Consensus of Stochastic Dynamical Multiagent Systems in Directed Networks via PI Protocols.

With the rapid development of swarm intelligence, the consensus of multiagent systems (MASs) has attracted substantial attention due to its broad range of applications in the practical world. Inspired by the considerable gap between control theory and engineering practices, this article is aimed at addressing the mean square consensus problems for stochastic dynamical nonlinear MASs in directed networks by designing proportional-integral (PI) protocols. In light of the general algebraic connectivity, consensus underlying PI protocols for a directed strongly connected network is investigated, and due to the M -matrix approaches, consensus with PI protocols for a directed network containing a spanning tree is studied. By constructing appropriate Lyapunov functions, combining with the stochastic analysis technique and LaSalle's invariant principles, some sufficient conditions are derived under which the stochastic dynamical MASs realize consensus in mean square. Numerical simulations are finally presented to illustrate the validity of the main results.