IEEE Trans Cybern. 2022 Sep;52(9):9736-9745. doi: 10.1109/TCYB.2021.3052775. Epub 2022 Aug 18.
This article addresses a consensus problem of second-order discrete-time agents in general directed networks with nonuniform position constraints, switching topologies, and communication delays. A projection operation is performed to ensure the agents stay in some given convex sets, and a distributed algorithm is employed for the consensus achievement of all agents. The analysis approach is to use a linear transformation to convert the original system into an equivalent system and then merge the nonlinear error term into the convex null of the agents' states so as to prove the consensus convergence of the system based on the properties of the non-negative matrices. It is shown that all agents finally converge to a consensus point while their positions stay in the corresponding constraint sets as long as the union of the communication graphs among each certain time interval is strongly connected even when the communication delays are considered. Finally, numerical simulation examples are given to show the theoretical results.
本文针对一般有向网络中二阶离散时间智能体的共识问题进行了研究，这些智能体具有非均匀位置约束、切换拓扑和通信延迟。通过投影操作来确保智能体保持在某些给定的凸集中，并采用分布式算法来实现所有智能体的共识。分析方法是使用线性变换将原始系统转换为等效系统，然后将非线性误差项合并到智能体状态的凸零集中，从而基于非负矩阵的性质证明系统的共识收敛性。结果表明，只要在每个给定时间间隔内的通信图的并集是强连通的，即使考虑了通信延迟，所有智能体最终也将收敛到一个共识点，同时它们的位置保持在相应的约束集中。最后，通过数值仿真示例验证了理论结果。
