Stochastic Consensus for Heterogeneous Multi-agent Networks With Constraints and Communication Noises

The mean-square consensus of the discrete-time heterogeneous multi-agent systems (HMASs) with convex position constraints, nonconvex velocity constraints and communication noises is reported in this paper, where the dynamics of HMASs are composed of first-order or second-order difference equations, and the noises are assumed to be martingale difference sequences. Firstly, a new algorithm is designed based on the information from neighbor agents with noises, and the original system is changed into an equivalent one by introducing a coordinate transformation. Secondly, when the communication graph is joint strongly connected, it is proved that mean-square consensus can be achieved by the properties of stochastic matrix, projection operator and martingale, and the position and velocity states of agents stay at the corresponding constraint sets. Specially, the situations of a network containing only first-order agents or second-order agents are considered, respectively. Finally, the correctness of the theoretical results is verified by numerical simulations.