Switching fuzzy controller design based on switching Lyapunov function for a class of nonlinear systems
Switching fuzzy controller design based on switching Lyapunov function for a class of nonlinear systems
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DOI：
10.1109/tsmcb.2005.852473
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发表时间：
2006-02
期刊：
影响因子：
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通讯作者：
H. Ohtake;Kazuo Tanaka;Hua O. Wang
中科院分区：
文献类型：
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作者：
H. Ohtake;Kazuo Tanaka;Hua O. Wang
针对一类非线性系统，提出了一种切换模糊控制器的设计方法。切换模糊模型是用来表示一个非线性系统的动态。在我们以前的论文中，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。本文设计了一种切换模糊控制器。首先，基于切换Lyapunov函数的切换模糊控制器的设计条件是以双线性矩阵不等式的形式给出的，这使得控制器的数值设计变得困难。然后，我们提出了一种新的控制器设计方法，利用增广系统。通过引入由切换模糊模型和稳定线性系统组成的增广系统，以线性矩阵不等式的形式给出了基于切换李雅普诺夫函数的控制器设计条件.因此，我们可以有效地设计切换模糊控制器，通过基于LMI的方法。一个设计实例说明了这种方法的实用性。此外，我们表明，本文提出的方法是可用的分段线性控制的研究领域。
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.