带控制时滞广义系统的PID型迭代学习算法

PID-Type Iterative Learning Control for Singular Systems with control delay

研究了一类线性时滞广义系统的迭代学习控制问题。针对广义系统的特点,引入迭代学习控制方法,给出了线性时滞广义系统的PID型迭代学习算法。结合矩阵广义逆理论,利用λ范数和Bellman引理,并从理论上给出了算法收敛性的完整证明。研究结果表明,只要充分利用广义系统的特点,寻找合适的收敛性分析方法,便可解决控制时滞广义系统的收敛性问题,对时滞广义系统迭代学习控制问题的研究具有重要的理论意义与应用价值。

The iterative learning control problem for a class of linear singular systems with time-delay is studied. According to the characteristics of singular systems, the Proportional Integration Differential （PID） type iterative learning control algorithm of the time-delay system is given by introducing method of iterative learning control. Using k norm and Bellman Lemma combined with the generalized in- verse theory, the convergence of the algorithm is complete proved theoretically. The results show that the convergence of the linear singular with time-delay can be solved considering the characteristics of the singular system and find the right method for convergence analysis. The research in this paper has important theoretical significance and practical value to the study of iterative learning control for sin gular systems.