A frequency-domain-based sufficient condition is derived to guarantee the globally asymptotic stability of the simplest Takagi-Sugeno （T-S） fuzzy control system by using the circle criterion. The analysis is perform...A frequency-domain-based sufficient condition is derived to guarantee the globally asymptotic stability of the simplest Takagi-Sugeno （T-S） fuzzy control system by using the circle criterion. The analysis is performed in the frequency domain, and hence the condition is of great significance when the frequency-response method, which is widely used in the linear control theory and practice, is employed to synthesize the simplest T-S fuzzy controller. Besides, this sufficient condition is featured by a graphical interpretation, which makes the condition straightforward to be used. Comparisons are drawn between the performance of the simplest T-S fuzzy controller and that of the linear compensator. Two numerical examples are presented to demonstrate how this sufficient condition can be applied to both stable and unstable plants.展开更多
The problems of stability and stabilization for the discrete Takagi-Sugeno（T-S） fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function（PLKF） in each maximal over...The problems of stability and stabilization for the discrete Takagi-Sugeno（T-S） fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function（PLKF） in each maximal overlapped-rules group（MORG）,a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved.Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme,and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed.The above two sufficient conditions only require finding common matrices in each MORG.Compared with the common Lyapunov-Krasovskii function（CLKF） approach and the fuzzy Lyapunov-Krasovskii function（FLKF） approach,these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved.Finally,simulation examples show that the proposed PLKF approach is effective.展开更多
A design method is presented for Takagi-Sugeno （T-S） fuzzy model based nonlinear sliding model controller. First, the closed-loop fuzzy system is divided into a set of dominant local linear systems according to oper...A design method is presented for Takagi-Sugeno （T-S） fuzzy model based nonlinear sliding model controller. First, the closed-loop fuzzy system is divided into a set of dominant local linear systems according to operating sub-regions. In each sub-region the fuzzy system consists of nominal linear system and a group of interacting systems. Then the controller composed two parts is designed. One part is designed to control the nominal system, the other is designed to control the interacting systems with sliding mode theory. The proposed controller can improve the robusmess and gnarantee tracking performance of the fuzzy system. Stability is guaranteed without finding a common positive definite matrix.展开更多
An indirect adaptive fuzzy control scheme is developed for a class of nonlinear discrete-time systems. In this method, two fuzzy logic systems are used to approximate the unknown functions, and the parameters of membe...An indirect adaptive fuzzy control scheme is developed for a class of nonlinear discrete-time systems. In this method, two fuzzy logic systems are used to approximate the unknown functions, and the parameters of membership functions in fuzzy logic systems are adjusted according to adaptive laws for the purpose of controlling the plant to track a reference trajectory. It is proved that the scheme can not only guarantee the boundedness of the input and output of the closed-loop system, but also make the tracking error converge to a small neighborhood of the origin. Simulation results indicate the effectiveness of this scheme.展开更多
文摘A frequency-domain-based sufficient condition is derived to guarantee the globally asymptotic stability of the simplest Takagi-Sugeno （T-S） fuzzy control system by using the circle criterion. The analysis is performed in the frequency domain, and hence the condition is of great significance when the frequency-response method, which is widely used in the linear control theory and practice, is employed to synthesize the simplest T-S fuzzy controller. Besides, this sufficient condition is featured by a graphical interpretation, which makes the condition straightforward to be used. Comparisons are drawn between the performance of the simplest T-S fuzzy controller and that of the linear compensator. Two numerical examples are presented to demonstrate how this sufficient condition can be applied to both stable and unstable plants.
基金supported in part by the Scientific Research Project of Heilongjiang Province Education Bureau(12541200)
文摘The problems of stability and stabilization for the discrete Takagi-Sugeno（T-S） fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function（PLKF） in each maximal overlapped-rules group（MORG）,a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved.Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme,and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed.The above two sufficient conditions only require finding common matrices in each MORG.Compared with the common Lyapunov-Krasovskii function（CLKF） approach and the fuzzy Lyapunov-Krasovskii function（FLKF） approach,these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved.Finally,simulation examples show that the proposed PLKF approach is effective.
文摘A design method is presented for Takagi-Sugeno （T-S） fuzzy model based nonlinear sliding model controller. First, the closed-loop fuzzy system is divided into a set of dominant local linear systems according to operating sub-regions. In each sub-region the fuzzy system consists of nominal linear system and a group of interacting systems. Then the controller composed two parts is designed. One part is designed to control the nominal system, the other is designed to control the interacting systems with sliding mode theory. The proposed controller can improve the robusmess and gnarantee tracking performance of the fuzzy system. Stability is guaranteed without finding a common positive definite matrix.
基金surported by Tianjin Science and Technology Development for Higher Education(20051206).
文摘An indirect adaptive fuzzy control scheme is developed for a class of nonlinear discrete-time systems. In this method, two fuzzy logic systems are used to approximate the unknown functions, and the parameters of membership functions in fuzzy logic systems are adjusted according to adaptive laws for the purpose of controlling the plant to track a reference trajectory. It is proved that the scheme can not only guarantee the boundedness of the input and output of the closed-loop system, but also make the tracking error converge to a small neighborhood of the origin. Simulation results indicate the effectiveness of this scheme.
