一类不确定运动系统的空间迭代学习控制
Spatial iterative learning control for a class of uncertain motion systems

本文讨论了一类在有限空间区间内重复运行的不确定运动系统的跟踪控制问题. 通过引入空间状态微分算子和空间复合能量函数, 提出了一种空间周期的自适应迭代学习控制算法. 首先利用空间状态微分算子, 将系统从时间域转化到空间域形式. 然后基于空间复合能量函数设计了控制器, 利用含限幅作用的参数自适应律逼近系统中的不确定性, 同时引入鲁棒项共同抑制非参数不确定性的影响. 通过严格的数学分析, 证明了在标准初始条件和随机有界初始误差两种情况下的跟踪误差收敛性. 最后通过列车仿真进一步验证了该算法的有效性.
In this paper, the tracking control problem for a class of uncertain motion systems which are iteratively running in the spatial domain is discussed. By introducing a spatial state differentiator operator and spatial composite energy function, a spatial period adaptive iterative learning control algorithm is proposed. First, the spatial state differentiator is utilized to transform the motion systems from the time formulation to the spatial formulation. Then, the controller is designed based on the spatial composite energy function. The system uncertainties are learned by the adapting law with projection operator, and an additional robust item is introduced to work concurrently with the learning mechanism to tackle the nonparametric uncertainties. With rigorous mathematical analysis, the convergence properties of tracking error are derived under the identical initial condition and random initial condition within a bound. Finally, a numerical example of a train tracking control is further provided to illustrate the effectiveness of the proposed algorithm.