Distributed Event-Triggered Time-Varying Formation Control Under Multiplicative Noises

This paper investigates the distributed event-triggered time-varying formation (DETTVF) control problem of linear multiagent systems (MASs) that are subject to some multiplicative measurement noises in uncertain communication settings. A static-gain DETTVF control protocol is first designed, together with a new triggering mechanism, to cope with multiplicative noises and reduce communication costs; sufficient conditions related to control gains as well as triggering functions are provided that ensure that the MAS achieves time-varying formation in the mean-square sense and the Zeno behavior is excluded. Moreover, to eliminate constraints on global information, an adaptive-gain DETTVF control protocol with multiplicative noises is constructed, which will be implemented in a fully distributed manner; and the corresponding sufficient conditions are also provided. Finally, some numerical examples are presented to verify the validity of the obtained theoretical results.