An SOS-Based Control Lyapunov Function Design for Polynomial Fuzzy Control of Nonlinear Systems
An SOS-Based Control Lyapunov Function Design for Polynomial Fuzzy Control of Nonlinear Systems
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DOI：
10.1109/tfuzz.2016.2578339
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发表时间：
2017-08
影响因子：
11.9
通讯作者：
Radian Furqon;Ying-Jen Chen;Motoyasu Tanaka;Kazuo Tanaka;Hua O. Wang
中科院分区：
文献类型：
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作者：
Radian Furqon;Ying-Jen Chen;Motoyasu Tanaka;Kazuo Tanaka;Hua O. Wang
针对非线性系统的多项式模糊控制问题，提出了一种基于平方和（SOS）的控制李雅普诺夫函数（CLF）设计方法。设计开始与多项式模糊模型，这是众所周知的通用逼近器完全取代（光滑）非线性系统动态。接下来，在CLF设计的框架中提供了以SOS表示的全局稳定条件，即，对于给定的非线性系统，一旦构造了CLF，应用Sontag控制律，显式地设计了具有非并行分布补偿形式的镇定控制器。此外，在相同的方式，在操作域上的半混沌稳定的条件推导出的全局稳定的条件。将全局和半全局稳定化问题转化为SOS优化问题，并将其转化为数值可行性问题。五个设计实例表明，我们提出的方法比现有的线性矩阵不等式和SOS方法的有效性。
This paper deals with a sum-of-squares (SOS)-based control Lyapunov function (CLF) design for polynomial fuzzy control of nonlinear systems. The design starts with exactly replacing (smooth) nonlinear systems dynamics with polynomial fuzzy models, which are known as universal approximators. Next, global stabilization conditions represented in terms of SOS are provided in the framework of the CLF design, i.e., a stabilizing controller with nonparallel distributed compensation form is explicitly designed by applying Sontag's control law, once a CLF for a given nonlinear system is constructed. Furthermore, semiglobal stabilization conditions on operation domains are derived in the same fashion as in the global stabilization conditions. Both global and semiglobal stabilization problems are formulated as SOS optimization problems, which reduce to numerical feasibility problems. Five design examples are given to show the effectiveness of our proposed approach over the existing linear matrix inequality and SOS approaches.