Discrete polynomial fuzzy systems control
Discrete polynomial fuzzy systems control
复制标题
DOI：
10.1049/iet-cta.2013.0645
复制
发表时间：
2014-03-06
影响因子：
2.6
通讯作者：
Wang, Hua O.
中科院分区：
文献类型：
--
作者：
Chen, Ying-Jen;Tanaka, Motoyasu;Wang, Hua O.
本文提出了一种基于平方和的离散多项式模糊系统的稳定控制和保性能控制方法。本文提出的SOS框架提供了一个新的范例，在现有的线性矩阵不等式（LMI）的方法离散Takagi-Sugeno（T-S）模糊模型。本研究首先引入一种新的离散多项式模糊模型，它比著名的离散T-S模糊模型更通用、更有效。考虑到操作域，稳定的控制设计条件，然后推导出基于状态相关的李雅普诺夫函数，包含二次李雅普诺夫函数作为特殊情况。因此，在这项研究中讨论的设计方法可以更一般的LMI设计方法的基础上二次李雅普诺夫函数。此外，本研究也讨论了一个保成本控制设计，这是通过最小化给定的性能函数的上界进行。在这项研究中推导出的所有设计条件可以表示在SOS和符号和数值求解通过SOSOPT和SeDuMi，分别。最后，以球杆系统为例，说明所提出的基于SOS的设计方法的实用性。
This study presents a sum-of-squares (SOS) approach to stable control and guaranteed cost control of discrete polynomial fuzzy systems. The SOS framework presented in this paper offers a new paradigm over the existing linear matrix inequality (LMI) approaches to discrete Takagi-Sugeno (T-S) fuzzy models. At first, this study, newly introduces a discrete polynomial fuzzy model that is more general and effective than the well-known discrete T-S fuzzy model. With considering the operating domain, stable control design conditions are then derived based on state-dependent Lyapunov functions that contain quadratic Lyapunov functions as a special case. Hence, the design approach discussed in this study could be more general than the LMI design approaches based on quadratic Lyapunov functions. Moreover, this study also discusses a guaranteed cost control design which is carried out by minimising the upper bound of a given performance function. All the design conditions derived in this study can be represented in terms of SOS and are symbolically and numerically solved via the SOSOPT and the SeDuMi, respectively. Finally, the ball-and-beam system is provided as an example to illustrate the utility of the proposed SOS-based design approach.