Two-Step Stability Analysis for General Polynomial-Fuzzy-Model-Based Control Systems
Two-Step Stability Analysis for General Polynomial-Fuzzy-Model-Based Control Systems
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DOI：
10.1109/tfuzz.2014.2315674
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发表时间：
2015-06
影响因子：
11.9
通讯作者：
H. Lam;Ligang Wu;J. Lam
中科院分区：
文献类型：
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作者：
H. Lam;Ligang Wu;J. Lam
研究了由多项式模糊模型表示的非线性对象和多项式模糊控制器连接成闭环的基于多项式模糊模型的控制系统的稳定性。三种情况下的多项式模糊控制器提出了一个匹配/不匹配的规则和/或前提隶属函数，这表明不同程度的控制器的复杂性，设计灵活性和稳定性分析结果的控制过程中考虑。提出了一个通用的多项式李雅普诺夫函数候选研究系统的稳定性。与已发表的工作，有没有约束的多项式李雅普诺夫函数候选人，这是独立的形式的多项式模糊模型。因此，它可以适用于更广泛的一类PFMB控制系统，并可能产生更宽松的稳定性分析结果。两步稳定性条件的平方和（SOS）的数值找到一个可行的解决方案。为了方便稳定性分析并放松稳定性分析结果，稳定性分析中考虑了隶属函数的边界信息，并将其纳入基于SOS的稳定条件中。最后通过仿真实例验证了该方法的有效性。
This paper investigates the stability of a polynomial-fuzzy-model-based (PFMB) control system formed by a nonlinear plant represented by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop. Three cases of polynomial fuzzy controllers are proposed for the control process with the consideration of a matched/mismatched number of rules and/or premise membership functions, which demonstrate different levels of controller complexity, design flexibility, and stability analysis results. A general polynomial Lyapunov function candidate is proposed to investigate the system stability. Unlike the published work, there is no constraint on the polynomial Lyapunov function candidate, which is independent of the form of the polynomial fuzzy model. Thus, it can be applied to a wider class of PFMB control systems and potentially produces more relaxed stability analysis results. Two-step stability conditions in terms of sum-of-squares (SOS) are obtained to numerically find a feasible solution. To facilitate the stability analysis and relax the stability analysis result, the boundary information of membership functions is taken into account in the stability analysis and incorporated into the SOS-based stability conditions. Simulation examples are given to illustrate the effectiveness of the proposed approach.