Sliding mode control for coordination in multi-agent systems with directed communication graphs

This paper focuses on the control of a team of agents designated either as leaders or followers and exchanging information over a directed communication network. The goal is to drive each follower to a target position that depends on its neighbors. To this purpose, we propose a decentralized control scheme based on sliding-mode techniques and study the position error propagation within the network using the notion of Input-to-State Stability (ISS). In particular, we derive sufficient conditions on the control parameters for guaranteeing that the error dynamics is ISS with respect to the leaders´ velocities. Moreover, we show that, under suitable assumptions, the sliding-mode part of the control law is capable of steering the position errors to zero in finite time. The theoretical results are backed up by numerical simulations.