Department of Electronics and Communication Engineering, Indian Institute of Technology, Guwahati, Guwahati-781039, Assam, India.
ISA Trans. 2010 Jan;49(1):27-38. doi: 10.1016/j.isatra.2009.07.005. Epub 2009 Aug 14.
In this paper, we consider fuzzy identification of uncertain nonlinear systems in Takagi-Sugeno (T-S) form for the purpose of robust fuzzy control design. The uncertain nonlinear system is represented using a fuzzy function having constant matrices and time varying uncertain matrices that describe the nominal model and the uncertainty in the nonlinear system respectively. The suggested method is based on linear programming approach and it comprises the identification of the nominal model and the bounds of the uncertain matrices and then expressing the uncertain matrices into uncertain norm bounded matrices accompanied by constant matrices. It has been observed that our method yields less conservative results than the other existing method proposed by Skrjanc et al. (2005). With the obtained fuzzy model, we showed the robust stability condition which provides a basis for different robust fuzzy control design. Finally, different simulation examples are presented for identification and control of uncertain nonlinear systems to illustrate the utility of our proposed identification method for robust fuzzy control.
在本文中，我们考虑了 Takagi-Sugeno（T-S）形式的不确定非线性系统的模糊辨识，目的是进行鲁棒模糊控制设计。不确定非线性系统使用具有常值矩阵和时变不确定矩阵的模糊函数表示，分别描述了标称模型和非线性系统中的不确定性。所提出的方法基于线性规划方法，包括标称模型和不确定矩阵的界的辨识，然后将不确定矩阵表示为不确定范数有界矩阵，并伴有常值矩阵。已经观察到，我们的方法比 Skrjanc 等人（2005 年）提出的其他现有方法产生的结果更为保守。利用所得到的模糊模型，我们给出了鲁棒稳定性条件，为不同的鲁棒模糊控制设计提供了基础。最后，提出了不同的不确定非线性系统的辨识和控制仿真示例，以说明我们提出的用于鲁棒模糊控制的辨识方法的实用性。
