Abstract
In this paper, both dissipation and stabilization of nonlinear T-S fuzzy systems with uncertain parameters are considered. By designing a new integral sliding mode control scheme, which sufficiently utilizes the special properties of T-S fuzzy membership functions, the difficulties induced by the uncertainties and external interference in T-S fuzzy systems are overcome by this new scheme. For the time delay and uncertainty, sufficient conditions are given to ensure the strict dissipation and asymptotic stability of the corresponding sliding mode dynamics. We propose a fuzzy integral sliding mode control law to drive the system trajectory to the fuzzy switching surface in the case of uncertainty and external interference. The realization of a fuzzy sliding mode controller for an inverted pendulum system proves the feasibility and superiority of our theoretical results.
Highlights
Takagi–Sugeno fuzzy model is to fit the same nonlinear system by multiple linear systems and to defuzzify it by fuzzy calculus reasoning
Its advantage is that it can express highly nonlinear complex system with less fuzzy rules and approximate to any accuracy [1]. erefore, the fuzzy control based on Takagi–Sugeno (T-S) fuzzy model [2] has become a research hot spot because of its wide applications in intelligent control theory and various complex practical system control [3,4,5,6,7,8,9,10,11,12]
It can continuously change according to the current state of the system in the dynamic process, forcing the system to move according to the state track of the predetermined “sliding mode,” which has the advantages of fast response and strong robustness. erefore, it has been widely used in various complex dynamical systems, such as time-delay systems [16,17,18,19], stochastic systems [20], and Markov jump systems [21,22,23]
Summary
Takagi–Sugeno fuzzy model is to fit the same nonlinear system by multiple linear systems and to defuzzify it by fuzzy calculus reasoning. In order to deal with this trouble, Chen et al [24,25,26] proposed an integral sliding mode control (ISMC, for short), which makes the system state slide along the sliding mode surface through the switching of control variables and makes the system invariant when it is disturbed by some external disturbances It reduces chattering and can make fast response while simplifying the structure complexity of the fuzzy control system. (1) A new T-S fuzzy system with stochastic disturbance with different input matrices and time delay is considered (2) A new integral fuzzy switching surface function is proposed for tackling the time delay case, and the dissipation and asymptotic stability of the sliding mode control system are obtained via this function (3) A novel fuzzy sliding mode controller is designed to ensure the reachability of sliding mode motion in the presence of matching uncertainties and interference signals e remaining parts of this paper are organized as follows. If A is a m a t ri x , denoted by ‖A‖ sup{‖Ax‖ : |x| 1} λmax(ATA), where λmax(A) means the largest eigenvalue of A
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