Universal Fuzzy Controllers for Nonaffine Nonlinear Systems
非仿射類非線性系統的通用模糊控制器問題研究
Student thesis: Doctoral Thesis
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Award date  24 Dec 2013 
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Permanent Link  https://scholars.cityu.edu.hk/en/theses/theses(df83544e5de74f8c85cc1392df6241fd).html 

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Abstract
TakagiSugeno (TS) 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 TS fuzzy models can only be used to represent affine nonlinear systems instead of general nonaffine nonlinear systems, and thus most existing TS fuzzymodelbased approaches can only be applied to affine nonlinear systems. But nonaffine nonlinear systems exist abundantly in practice and it is thus desirable to develop more general TS fuzzymodelbased approaches to nonaffine nonlinear systems.
In this thesis, some new robust stabilization approaches to deterministic/stochastic nonaffine nonlinear systems based on TS 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 nonaffine nonlinear systems based on TS fuzzy models. These issues have been rarely discussed before and are often recognized as open problems in fuzzy control theory in several survey papers. The merits 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 softwares; 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 controller problem based on a class of generalized TS fuzzy models. By using their universal function approximation capability, this kind of generalized TS fuzzy models are shown to be universal fuzzy models to nonaffine nonlinear systems under some sufficient conditions. An approach to stabilization controller design for nonaffine nonlinear systems based on this kind of generalized TS fuzzy models is also developed. The results 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 nonaffine nonlinear systems modeled by I toˆ 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 nonaffine nonlinear systems under some sufficient conditions. An approach to stabilization controller design for stochastic nonaffine nonlinear systems is then developed through their stochastic generalized TS 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 nonaffine nonlinear systems represented by TS fuzzy models with time delay. It is noted that the existing fuzzy SMC approaches rely on some very restrictive assumptions. Aiming to remove these assumptions, a novel dynamic sliding mode control (DSMC) scheme for TS fuzzy models is proposed. By using a class of fuzzy dynamic slidingmode controllers, sufficient conditions for the reachability of the sliding surface and asymptotic stability of the sliding motion are formulated in the form of linear matrix inequalities (LMIs).
Then, the socalled universal fuzzy integral slidingmode 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 TS 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 TS 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 slidingmode controllers for two classes of nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral slidingmode controllers, are provided.
Finally, we further investigate the universal integral slidingmode controller problem for stochastic nonlinear systems. First, a novel dynamic integral sliding mode control (DISMC) scheme is developed for stochastic nonlinear systems based on their stochastic TS 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 closedloop control system trajectories are kept on the integral sliding surface almost surely since the initial 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 slidingmode controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral slidingmode controllers, are also provided.
In this thesis, some new robust stabilization approaches to deterministic/stochastic nonaffine nonlinear systems based on TS 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 nonaffine nonlinear systems based on TS fuzzy models. These issues have been rarely discussed before and are often recognized as open problems in fuzzy control theory in several survey papers. The merits 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 softwares; 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 controller problem based on a class of generalized TS fuzzy models. By using their universal function approximation capability, this kind of generalized TS fuzzy models are shown to be universal fuzzy models to nonaffine nonlinear systems under some sufficient conditions. An approach to stabilization controller design for nonaffine nonlinear systems based on this kind of generalized TS fuzzy models is also developed. The results 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 nonaffine nonlinear systems modeled by I toˆ 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 nonaffine nonlinear systems under some sufficient conditions. An approach to stabilization controller design for stochastic nonaffine nonlinear systems is then developed through their stochastic generalized TS 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 nonaffine nonlinear systems represented by TS fuzzy models with time delay. It is noted that the existing fuzzy SMC approaches rely on some very restrictive assumptions. Aiming to remove these assumptions, a novel dynamic sliding mode control (DSMC) scheme for TS fuzzy models is proposed. By using a class of fuzzy dynamic slidingmode controllers, sufficient conditions for the reachability of the sliding surface and asymptotic stability of the sliding motion are formulated in the form of linear matrix inequalities (LMIs).
Then, the socalled universal fuzzy integral slidingmode 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 TS 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 TS 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 slidingmode controllers for two classes of nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral slidingmode controllers, are provided.
Finally, we further investigate the universal integral slidingmode controller problem for stochastic nonlinear systems. First, a novel dynamic integral sliding mode control (DISMC) scheme is developed for stochastic nonlinear systems based on their stochastic TS 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 closedloop control system trajectories are kept on the integral sliding surface almost surely since the initial 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 slidingmode controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral slidingmode controllers, are also provided.