.1 --- Introduction --- p.98Chapter 5.2 --- Choice of Controller --- p.99Chapter 5.3 --- Derivation of the MRAFC adaptive laws --- p.102Chapter 5.4 --- Example: Stabilization of a pendulum --- p.109Chapter 6 --- MRAFC on a Class of Nonlinear Systems: Type II --- p.112Chapter 6.1 --- Introduction --- p.113Chapter 6.2 --- Fuzzy System as Function Approximator --- p.114Chapter 6.3 --- Construction of MRAFC for the nonlinear systems --- p.118Chapter 6.4 --- Input-Output Linearization --- p.130Chapter 6.5 --- MRAFC with Input-Output Linearization --- p.132Chapter 6.6 --- Example --- p.136Chapter 7 --- Analysis of MRAFC System --- p.140Chapter 7.1 --- Averaging technique --- p.140Chapter 7.2 --- Parameter convergence --- p.143Chapter 7.3 --- Robustness --- p.152Chapter 7.4 --- Simulation --- p.157Chapter 8 --- Application of MRAFC scheme on Manipulator Control --- p.166Chapter 8.1 --- Introduction --- p.166Chapter 8.2 --- Robot Manipulator Control --- p.170Chapter 8.3 --- MRAFC on Robot Manipulator Control --- p.173Chapter 8.3.1 --- Part A: Nonlinear-function feedback fuzzy controller --- p.174Chapter 8.3.2 --- Part B: State-feedback fuzzy controller --- p.182Chapter 8.4 --- Simulation --- p.186Chapter 9 --- Conclusion --- p.199Chapter A --- Implementation of MRAFC Scheme with Practical Issues --- p.203Chapter A.1 --- Rule Generation by MRAFC scheme --- p.203Chapter A.2 --- Implementation Considerations --- p.211Chapter A.3 --- MRAFC System Design Procedure --- p.215Bibliography --- p.21

A study in the use of fuzzy logic in the management of an automotive heat engine / electric hybrid vehicle powertrain

This thesis addresses the problem of the instant-by-instant control of the powertrain of a hybrid heat engine/electric vehicle. In the absence of a prototype vehicle on which the work could be carried out the work has taken the form of computer simulation experiments. In order to develop the powertrain control strategies, a computer model of a conceptual hybrid vehicle is then developed, containing components from real, production and prototype vehicles. The use of this component based modelling approach allows the models to be validated by comparing their predictions with the performance of the real vehicles in which the components are used. The previous work conducted in the field of hybrid vehicle powertrain control is then reviewed. It is found that fuzzy logic could potentially provide a means of controlling the hybrid powertrain in a realistic manner, in which some of the disadvantages of previous hybrid powertrain control strategies could be overcome. The results of initial simulation experiments are then reported, finding that whilst the basic method appears to have the potential to successfully control the powertrain, there is a need for an adaptive fuzzy powertrain controller. A review is then presented of previous work conducted in the field of adaptive fuzzy control, finding that none of the reported adaptive fuzzy control methods are capable of being easily applied in the case of the hybrid powertrain. An adaptive fuzzy controller is then developed, whose rule modification strategy is specifically designed to work in the hybrid powertrain control problem. This initial adaptive powertrain controller is then modified to improve its ability to control the overall performance of a hybrid vehicle, whilst maintaining vehicle driveability. It is found that this controller is able to adapt to the different driving styles of individual vehicle users within the space of a few simulated urban journeys. Experiments are then performed in which improvements in the overall efficiency of the vehicle powertrain are investigated. It is found that significant improvements in the operation of the powertrain are impossible, due to some of the features of the vehicle model and constraints placed upon the control strategy. Conclusions are then drawn, for the work done in the field of hybrid vehicle powertrain control and, also, for the work done in adaptive methods of fuzzy control. The most significant contribution in the field of hybrid powertrain control is the development of a controller that can adapt to the habits of different users. The most significant contribution in the field of fuzzy control is the form of the basic hybrid powertrain controller and the use of small fuzzy controllers in the powertrain controller adaptation strategy

Dynamical systems : control and stability

Proceedings of the 13th Conference „Dynamical Systems - Theory and Applications" summarize 164 and the Springer Proceedings summarize 60 best papers of university teachers and students, researchers and engineers from whole the world. The papers were chosen by the International Scientific Committee from 315 papers submitted to the conference. The reader thus obtains an overview of the recent developments of dynamical systems and can study the most progressive tendencies in this field of science