Zhang Huaguang, Wang Yingying, Wang Yingchun, Zhang Jianyu
IEEE Trans Cybern. 2020 Mar;50(3):1037-1046. doi: 10.1109/TCYB.2018.2879839. Epub 2019 Jan 17.
In this paper, a novel robust controller for continuous stochastic polynomial fuzzy systems is investigated. The aim of the proposed method is to eliminate the restrictive assumptions that the local input matrix B must be uniform and the sliding mode surface proposed did not consider the stochastic perturbations, which are required in most existing results. At the same time, the proposed method could handle the system with matched external disturbances. First, a novel vector integral sliding mode surface (VISMS) is constructed according to the basis matrix [Formula: see text]. The sliding mode surface parameter matrix [Formula: see text] can be obtained through the provided sum of squares conditions. Second, by using an improved Lyapunov method and a new proposed lemma, a novel sliding mode control law is designed to keep the state of the closed-loop systems on the VISMS approximately since the initial time. Third, a practical example and a numerical one are provided to illustrate the validity of the proposed approach.
本文研究了一种用于连续随机多项式模糊系统的新型鲁棒控制器。所提方法的目的是消除大多数现有结果中所需的局部输入矩阵B必须均匀以及所提出的滑模面未考虑随机扰动等限制假设。同时，所提方法能够处理具有匹配外部干扰的系统。首先，根据基矩阵[公式：见原文]构造了一种新型向量积分滑模面（VISMS）。滑模面参数矩阵[公式：见原文]可通过所提供的平方和条件获得。其次，通过使用改进的李雅普诺夫方法和新提出的引理，设计了一种新型滑模控制律，以使闭环系统的状态从初始时刻起近似保持在VISMS上。第三，给出了一个实际例子和一个数值例子来说明所提方法的有效性。
