基于广义跟踪误差的一阶非线性时滞系统自适应迭代学习控制

An adaptive interative learning control of the first-order nonlinear delay system based on generalized tracking error

针对一类具有未知时变时滞的一阶非线性参数化系统,提出一种自适应迭代学习控制方案。通过利用边界层函数构造广义跟踪误差,消除了迭代学习控制初始精确定位的限制。为避免因引入边界层函数而产生的奇异性问题,引入双曲正切函数,并根据双曲正切函数的性质,通过构造Lyapunov-krasovskii型复合能量函数证明了所有信号的有界性和跟踪误差的收敛性。仿真算例验证了所提出方案的有效性。

An adaptive iterative learning control （AILC） scheme was proposed for a class of first-order nonlinear param- eterized systems with unknown time-varying delays. By utilizing boundary layer function to construct generalized track- ing error, the assumption of initial condition for iterative learning control （ILC） was removed. The possible singularity problem arising from boundary layer function was avoided by introducing the hyperbolic tangent function. According to the characteristic of hyperbolic tangent function, the boundedness of all signals and the convergence of tracking errors were proved in two cases by constructing Lyapuonv-Krasovskii-Like composite energy function （CEF）. Finally a simu- lation example demonstrates the effectiveness of the control scheme.