Fully distributed synchronization on directed graphs via self-triggered control with positive minimum inter-event times

Abstract

The fully distributed synchronization problem is studied for heterogeneous linear multi-agent systems (MASs) on a directed graph by observer-based adaptive self-triggered control schemes guaranteed positive minimum inter-event times (MIETs). An improved adaptive observer used to estimate the leader state under composite triggering mechanisms is proposed to achieve the combination of event-triggered communication and control, which can be implemented in a self-triggered fashion. A positive auxiliary function serves as the triggered condition for updating the control protocol of the observer, and the feature of this design is that inter-event times have a positive lower bound. No global information related to the communication graph is required throughout the designed paradigm. By augmenting the observer and follower dynamics, optimality is imposed for a network of augmented systems in designing the control protocol to achieve synchronization among agents. Finally, the availability of the proposed theoretical results is demonstrated by a group of two-mass–spring systems.