一类非线性系统的自适应模糊控制器设计及稳定性分析

Design of an Adaptive Fuzzy Controller for Nonlinear Systems and the Stability Analysis

首先建立一种动态T–S模糊子系统,用于估计非线性系统,然后设计一种稳定的参考模型,其前件与T–S模糊子系统相同.在此基础上,提出一种反馈控制器,其控制矩阵采用线性矩阵不等式(LMI)的方法进行求解,使得在数学模型已知的情况下,闭环系统渐近稳定.此外,为补偿和消除实际系统中常存在的参数不确定性和外部干扰的影响,进一步提出一种自适应模糊控制器,能够在保障系统性能的情况下,补偿参数不确定性,并去除外界干扰的影响.最后,采用李亚普诺夫合成法证明闭环系统的稳定性.仿真验证了该方法的有效性.

Some dynamic T-S fuzzy subsystems were presented to approximate a nonlinear system.The stable reference model with the same fuzzy sets as those of the T-S fuzzy subsystems rule was established.To make the states of the closed-loop system follow those of the reference modela,feedback controller was designed.The control gain can be solved by LMI approach.The closed-loop systems can be stable when the exact models are known.To compensate and eliminate the pa-rameter uncertainty and disturbance usually existing in the practical plant,an adaptive fuzzy controller was further pro-posed.It can achieve the better performancec,ompensate the parameter uncertainty and alleviate the disturbance.Finally Lyapunov constitute technique was used to prove the stability of the closed loop systems.The simulations results illustrated the effectiveness of this approach.