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中文摘要：
针对离散T—S模糊系统的轨迹跟踪控制问题，提出了基于离散Legendre正交多项式的迭代学习算法．该方法利用离散Legendre正交多项式展开技术及其移位运算矩阵，导出了系统基于离散Legendre多项式展开的近似模型，建立了输入量与输出量之间的代数方程约束关系．在此基础上，用迭代学习的方法可修正输入量的Legendre多项式系数，所得算法可用于具有任意相对阶的离散非线性系统．仿真实例表明了该算法的有效性．
英文摘要：
An iterative learning control （ILC） algorithm based on discrete Legendre orthogonal polynomials was developed to address the trajectory tracking of discrete T - S fuzzy system. First, the method parameterized a discrete T- S fuzzy system using discrete Legendre polynomials expansion. Then, an approximated model for the system was deduced by employing the shift operational matrix of discrete Legendre polynomiasl. Based on the model, the discrete Legendre orthogonal polynomials＇ coefficients of control function were adjusted by an iterative learning law. The proposed algorithm can be applied to the discrete nonlinear systems with arbitrary relative degree. Simulation results illustrate the effectiveness of the new method.
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