一类非线性系统的初态迭代学习控制

针对一类非线性系统，提出了具有初态学习的开闭环PD型迭代学习算法，并给出了该算法的收敛充分条件。依据此收敛条件，可确定初态学习律和输入学习律的学习增益，而不必依赖系统的结构和参数，从而放宽了对初始定位的要求。初态学习允许在每次迭代开始时，其初态与期望初态有一定的定位误差，并允许初态在收敛条件范围内任意设置。利用压缩映射分析方法，证明了系统在任意初态下经过几次迭代后，实际输出能完全跟踪上期望轨迹。最后，通过仿真实例验证了所提算法的有效性和可行性。

Iterative Learning Control with Initial State Learning for a Class of Nonlinear System

In this paper, fora class of nonli-near systerr~, an open-closed-loop PD-type iterative learn- ing principle with initial state learning is proposed and the sufficient condition for convergence is put for- warded. Based on this convergence condition, without depending on the system structure and parame- ters, the learning gains of initial state learning law and input learning law can be determined to relax the requirement on initial position. The initial state learning principle allows a certain degree of orientation bias between actual initial state and desired initial state at the beginning of iteration, and the actual ini- tial state can be set arbitrarily in the convergence condition. Using the contraction mapping method, it is proved that the output of the system with an arbitrary initial state can track the expected trajectory com- pletely after several iterations. Finally, the simulation results testify the proposed algorithm is effective and feasible.