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

Intelligent Adaptive Motion Control for Ground Wheeled Vehicles

In this paper a new intelligent adaptive control is applied to solve a problem of motion control of ground vehicles with two independent wheels actuated by a differential drive. The major objective of this work is to obtain a motion control system by using a new fuzzy inference mechanism where the Lyapunov’s stability can be assured. In particular the parameters of the kinematical control law are obtained using an intelligent Fuzzy mechanism, where the properties of the Fuzzy maps have been established to have the stability above. Due to the nonlinear map of the intelligent fuzzy inference mechanism (i.e. fuzzy rules and value of the rule), the parameters above are not constant, but, time after time, based on empirical fuzzy rules, they are updated in function of the values of the tracking errors. Since the fuzzy maps are adjusted based on the control performances, the parameters updating assures a robustness and fast convergence of the tracking errors. Also, since the vehicle dynamics and kinematics can be completely unknown, a dynamical and kinematical adaptive control is added. The proposed fuzzy controller has been implemented for a real nonholonomic electrical vehicle. Therefore system robustness and stability performance are verified through simulations and experimental studies

Generalized dynamical fuzzy model for identification and prediction

In this paper, the development of an improved Takagi Sugeno (TS) fuzzy model for identification and chaotic time series prediction of nonlinear dynamical systems is proposed. This model combines the advantages of fuzzy systems and Infinite Impulse Response (IIR) filters, which are autoregressive moving average models, to create internal dynamics with just the control input. The structure of Fuzzy Infinite Impulse Response (FIIR) is presented, and its learning algorithm is described. In the proposed model, the Butterworth analogue prototype filters are estimated using the obtained membership functions. Based on the founding orders of the analogue filters, the IIR filters could be constructed. The IIR filters are introduced to each TS fuzzy rule which produces local dynamics. Gustafson-Kessel (GK) clustering algorithm is used to generate the clusters which will be used to find the number of the IIR parameters for each rule. The hybrid genetic algorithm and simplex method are used to identify the consequence parameters. The stability of the obtained model is studied. To demonstrate the performance of this modeling method, three examples have been chosen. Comparative results between the FIIR model on one hand, and the traditional TS fuzzy model, the neural networks and the neuro-fuzzy network on the other hand. The results show that the proposed method provides promising identification result

Robust H∞ control for discrete-time fuzzy systems with infinite-distributed delays

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is concerned with the robust H∞ control problem for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delays and uncertain parameters. The time delay is assumed to be infinitely distributed in the discrete-time domain, and the uncertain parameters are norm-bounded. By using the linear matrix inequality (LMI) technique, sufficient conditions are derived for ensuring the exponential stability as well as the H infin performance for the closed-loop fuzzy control system. It is also shown that the controller gain can be characterized in terms of the solution to a set of LMIs, which can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures

Mathematical control of complex systems 2013

Mathematical control of complex systems have already become an ideal research area for control engineers, mathematicians, computer scientists, and biologists to understand, manage, analyze, and interpret functional information/dynamical behaviours from real-world complex dynamical systems, such as communication systems, process control, environmental systems, intelligent manufacturing systems, transportation systems, and structural systems. This special issue aims to bring together the latest/innovative knowledge and advances in mathematics for handling complex systems. Topics include, but are not limited to the following: control systems theory (behavioural systems, networked control systems, delay systems, distributed systems, infinite-dimensional systems, and positive systems); networked control (channel capacity constraints, control over communication networks, distributed filtering and control, information theory and control, and sensor networks); and stochastic systems (nonlinear filtering, nonparametric methods, particle filtering, partial identification, stochastic control, stochastic realization, system identification)

Mathematical problems for complex networks

Copyright @ 2012 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is made available through the Brunel Open Access Publishing Fund.Complex networks do exist in our lives. The brain is a neural network. The global economy is a network of national economies. Computer viruses routinely spread through the Internet. Food-webs, ecosystems, and metabolic pathways can be represented by networks. Energy is distributed through transportation networks in living organisms, man-made infrastructures, and other physical systems. Dynamic behaviors of complex networks, such as stability, periodic oscillation, bifurcation, or even chaos, are ubiquitous in the real world and often reconfigurable. Networks have been studied in the context of dynamical systems in a range of disciplines. However, until recently there has been relatively little work that treats dynamics as a function of network structure, where the states of both the nodes and the edges can change, and the topology of the network itself often evolves in time. Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication and bioinformatics