Design of stable fuzzy controller for non-linear systems subject to imperfect premise matching based on grid-point approach
Design of stable fuzzy controller for non-linear systems subject to imperfect premise matching based on grid-point approach
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DOI：
10.1049/iet-cta.2009.0307
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发表时间：
2010-12
影响因子：
2.6
通讯作者：
H. Lam
中科院分区：
文献类型：
--
作者：
H. Lam
本研究探讨模糊模型控制系统的稳定性。基于非线性系统的T-S模糊模型，提出了一种基于网格点技术的模糊控制器来闭合反馈回路。GP被定义为非线性系统的子操作域。对于每个GP，相应的GP模糊控制器被用来控制系统。由于每个GP中的非线性比全工作域的非线性低，因此有利于使用GP控制技术产生松弛稳定性分析结果，该GP控制技术考虑了隶属函数和工作域的性质。此外，不同于大多数的模糊控制方法，所提出的一个可以应用到FMB控制系统的不完美的前提匹配的模糊模型和模糊控制器不共享相同的前提隶属函数。因此，一些简单的隶属函数可以用于模糊控制器，以降低实现成本。基于李雅普诺夫稳定性理论，以线性矩阵不等式的形式给出了系统的稳定性条件，从而保证了系统的稳定性，便于控制器的综合。仿真例子证明了所提出的FMB控制方案的优点，使用建议的GP技术。
This study investigates the systems stability of fuzzy-model-based (FMB) control systems. Based on the T-S fuzzy model representing the non-linear system, a fuzzy controller using grid-point (GP) technique is proposed to close the feedback loop. A GP is defined as the sub-operating domain of the non-linear system. For each GP, a corresponding GP fuzzy controller is employed to control the system. As the non-linearity in each GP is lower compared to that of the full operating domain, it is in favour of yielding relaxed stability analysis result using the GP control technique of which the nature of the membership functions and operating domain are taken into account. Furthermore, unlike most of the fuzzy control approaches, the proposed one can be applied to FMB control systems subject to imperfect premise matching that the fuzzy model and fuzzy controller do not share the same premise membership functions. As a result, some simple membership functions can be employed for the fuzzy controllers to lower the implementation cost. Based on the Lyapunov stability theory, stability conditions in terms of linear matrix inequalities are derived to guarantee the system stability and facilitate the controller synthesis. Simulation examples are given to demonstrate the merits of the proposed FMB control scheme using the proposed GP technique.