Optimal Consensus of MAS via Minimal Communication Links

This paper proposes a decentralized design approach of optimal consensus protocols of the multi-agent system (MAS) via the directed-spanning-tree (DST)-based linear transformation. The protocol is designed by using DST-based minimal communication links. Firstly, the optimal consensus problem of MASs is transformed into the optimal control problem by constructing the linear transformation based on a DST of the communication topology. Secondly, a new distributed protocol is designed by using only the neighbor information on the DST and the optimal control gain is obtained by using the linear matrix inequality (LMI), which is a completely decentralized design method. Finally, some examples are given to verify the results.