基于T-S模型的非线性系统的迭代学习控制

Iterative Learning Control for Nonlinear System Based on T-S Model

针对T-S模糊系统的轨迹跟踪控制问题,提出了基于正交多项式的迭代学习算法。该方法首先推导了T-S模糊全局系统的等价系统,然后利用正交多项式级数展开技术和其积分运算矩阵,将等价系统的微分方程转化为代数方程。在此基础上,用迭代学习的方式来修正输入量的正交多项式系数。所得算法对于具有任意相对阶的非线性系统,可用输出误差信号本身来构造学习律。仿真实例表明了新算法的有效性。

An iterative learning control （ILC） algorithm based on orthogonal polynomials was developed to address the trajectory tracking of T-S fuzzy systems. First, the method derived equivalence system of T-S fuzzy system. Then, the differential equations of equivalence system were reduced to a set of linear algebraic equations by employing orthogonal polynomials expansion and the operational matrix of integration of orthogonal polynomials. The orthogonal polynomials’ coefficients of control function were adjusted by an iterative learning law. The proposed algorithm could only use the error signals to update the control input for nonlinear system with arbitrary relative degree. Simulation results demonstrate the effectiveness of the new method.