Leader‐following consensus of stochastic dynamical multi‐agent systems with fixed and switching topologies under proportional‐integral protocols.

With the rapid development of swarm intelligence, consensus problem for multi‐agent systems (MASs) has attracted substantial attention. To deal with the leader‐following consensus problems in stochastic dynamical MASs with fixed and switching topologies, this article designed proportional‐integral (PI) control protocols. On the basis of algebraic graph theory and stochastic analysis techniques, by selecting appropriate Lyapunov functions, it is theoretically shown that leader‐following consensus of MASs with stochastic dynamics underlying fixed and switching topologies can be achieved in mean square, respectively. Sufficient criteria are derived for selecting the PI control gains. Finally, the theoretical results are illustrated through several numerical simulations. [ABSTRACT FROM AUTHOR]