This paper investigates the iterative learning control for continuous-time multi-agent formation systems to realize the desired formation, where the trial lengths could be randomly varying at each iteration. To be specific, an ILC (iterative learning control) protocol with an iteratively moving average operator is established for multiple nonlinear agents with switching topologies, where a modified formation tracking error is defined and the control information from several previous trials is used to deal with the varying trail lengths. The convergence conditions are derived by using a redefied λ-norm with mathematical expectation for both the zero and varying initial shift cases, which ensure that the formation performance can still be maintained during the whole motion process when the actual trial length is greater or less than the desired one. In the end, simulation results illustrate the effectiveness of the proposed method.

本文研究了连续时间多智能体编队系统的迭代学习控制，以实现所需的编队，在这种情况下，每次迭代的试验长度可以随机变化。具体来说，针对具有切换拓扑的多个非线性主体，建立了具有迭代移动平均算子的ILC（迭代学习控制）协议，其中定义了修正的编队跟踪误差，并且使用了来自先前几次试验的控制信息来处理不同的步长。通过使用重新定义的λ得出收敛条件-对零和变化的初始班次情况都具有数学期望的范数，这可以确保当实际试验长度大于或小于所需试验长度时，仍可以在整个运动过程中保持地层性能。最后，仿真结果说明了该方法的有效性。