一类非线性迭代学习控制系统的鲁棒收敛性

讨论了对于一类非线性动态系统施加高阶Ｄ型迭代学习算法时构成的迭代学习控制系统的鲁棒收敛性．证明了当系统初始状态逐渐固定在靠近期望初态的某一点上时，系统控制、状态、输出会收敛到相应期望轨迹的邻域内．同时，证明了在渐近理想重复初始条件下的算法收敛性．仿真结果表明，开闭环配合的学习律是克服初态偏移的一种有效途径

Robust convergence of a class of nonlinear iterative learning control systems

The robust convergence of a class of nonlinear systems under the action of higher order D type learning algorithm is proved in this paper. It is shown that if the errors of initial conditions are asymptotically invariable,the control input,the state,and the output errors of the systems are all asymptotically bounded. Moreover,the control input,the state,and the output errors converge uniformly to zero as the initial conditions are asymptotically strictly repetitive. A numerical example is given to demonstrate the performance of the iterative learning control systems.