Ohtake Hiroshi, Tanaka Kazuo, Wang Hua O
Department of Mechanical Engineering and Intelligent Systems, The University of Electro-Communications, Chofu, Tokyo 182-8585, Japan.
IEEE Trans Syst Man Cybern B Cybern. 2006 Feb;36(1):13-23. doi: 10.1109/tsmcb.2005.852473.
This paper presents a switching fuzzy controller design for a class of nonlinear systems. A switching fuzzy model is employed to represent the dynamics of a nonlinear system. In our previous papers, we proposed the switching fuzzy model and a switching Lyapunov function and derived stability conditions for open-loop systems. In this paper, we design a switching fuzzy controller. We firstly show that switching fuzzy controller design conditions based on the switching Lyapunov function are given in terms of bilinear matrix inequalities, which is difficult to design the controller numerically. Then, we propose a new controller design approach utilizing an augmented system. By introducing the augmented system which consists of the switching fuzzy model and a stable linear system, the controller design conditions based on the switching Lyapunov function are given in terms of linear matrix inequalities (LMIs). Therefore, we can effectively design the switching fuzzy controller via LMI-based approach. A design example illustrates the utility of this approach. Moreover, we show that the approach proposed in this paper is available in the research area of piecewise linear control.
本文提出了一类非线性系统的切换模糊控制器设计方法。采用切换模糊模型来表示非线性系统的动态特性。在我们之前的论文中，我们提出了切换模糊模型和切换李雅普诺夫函数，并推导了开环系统的稳定性条件。在本文中，我们设计了一种切换模糊控制器。我们首先表明，基于切换李雅普诺夫函数的切换模糊控制器设计条件是以双线性矩阵不等式的形式给出的，这在数值上难以设计控制器。然后，我们提出了一种利用增广系统的新控制器设计方法。通过引入由切换模糊模型和一个稳定线性系统组成的增广系统，基于切换李雅普诺夫函数的控制器设计条件以线性矩阵不等式（LMI）的形式给出。因此，我们可以通过基于LMI的方法有效地设计切换模糊控制器。一个设计实例说明了该方法的实用性。此外，我们表明本文提出的方法在分段线性控制的研究领域是可行的。
