Robust self-triggered coordination with ternary controllers

TL;DR

This paper introduces a robust self-triggered coordination scheme for networked systems using ternary controllers, ensuring finite-time convergence and robustness against clock skews, delays, and communication limitations.

Contribution

It presents a novel hybrid dynamical system framework combining ternary controllers with self-triggered communication, including variants for asymptotic consensus and gossip-based communication.

Findings

Ensures finite-time convergence to a neighborhood of consensus.

Demonstrates robustness to clock skews, delays, and communication errors.

Introduces variants for asymptotic consensus and gossip communication.

Abstract

This paper regards coordination of networked systems, which is 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 collect, at each sampling time, relative measurements of their neighbors' states: the collected information is then used to update the control and determine the following sampling time. We prove that the proposed scheme ensures finite-time convergence to a neighborhood of a consensus state. 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, we design a time-varying controller which asymptotically drives the system to consensus. Second, we adapt our framework to a communication model in which an agent does not poll all its neighbors simultaneously, but single neighbors instead. This communication policy actually leads to a self-triggered "gossip" coordination system.