A Novel Path-Following-Method-Based Polynomial Fuzzy Control Design
A Novel Path-Following-Method-Based Polynomial Fuzzy Control Design
复制标题
DOI：
10.1109/tcyb.2019.2956495
复制
发表时间：
2019-12
影响因子：
11.8
通讯作者：
Ying-Jen Chen;Kazuo Tanaka;Motoyasu Tanaka;S. Tsai;Hua O. Wang
中科院分区：
文献类型：
--
作者：
Ying-Jen Chen;Kazuo Tanaka;Motoyasu Tanaka;S. Tsai;Hua O. Wang
本文提出了一种新的基于路径跟踪方法的多项式模糊控制设计。通过对镇定问题的研究，提出了用双线性平方和（SOS）约束表示的非凸镇定准则，以补充现有的凸镇定准则。基于多项式Lyapunov函数并考虑操作域，采用系统吸引域（ROA）分析方法设计了稳定控制。由于所提出的镇定准则保持非凸形式，因此可以避免由非凸（双线性）约束转化为凸（SOS）约束所引起的保守性。此外，本文提出的非凸稳定准则不存在文献中对凸变换的Lyapunov函数候选者的限制。多项式模糊控制系统的镇定分析涉及的是双模糊求和问题，该问题可以看作是可合性问题。因此，将基于sos的组合松弛技术应用于所提出的稳定准则。由于所提出的非凸镇定准则是用双线性SOS约束表示的，因此采用路径跟踪方法求解双线性SOS问题。最后，给出了设计实例，证明了所提出的非凸稳定准则是对现有凸稳定准则的补充。
This article presents a novel path-following-method-based polynomial fuzzy control design. By examining the stabilization problem, the nonconvex stabilization criterion represented in terms of bilinear sum-of-squares (SOS) constraints is proposed to complement the existing convex stabilization criteria. Based on the polynomial Lyapunov function and considering the operation domain, the stabilization control is designed with a systematic region of attraction (ROA) analysis method. Since the proposed stabilization criterion remains in nonconvex form, the conservativeness caused by the transformation from nonconvex (bilinear SOS) constraints into convex (SOS) constraints can be avoided. Moreover, the restriction on the Lyapunov function candidates for the convex transformation in the literature does not exist in the proposed nonconvex stabilization criterion. The stabilization analysis for polynomial fuzzy control systems is concerned with the double fuzzy summation problem that can be treated as the copositivity problem. Therefore, the SOS-based copositive relaxation technique is applied for the proposed stabilization criterion. Since the proposed nonconvex stabilization criterion is represented in terms of bilinear SOS constraints, the path-following method is employed for solving the bilinear SOS problem. Finally, design examples are provided to demonstrate that the proposed nonconvex stabilization criterion complements the existing convex stabilization criteria.