Simultaneous Arrival to Origin Consensus of First-order Multi-agent Systems*

In this paper, simultaneous arrival to origin (SATO) consensus problem of first-order multi-agent systems is investigated. The goal of this paper is to make the system achieve consensus simultaneously by designing a control protocol based on local information. In order to realize this objective, local variables with time-varying gains are introduced first. Then a class of feedback control protocols combined the norm-normalized(NN) sign functions with the local variables are designed. It is proved that all the errors will reach origin simultaneously. And the the multi-agent systems can achieve consensus at the same time. A simulation example is used to demonstrate the effectiveness of the designed control laws.