Time-Varying Constrained Consensus of Asynchronous Discrete-Time Multi-agent System

This paper discusses the time-varying constrained consensus problem of asynchronous discrete-time multi-agent system that all agents are constrained in non-empty closed convex sets changing over time. We introduce an enlarged multi-agent system to deal with asynchronous communication where the communication graphs are assumed to be directed, unbalanced and dynamically changing, and their union graph is strongly connected. Based on the properties of projection operator, the original system is proven to reach consensus in the case that the constraint sets have nonempty intersection. For the case that constraint sets have limit set, the constrained consensus can be reached based on geometric properties of constraint sets. Finally, we give two numerical examples to show the effectiveness and correctness of the method.