Qiu Qian, Su Housheng, Zeng Zhigang
IEEE Trans Cybern. 2022 Aug;52(8):7742-7752. doi: 10.1109/TCYB.2021.3050729. Epub 2022 Jul 19.
In this article, we investigate the distributed adaptive consensus problem of parabolic partial differential equation (PDE) agents by output feedback on undirected communication networks, in which two cases of no leader and leader-follower with a leader are taken into account. For the leaderless case, a novel distributed adaptive protocol, namely, the vertex-based protocol, is designed to achieve consensus by taking advantage of the relative output information of itself and its neighbors for any given undirected connected communication graph. For the case of leader-follower, a distributed continuous adaptive controller is put forward to converge the tracking error to a bounded domain by using the Lyapunov function, graph theory, and PDE theory. Furthermore, a corollary that the tracking error tends to zero by replacing the continuous controller with the discontinuous controller is given. Finally, the relevant simulation results are further demonstrated to demonstrate the theoretical results obtained.
在本文中，我们研究了抛物型偏微分方程（PDE）智能体在无向通信网络上通过输出反馈的分布式自适应一致性问题，其中考虑了无领导者和有领导者的领导者-跟随者两种情况。对于无领导者的情况，设计了一种新颖的分布式自适应协议，即基于顶点的协议，以利用自身及其邻居的相对输出信息，针对任何给定的无向连通通信图实现一致性。对于领导者-跟随者的情况，提出了一种分布式连续自适应控制器，通过使用李雅普诺夫函数、图论和偏微分方程理论，将跟踪误差收敛到一个有界域。此外，给出了一个推论，即通过用不连续控制器替换连续控制器，跟踪误差趋于零。最后，进一步展示了相关的仿真结果以证明所获得的理论结果。
