An SOS-based observer design for polynomial fuzzy systems
An SOS-based observer design for polynomial fuzzy systems
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DOI：
10.1109/acc.2011.5990791
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发表时间：
2011-08
期刊：
影响因子：
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通讯作者：
Kazuo Tanaka;H. Ohtake;T. Seo;Hua O. Wang
中科院分区：
文献类型：
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作者：
Kazuo Tanaka;H. Ohtake;T. Seo;Hua O. Wang
针对一类更一般的多项式模糊系统，提出了一种基于平方和(SOS)的观测器设计方法，其多项式矩阵Ai(x(T))和Bi(x(T))允许依赖于状态x(T)。首先，我们简要总结了前人关于两类有限多项式模糊系统基于SOS的观测器设计的工作。为了克服一般系统不能实现所谓分离原理设计的困难，本文提出了一种实用的多项式模糊控制器和多项式模糊观测器的设计方法，在保证整个控制系统的稳定性的同时，使状态估计误差(通过观测器)收敛到零。本文讨论的设计方法比现有的线性矩阵不等式方法(T-S模糊控制器和观测器的设计)更具一般性，也比以前基于SOS的观测器设计更具一般性。为了说明该设计方法的有效性，给出了一个设计实例。算例表明，对于更一般的多项式模糊系统，我们的SOS方法对基于多项式模糊观测器的控制是有效的。
This paper presents a sum of squares (SOS, for brevity) based observer design for a more general class of polynomial fuzzy systems with the polynomial matrices Ai(x(t)) and Bi(x(t)) that are permitted to be dependent of the states x(t). First, we briefly summarize previous works on SOS-based observer designs for two limited classes of polynomial fuzzy systems. To overcome the difficulty of the fact that does not realize the so-called separation principle design for the more general class, this paper provides a practical design procedure of a polynomial fuzzy controller and a polynomial fuzzy observer without lack of guaranteeing the stability of the overall control system in addition to converging state estimation error (via the observer) to zero. The design approach discussed in this paper is more general than the existing LMI approaches (to T-S fuzzy controller and observer designs) and also than the previous SOS-based observer designs. To illustrate the validity of the design approach, a design example is provided. The example shows the utility of our SOS approach to the polynomial fuzzy observer-based control for the more general class of polynomial fuzzy systems.