一类离散模糊系统的迭代学习控制算法

Iterative Learning Control Algorithm for a Kind of Discrete Fuzzy System

针对离散T-S模糊系统的终端控制问题,提出了一种基于离散Legendre正交多项式的迭代学习算法。该算法把待求控制量表示为离散Legendre正交多项式的线性组合,将求控制量问题转化为求离散Legendre正交多项式系数问题。在此基础上,用迭代学习的方式来修正控制量的离散Legendre系数,并运用不确定离散系统的H∞设计方法求解学习增益矩阵。最后以机器人为例进行仿真,仿真结果表明了所提算法能实现工业机器人的精确定位。

An iterative learning control algorithm based on discrete Legendre orthogonal polynomials is developed to address the terminal control problem of discrete T-S fuzzy systems. The method parameterizes the control function by discrete Legendre orthogonal polynomials. Then, the control problem becomes one of finding the discrete Legendre polynomials coefficients of control function. The discrete Legendre polynomial coefficients of control function are adjusted by an iterative learning law, and the learning gain matrix is designed via H∞ control of uncertain discrete systems. The simulation results of the precise positioning control of an industry robot show the effectiveness of the proposed scheme.