Distributed constrained consensus for discrete multi-agent systems with additive noises

In this paper, we investigate the constrained consensus problem for discrete multi-agent systems subject to additive noises. Each agent can only receive relative state measurements corrupted by noises from its neighbours. Two control protocols are designed under some mild assumptions of the noises and the structure of the network. The first protocol is designed with constant control gain, and the constrained consensus error bound is obtained. Asymptotic constrained consensus can be further achieved under the second control protocol in which case time-varying gains are adopted. Finally, two numerical examples are given to illustrate the effectiveness of our results.