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

ABSTRACT 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.