初态学习下非仿射非线性系统的迭代学习控制

Iterative learning control with initial state learning for non-affine nonlinear systems

针对非仿射非线性系统,提出初态学习律,并给出关于初态学习的收敛性充分条件.初态学习使得系统在每次迭代开始时,不严格要求其初态与期望初态重合或者固定于某一具体位置上,而是允许存在一定的定位偏差.利用压缩映射分析方法,推导出在初态学习下的开环学习律、闭环学习律、开闭环学习律的收敛性充分条件,证明了迭代学习控制系统关于初始定位误差的鲁棒收敛性.依据此收敛性条件,可确定输入学习律及初态学习律的学习增益.理论分析与数值仿真表明初态学习下迭代学习算法的有效性.

In this paper, an initial state learning principle is proposed for non-affine nolinear system and the sufficient condition for convergence is put forward. The learning pirnciple will not fix the initial cndition on the expected condition or fix the initial condition on the speciific condition at the beginning of each iteration. A certain degree of orientation bias in the initial conditon is allowed. Using the contraction mapping method, the sufficient conditions for the convergence in the state of open-loop learning, closed-loop learning, and open＇closed-loop learning in the proposed learning algorithms are derived. The robust convergence of initial positioning error in iterative learning control system is proved. Based on this convergence condition, the learning gain of initial learning principle and input learning principle can be determined. The theoretical analysis and numerical simulation show that the proposed learning algorithms is effective.