Finite-time consensus for multi-agent systems with directed dynamically changing topologies

Due to the complexity of communication topologies, only a few works addressed the issues of finite-time convergence for multi-agent systems with directed switching topologies, whose analyses might be unclear and some assumptions seem to be a bit strong. In this study, finite-time consensus of continuous-time nonconvex-constrained multi-agent systems with directed dynamically changing topologies is addressed. Firstly, a distributed finite-time consensus algorithm is introduced for continuous-time multi-agent systems. It is proved that agents will achieve consensus in finite time as long as the graphs have a joint spanning tree. Subsequently, we consider a constrained system whose control inputs are subjected to nonconvex sets and give a distributed nonsmooth finite-time consensus algorithm. It is proved that consensus can be achieved in finite time while keeping agents' control inputs staying in the constraint sets. Furthermore, the distributed consensus algorithm is extended to the case with disturbances and the sufficient conditions are given to guarantee the achievement of consensus in finite time. Finally, numerical examples are included to demonstrate the effectiveness of theoretical conclusions.