Constrained consensus of asynchronous discrete-time multi-agent systems with time-varying topology

•The union graph is assumed to be strongly connected over each finite interval.•An approach is proposed to transform the original network to a synchronous one.•We show that the linear part converges and the projection error vanishes over time.

In this paper, the constrained consensus problem is studied for asynchronous discrete-time multi-agent system, where each agent needs to lie in a closed convex constraint set while reaching consensus. The communication graphs are assumed to be directed, unbalanced, dynamically changing. In addition, their union graph is assumed to be strongly connected among certain intervals of finite length. To deal with the asynchronous communications among agents, the original asynchronous system is equivalently transformed to the synchronous one by adding new agents. By employing the properties of the projection on the convex sets, the distance from the states of the agents in the newly constructed system to the intersection set of all agents’ constraint sets is estimated. Based on this estimation, the original system is proven to reach consensus by showing that the linear parts of the newly constructed systems converge and the nonlinear parts vanish over time. Finally, two numerical examples are provided to show the effectiveness of the theoretical results.