基于初态学习的遗忘因子迭代学习控制研究

Iterative Learning Control with Forgetting Factor Based on Initial State Learning

在带遗忘因子的迭代学习控制(iterative learning control,ILC)理论收敛性研究中,系统收敛误差将收敛至零的某一邻域内.为具体分析并抑制遗忘因子取值对系统收敛误差的影响,提出了一种由相邻控制向量组成的带遗忘因子初态学习开环D型ILC算法,并利用算子谱理论对算法收敛性进行了严格证明.在此基础上,分析了遗忘因子对系统收敛误差的具体影响.该算法消除了系统初始控制向量对收敛误差的影响,扩大了系统初始控制向量取值范围;有效利用多个系统信息,一定程度上克服了遗忘因子对系统输出误差的影响.仿真实验验证了该算法的有效性.

In the convergence of iterative learning control with the forgetting factor, the common conclusion is that output error converges to the neighborhood of zero. For analysis and to reduce the impact of the forgetting factor on system convergence error, we propose an open-loop D-type iterative learning control algorithm that incorporates the forgetting factor and the initial learning, which consist of adjacent control vectors. We then demonstrate its convergence with operator spectrum theory. On this basis, we analyze the impact of the forgetting factor on system convergence error. The proposed algorithm can eliminate the influence and expand the value range of a system＇s initial control vector. Multiple system information is used to effectively overcome to some extent the influence of the forgetting factor on the convergence error. The simulation results verify the validity of the proposed algorithm.