Dynamic Event-triggered Control in Discrete-time Multi-agent Consensus over Directed Topologies

Abstract

In this paper, we study the problem of multi-agent consensus in networks of discrete-time integrator agents with directed topologies. With the aim to reduce the frequency of interaction among agents for saving energy expenses, we develop three triggering-based protocols for strongly connected agent networks. Our common strategy is to use triggering protocols that take account of the state values received from neighbors in determining the event times. The first two protocols are event-triggering type, where the thresholds are state dependent so that when the agents are far from consensus, the events take place less frequently. The two protocols are called static and dynamic depending on the use of auxiliary variables in determining the thresholds. The third protocol is self-triggering type, where at each triggering time, an agent computes the time for its next transmission, which is communicated to its neighbors together with its state data. For these protocols, we present Lyapunov-based design methods, and demonstrate their efficacy through numerical examples.