线性广义系统P型迭代学习控制离散频域收敛性

摘要

针对一类线性广义系统,研究其P型迭代学习控制在离散频域中的收敛性态.在离散频域中,对广义系统进行奇异值分解后,利用傅里叶级数系数的性质和离散的Parseval能量等式,推演了一阶P型迭代学习控制律跟踪误差的离散能量频谱的递归关系和特性,获得了学习控制律收敛的充分条件;讨论了二阶P型迭代学习控制律的收敛条件.仿真实验验证了理论的正确性和学习律的有效性.%For a class of linear singular systems, this paper studies on the convergence characteristics of P-type iterative learning control in discrete frequency domain. Firstly, in the discrete frequency domain, the singular value decomposi-tion of the singular systems is carried out. Using the properties of Fourier series and the discrete frequency Parseval's en-ergy equality, the discrete energy spectrum recursive relation and character of the tracking errors are deduced. And the suf-ficient condition for monotone convergence of the first-order P-type iterative learning control law is obtained. Then, the convergence of the second-order learning law is discussed. The simulation experiment validates the correctness of the the-ory and the validity of this algorithm.