Construction of Adaptive Consensus Gains for Multiagent Systems with Multiplicative Noise

The leader-following consensus of linear multiagent systems with multiplicative noise and adaptive gains is investigated under the fixed directed graph. Because of multiplicative noise, the agents interacting with the leader can only obtain the inaccurate information. Firstly, this paper designs the adaptive gains of multiagent systems, which can converge to some fixed values and force the states to synchronize. Different from the mandatory gains, the adaptive gains depend on the states of agents and can be adjusted with the change of states. Secondly, it is shown that the multiagent systems without time delay can obtain mean square consensus under the adaptive gains. Moreover, in the presence of multiplicative noise and communication delay, the mean square consensus is also acquired in the same adaptive gains. Finally, the validity of the conclusion is simulated by an example.