Universal Fuzzy Controllers For Non-affine Nonlinear Systems

Takagi-Sugeno (T-S) type fuzzy models have been treated as one of the most useful tools to modeling and control design of complex nonlinear systems, due to their relatively simple structure and universal function approximation capability. However it has been recently shown that the commonly used T-S fuzzy models can only be used to represent affine nonlinear systems instead of general non-affine nonlinear systems, and thus most existing T-S fuzzy models based approaches can only be applied to affine nonlinear systems. But non-affine nonlinear systems exist abundantly in practice and it is thus desirable to develop more general T-S fuzzy model based approaches to non-affine nonlinear systems.In this thesis, some new robust stabilization approaches to deterministic/stochastic non-affine nonlinear systems based on T-S fuzzy models will be developed. The main attention will be focused on universal function approximation, universal fuzzy models, and universal fuzzy controllers for deterministic/stochastic non-affine nonlinear sys-tems based on T-S fuzzy models. These issues have been rarely discussed before and recognized as open problems in fuzzy control theory in several survey papers. The mer-its of the proposed approaches lie in that,(i) the control design can be accomplished in terms of linear matrix inequalities which can be effectively solved by available soft-ware; and (ii) the nonlinear systems under study are much more general than those in most existing works.Firstly, we investigate the universal fuzzy model problem and universal fuzzy con-troller problem based on a class of generalized T-S fuzzy models. By using their uni-versal function approximation capability, this kind of generalized T-S fuzzy models are shown to be universal fuzzy models to non-affine nonlinear systems under some sufficient conditions. An approach to robust controller design for non-affine nonlinear systems based on this kind of generalized T-S fuzzy models is also developed. The re-sults of universal fuzzy controllers for two classes of nonlinear systems are then given, and constructive procedures to obtain the universal fuzzy controllers are also provided. Secondly, attention goes to the universal fuzzy model problem and universal fuzzy controller problem for stochastic non-affine nonlinear systems modeled by Ito type stochastic differential equations. The underlying mechanism of stochastic fuzzy logic is first discussed and a stochastic generalized fuzzy model with new stochastic fuzzy rule base is then given. Based on their function approximation capability, this kind of stochastic generalized fuzzy models are shown to be universal fuzzy models for stochastic non-affine nonlinear systems under some sufficient conditions. An approach to stabilization controller design for stochastic non-affine nonlinear systems is then developed through their stochastic generalized T-S fuzzy approximation models. The results of universal fuzzy controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy controllers, are also provided.Then, attention is focused on sliding mode control (SMC) of deterministic/stochastic non-affine nonlinear systems represented by T-S fuzzy models with time delay. It is noted that the existing fuzzy SMC approaches rely on some very restrictive assump-tions. Aiming to remove these assumptions, a novel dynamic sliding mode control (DSMC) scheme for T-S fuzzy models is proposed. By using a class of fuzzy dynamic sliding-mode controllers, sufficient conditions for the reachability of the sliding sur-face and asymptotic stability of the sliding motion are formulated in the form of linear matrix inequalities (LMIs).Then, the so-called universal fuzzy integral sliding-mode controller problem for deterministic nonlinear systems is investigated. A novel fuzzy dynamic integral sliding mode control (DISMC) scheme is developed for nonlinear systems based on their T-S fuzzy approximation models. One of the key features of the new DISMC scheme is that the restrictive assumption that all local linear systems of the T-S fuzzy models share a common input matrix, which is required in most existing fuzzy integral sliding mode control (ISMC) approaches, is removed. Furthermore, the results of universal fuzzy integral sliding-mode controllers for two classes of nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral sliding-mode controllers, are provided.Finally, we further investigate the universal integral sliding-mode controller prob- lem for stochastic nonlinear systems. First, a novel dynamic integral sliding mode control (DISMC) scheme is developed for stochastic nonlinear systems based on their stochastic T-S fuzzy approximation models. The key advantage of the proposed DISMC scheme is that two very restrictive assumptions in most existing ISMC approaches to stochastic fuzzy systems have been removed. It is shown that the closed-loop control system trajectories are kept on the integral sliding surface almost surely since the ini-tial time, and moreover the stochastic stability of the sliding motion can be guaranteed in terms of linear matrix inequalities (LMIs). The results of universal fuzzy integral sliding-mode controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral sliding-mode controllers, are also provided.