期望轨迹可变的非线性时变系统迭代学习控制

]Iterative learning control of non-identical desired trajectories for a class of nonlinear time-varying systems

针对一类存在扰动的未知非线性时变系统,提出了一种在不同次迭代运行过程中期望轨迹可变的迭代学习控制算法.该算法首先构造含未知参数项的系统逆控制,然后利用小波级数逼近逆系统的未知非线性参数,其最佳逼近系数与系统的期望轨迹无关,最后在迭代过程中通过学习的方法修正小波逼近系数,并采用变结构技术抑制系统干扰的影响,设计了在期望轨迹变化情况下的鲁棒迭代学习控制律.算法的收敛性分析表明,随着迭代次数的增加,逼近系数与最佳系数的差异减小.针对机械臂系统的仿真表明轨迹跟踪误差逐次减小并收敛,说明了算法的有效性.

A new iterative learning control algorithm was proposed for a class of unknown nonlinear timevarying systems with exogenous disturbance, and the algorithm is applied to the case of variable desired trajectories between any two consecutive iterations. Firstly, the inverse control with unknown parameters is designed; and then a wavelet series are employed to approximate the inverse plant nonlinearities, whose ideal coefficients are irrelevant to the desired trajectories; finally, the wavelet approximation coefficients are adapted by iteratively learning, and the robust iterative learning control law is synthesized based on the variable structure technique to overcome the system uncertainty. The algorithm convergence analysis showed that the differences between actual and ideal coefficients are monotonically decreasing with the iteration. The convergence of the tracking error was shown by a simulation on a manipulator, which demonstrated the effectiveness of the algorithm.