非线性重复运动系统的双迭代优化学习控制

Double iterative optimal learning control of nonlinear repetitive motion system

本文针对一类具有非参数不确定性和输出约束的非线性系统,提出一种双迭代优化学习控制策略,将复杂的迭代学习过程简化为两个相对简单的迭代控制器.首先引入一类饱和非线性函数不仅可以满足系统的位置约束,同时能够保证系统跟踪误差收敛于给定的邻域,然后针对每次迭代初始误差设计参考轨迹自修正策略,在每个迭代周期上设置一个固定的调整时间域,根据上次迭代的输出调整下一次迭代的参考轨迹.双迭代的控制结构可以同时更新两个迭代控制器的参数,来处理系统的非参数不确定性.进一步利用Barrier复合能量函数证明双迭代控制策略的收敛性和稳定性,并给出收敛条件.最后,通过一个算例证明了该控制策略的有效性.

In this work,a double iterative optimal learning control strategy is proposed for a nonlinear systems with non-parametric uncertainties and output constraints.Firstly,a class of saturated nonlinear functions is introduced,which can not only satisfy the position constraints of the system,but also ensure that the tracking error converges to the given neighborhood.Then,a reference trajectory self-tuning strategy is designed for the initial error of each iteration.A fixed adjustment time domain is set in each iteration cycle,and the reference trajectory of the next iteration is adjusted according to the output of the last iteration.The dual iterative control structure can update the parameters of the two iterative controllers at the same time to deal with the non-parametric uncertainties of the system.Furthermore,the convergence and stability of the double iterative control strategy are proved by using the barrier composite energy function.Finally,an example is given to prove the effectiveness of the control strategy.