Synchronization of Lagrangian networks with a directed graph via aperiodically intermittent pinning control

Synchronization of Lagrangian networks with a directed graph via aperiodically intermittent pinning control was developed in this paper. By applying linear feedback injections to a fraction of agents at discontinuous time, all the agents described by Lagrangian systems can be regulated to follow a synchronization state. Based on aperiodically intermittent pinning control, some simple yet general synchronization criteria are derived. Compared with some existing works on control problem of Lagrangian networks, the distinctive advantages of the proposed controllers here include: (i) discontinuous-time control input; (ii) only a fraction of agents to be controlled; (iii) independence on the knowledge of system models. As a direct application, the results are illustrated by a Lagrangian network composing of six two-link revolute manipulators. Subsequently, numerical simulations with different kinds of pinning schemes demonstrate the effectiveness of the proposed control strategy.