A CENTER MANIFOLD THEORY-BASED APPROACH TO THE STABILITY ANALYSIS OF STATE FEEDBACK TAKAGI-SUGENO-KANG FUZZY CONTROL SYSTEMS

The aim of this paper is to propose a stability analysis approach based on the application of the center manifold theory and applied to state feedback Takagi-Sugeno-Kang fuzzy control systems. The approach is built upon a similar approach developed for Mamdani fuzzy controllers. It starts with a linearized mathematical model of the process that is accepted to belong to the family of single input second-order nonlinear systems which are linear with respect to the control signal. In addition, smooth right-hand terms of the state-space equations that model the processes are assumed. The paper includes the validation of the approach by application to stable state feedback Takagi-Sugeno-Kang fuzzy control system for the position control of an electro-hydraulic servo-system

Analysis of stability of p-fuzzy dynamic systems with applications in biomathematic

Orientador: Rodney Carlos BassaneziTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientificaResumo: Um sistema dinâmico p-fuzzy é um sistema cuja dinâmica é obtida através de um sistema baseado em regras fuzzy. Neste trabalho, realizamos um estudo analítico da estabilidade dos sistemas dinâmicos p-fuzzy. Estabelecemos condições necessárias e suficientes para existência de ponto de equilíbrio para sistemas p-fuzzy unidimensionais e bidimensionais e derivamos condições para estabilidade deste ponto. Vimos que, uma condição suficiente para existência de ponto de equilíbrio é uma mudança de sinal na saída do controlador. Este trabalho mostra ainda, que a estabilidade de um ponto de equilíbrio depende, principalmente, das variáveis de entradas e saídas do sistema baseado em regras fuzzy associado ao sistema p-fuzzy. Além dos diversos resultados matemáticos encontrados, com demonstrações rigorosas, realizamos inúmeros experimentos computacionais e obtivemos resultados que atestam a veracidade de da teoria aqui proposta. Apresentamos ainda, algumas aplicações em Biomatemática onde podemos comprovar, em situações concretas, a eficácia, versatilidade e robustez da teoria desenvolvidaAbstract: A p-fuzzy dynamic system is a system whose dynamics is obtained through a fuzzy rule-based systems. ln this work we present an analytical study of the stability of p-fuzzy dynamic systems. We establish necessary and sufficient conditions to existence of equilibrium point for one variable and two variable p-fuzzy systems and, we derive conditions for stability of this point. We saw that, a sufficient condition for existence of equilibrium point is a change of signal in the output of the controller This work still shows, that the stability of an equilibrium point depends, mainly, fuzzy rule-based systems's input-output. Many mathematical results has been found and demonstrated rigorously. We still made many computational experiments and its results show that all developed mathematical theory is efficient. We still present, some applications in Biomathematics where we can prove, in real situations, the efficiency, versatility and robustness of the developed theory in this workDoutoradoDoutor em Matemática Aplicad

Navigational Path Analysis of Mobile Robot in Various Environments

This dissertation describes work in the area of an autonomous mobile robot. The objective is navigation of mobile robot in a real world dynamic environment avoiding structured and unstructured obstacles either they are static or dynamic. The shapes and position of obstacles are not known to robot prior to navigation. The mobile robot has sensory recognition of specific objects in the environments. This sensory-information provides local information of robots immediate surroundings to its controllers. The information is dealt intelligently by the robot to reach the global objective (the target). Navigational paths as well as time taken during navigation by the mobile robot can be expressed as an optimisation problem and thus can be analyzed and solved using AI techniques. The optimisation of path as well as time taken is based on the kinematic stability and the intelligence of the robot controller. A successful way of structuring the navigation task deals with the issues of individual behaviour design and action coordination of the behaviours. The navigation objective is addressed using fuzzy logic, neural network, adaptive neuro-fuzzy inference system and different other AI technique.The research also addresses distributed autonomous systems using multiple robot

New Approaches in Automation and Robotics

The book New Approaches in Automation and Robotics offers in 22 chapters a collection of recent developments in automation, robotics as well as control theory. It is dedicated to researchers in science and industry, students, and practicing engineers, who wish to update and enhance their knowledge on modern methods and innovative applications. The authors and editor of this book wish to motivate people, especially under-graduate students, to get involved with the interesting field of robotics and mechatronics. We hope that the ideas and concepts presented in this book are useful for your own work and could contribute to problem solving in similar applications as well. It is clear, however, that the wide area of automation and robotics can only be highlighted at several spots but not completely covered by a single book

TS fuzzy approach for modeling, analysis and design of non-smooth dynamical systems

There has been growing interest in the past two decades in studying the physical model of dynamical systems that can be described by nonlinear, non-smooth differential equations, i.e. non-smooth dynamical systems. These systems exhibit more colourful and complex dynamics compared to their smooth counterparts; however, their qualitative analysis and design are not yet fully developed and still open to exploration. At the same time, Takagi-Sugeno (TS) fuzzy systems have been shown to have a great ability to represent a large class of nonlinear systems and approximate their inherent uncertainties. This thesis explores an area of TS fuzzy systems that have not been considered before; that is, modelling, stability analysis and design for non-smooth dynamical systems. TS fuzzy model structures capable of representing or approximating the essential dis- continuous dynamics of non-smooth systems are proposed in this thesis. It is shown that by incorporating discrete event systems, the proposed structure for TS fuzzy models, which we will call non-smooth TS fuzzy models, can accurately represent the smooth (or contin- uous) as well as non-smooth (or discontinuous) dynamics of different classes of electrical and mechanical non-smooth systems including (sliding and non-sliding) Filippov's systems and impacting systems. The different properties of the TS fuzzy modelling (or formalism) are discussed. It is highlighted that the TS fuzzy formalism, taking advantage of its simple structure, does not need a special platform for its implementation. Stability in its new notion of structural stability (stability of a periodic solution) is one of the most important issues in the qualitative analysis of non-smooth systems. An important part of this thesis is focused on addressing stability issues by extending non- smooth Lyapunov theory for verifying the stability of local orbits, which the non-smooth TS fuzzy models can contain. Stability conditions are proposed for Filippov-type and impacting systems and it is shown that by formulating the conditions as Linear Matrix inequalities (LMIs), the onset of non-smooth bifurcations or chaotic phenomena can be detected by solving a feasibility problem. A number of examples are given to validate the proposed approach. Stability robustness of non-smooth TS fuzzy systems in the presence of model uncertainties is discussed in terms of non-smoothness rather than traditional observer design. The LMI stabilization problem is employed as a building block for devising design strategies to suppress the unwanted chaotic behaviour in non-smooth TS fuzzy models. There have been a large number of control applications in which the overall closed-loop sys tem can be stabilized by switching between pre-designed sub-controllers. Inspired by this idea, the design part of this thesis concentrates on fuzzy-chaos control strategies for Filippov-type systems. These strategies approach the design problem by switching be- tween local state-feedback controllers such that the closed-loop TS fuzzy system of interest rapidly converges to the stable periodic solution of the system. All control strategies are also automated as a design problem recast on linear matrix inequality conditions to be solved by modern optimization techniques. Keywords: Takagi-Sugeno fuzzy systems, non-smooth Lyapunov theory, non-smooth dy- namical systems, piecewise-smooth dynamical systems, structural stability, discontinuity- induced bifurcation, chaos controllers, dc-dc converters, Filippov's system, impacting system, linear matrix inequalities.EThOS - Electronic Theses Online ServiceGBUnited Kingdo