离散时变多智能体系统有限时间一致性迭代学习控制

针对一类离散时变多智能体系统,通过引入虚拟领导者产生期望轨迹的方法,将虚拟领导者和所有智能体组成固定的拓扑结构,在此基础上,提出一种离散时间迭代学习控制算法.该算法对多智能体系统中的每个智能体都设计一个控制器,各控制器都是利用上一次迭代时,该智能体与虚拟领导者之间的跟踪误差和该智能体与相邻智能体之间的跟踪误差,通过拓扑结构中通信权值的组合不断修正上一次的控制律,从而获得理想控制律.同时,基于范数理论严格证明所提出算法的收敛性,并给出算法在$\lambda$-范数意义下的收敛条件.该算法能够使离散时变多智能体的输出随着迭代次数的增加在有限时间区间内完全跟踪期望轨迹.理论分析和仿真结果都表明了所提出算法的有效性.

Finite-time consensus iterative learning control of discrete time-varying multi-agent systems

For a class of discrete time-varying multi-agent systems, a topology is made up of virtual leaders and all agents, and a kind of discrete time iterative learning control algorithm is proposed based on the topological structure by introducing a virtual leader to generate the expected trajectory. The algorithm uses the tracking error between each agent and the virtual leader and neighbor during the last iteration, to revise successively the last control law through the combination of the communication weights in the topological structure, and to get the ideal control law. And this paper proves the convergence of the proposed algorithm based on the norm theory, and gives the convergence condition in the sense of $\lambda$-norm. The algorithm can make the output of the discrete time-varying multi-agent completely track the desired trajectory in the finite time interval with the increase of the number of iterations. Both theoretical and simulation results show the effectiveness of the proposed algorithm.