Constrained consensus with multiplicative noises

In this paper, we consider the constrained consensus problem of discrete multi-agent systems subject to multiplicative noises. Each agent can only receive information corrupted by noises from its neighbors. The intensities of these noises are dependent on the distance between neighbors' states. By using such inaccurate local information, a distributed control law is proposed to drive the agents to reach consensus on a given constraint set. Under some mild assumptions of the noises and the structure of network, both fixed topology case and switching topology case are analyzed. Control gains are designed for both cases to guarantee mean square constrained consensus and almost sure constrained consensus. Two numerical examples are given to illustrate the effectiveness of our results.