Vu Van-Phong, Wang Wen-June
IEEE Trans Cybern. 2021 Apr;51(4):1929-1942. doi: 10.1109/TCYB.2019.2895233. Epub 2021 Mar 17.
This paper proposes a novel method to synthesize a controller for stabilizing the nonlinear large-scale system which is represented by a large-scale polynomial Takagi-Sugeno (T-S) fuzzy system. The large-scale system consists of a set of the uncertain polynomial T-S fuzzy system with interconnection terms. Modeling the large-scale nonlinear system under the framework of the polynomial form will decrease both the modeling errors and the number of fuzzy rules with respect to the conventional large-scale T-S fuzzy system. In addition, because of the existence of uncertainties, the synthesizing controller for the large-scale polynomial fuzzy system becomes much more challenging and has not been investigated in the previous studies. In this paper, a controller is synthesized to simultaneously eliminate the impact of the uncertainties and stabilize the system. With the aid of Lyapunov theory, sum-of-square technique, and S-procedure, the conditions for controller synthesis are derived in the main theorems. Finally, two examples are illustrated to show the effectiveness and merit of the proposed method.
本文提出了一种新颖的方法来合成一个控制器，用于稳定由大规模多项式高木-菅野（T-S）模糊系统表示的非线性大规模系统。该大规模系统由一组带有互联项的不确定多项式T-S模糊系统组成。在多项式形式的框架下对大规模非线性系统进行建模，相对于传统的大规模T-S模糊系统，将减少建模误差和模糊规则的数量。此外，由于不确定性的存在，为大规模多项式模糊系统合成控制器变得更具挑战性，且在以往研究中尚未得到探讨。本文合成了一个控制器，以同时消除不确定性的影响并稳定系统。借助李雅普诺夫理论、平方和技术以及S-过程，在主要定理中推导了控制器合成的条件。最后，通过两个例子说明了所提方法的有效性和优点。
