基于解析结构的模糊控制器的稳定性和一致逼近性分析

基于模糊控制的解析结构理论，设计了输入变量采用三角形、全交迭，等差间距分布的隶属函数，输出变量采用对称、均匀分布的单点隶属函数和线性控制规则的二维模糊控制器，推导了模糊控制器的解析表达式。利用Lyapunov 第二法论证了该模糊控制系统在平衡点处的局部稳定性，并证明了模糊控制器的一致逼近性。
关键词：模糊控制器；解析结构；稳定性；一致逼近性
Abstract: Based on the theory of analytical structure, a fuzzy controller with two inputs and one output is designed in this paper, whose input-membership is triangular, full-overlapped, unevenly and difference-space distribution, output-membership is symmetric, singleton and evenly distribution. With the analytical expression of fuzzy controller, it is discussed that the fuzzy control system has the same local stability as a linear PI controller at equilibrium point, and then it is proved that the fuzzy controller is universal approximation.
Key words: fuzzy controller, analytical structures, stability, universal approximation,