存在未知时滞非线性系统的迭代变区间预测迭代学习控制

Predictive iterative learning control for nonlinear systems with unknown time delay and iteratively varying trial lengths

本文针对机理模型未知的非线性非仿射多入多出(MIMO)离散时间系统,研究了系统同时存在未知时滞和迭代变化运行时间区间的预测迭代学习控制(PILC)问题.首先利用未知时滞的上下界信息建立了一种新型的动态线性化(DL)模型,理论分析表明该模型能够等价描述本文所考虑的存在未知时滞的未知非线性系统.同时,设计一种新的数据补偿机制用以处理由于系统运行时间区间迭代变化而引起的数据丢失问题.基于所建立的DL模型和数据补偿机制,设计了能够同时处理未知时滞和迭代变化运行时间区间的预测迭代学习控制方法.通过严格的理论分析同时给出了建模误差和跟踪控制误差的收敛性质.最后,通过仿真进一步验证了所提方法的有效性.

This paper investigates the predictive iterative learning control(PILC)problem for a class of nonlinear and nonaffine multiple-input multiple-output(MIMO)discrete-time systems with unknown system mechanism model and under both unknown time delay and iteratively varying trial lengths.First,a new dynamic linearization(DL)model is developed by virtue of the upper and lower bound information of the unknown time delay,and the theoretical analysis shows that the constructed model can equivalently describe the unknown nonlinear system with unknown time delay considered in this paper.At the same time,a new data compensation mechanism is introduced to deal with the problem of data loss caused by the varying trial lengths at each iteration of the system.Based on the developed DL model and data compensation mechanism,a predictive iterative learning control method is designed that can handle both the unknown time delay and the iteratively varying trial lengths.The convergence properties of both the modeling error and the tracking control error are given through rigorous theoretical analysis.Simulation results further verify the effectiveness of the proposed method.