Robust Self-Triggered Coordination With Ternary Controllers

Abstract

This paper regards the coordination of networked systems, studied in the framework of hybrid dynamical systems. We design a coordination scheme which combines the use of ternary controllers with a self-triggered communication policy. The communication policy requires the agents to measure, at each sampling time, the difference between their states and those of their neighbors. The collected information is then used to update the control and determine the following sampling time. We show that the proposed scheme ensures finite-time convergence to a neighborhood of a consensus state: the coordination scheme does not require the agents to share a global clock, but allows them to rely on local clocks. We then study the robustness of the proposed self-triggered coordination system with respect to skews in the agents' local clocks, to delays, and to limited precision in communication. Furthermore, we present two significant variations of our scheme. First, assuming a global clock to be available, we design a time-varying controller which asymptotically drives the system to consensus. The assumption of a global clock is then discussed, and relaxed to a certain extent. Second, we adapt our framework to a communication model in which each agent polls its neighbors separately, instead of polling all of them simultaneously. This communication policy actually leads to a self-triggered "gossip" coordination system

Self-triggered rendezvous of gossiping second-order agents

“…This paper enlarges the class of systems for which the selftriggered distributed control proposed in [6] applies. In doing so, it explores a new investigation line based on the cutbalance condition of [8].…”

“…In a number of recent works [12], [18], [7], [6], [19], [5], authors have been focusing on cooperative control problems in which the agents do not exchange information continuously but rather at times that are decided based on current local measurements. These coordination strategies can be of two types: event-triggered or self-triggered coordination control.…”

“…The focus in [6] was on first-order multi-agent systems. Nevertheless, as argued in [2], [16], in the majority of coordination problems neglecting the dynamics of the systems is not possible.…”

“…Indeed, one of the difficulties that we face when going from first-order to second-order agents is that the Lyapunov-based analysis that was pursued in [6] can not be directly extended. Instead of insisting on the search for an appropriate Lyapunov function (a topic that could nevertheless be of interest for future research), we pursue here a different approach relying on the results of [8].…”

“…These coordination strategies can be of two types: event-triggered or self-triggered coordination control. The focus of this paper is on the second class of coordination control algorithms and is inspired by the socalled self-triggered gossiping algorithms of [6]. …”