基于向量图分析的一种迭代学习控制算法及其鲁棒性

Iterative learning control algorithm based on vector plots analysis and its robustness

为了增强迭代学习控制的鲁棒性,加快学习过程的收敛速度,而又不过多地依赖于系统内部信息,本文基于向量图分析思路,利用输入空间的向量构造三角形修正结构,得到了一种新的迭代学习控制算法．该算法根据跟踪误差的大小,调节输入控制量在三角形的一条边上滑动,在跟踪误差较大时,算法能找到控制期望的大致位置并加速收敛,在跟踪误差较小时,能将控制量稳定在其期望的很小邻域内,理论上证明了该邻域直径大小为跟踪误差的二阶无穷小．数值仿真结果说明了它的有效性和优越性．

Based on vector plot analysis method, a new ILC（iterative learning control） algorithm is PrOPosed by constructing triangle amending structure in the input vector space. The algorithm can enhance the ILC robustness and accelerate the convergence of learning process by adjusting the control input to slide along an edge of the triangle, based on the norm of tracking error. When the tracking error is comparatively large, the algorithm can locate an appropriate position for control input expectation and then accelerate the convergence. If the tracking error is comparatively small, the algorithm can restrict the control input in a very small neighborhood of its expectation with a diameter being the second order infinitesimal of tracking error. Numerical simulations show its effectiveness and advantage.