On dual-rate consensus under transmission delays

TL;DR

This paper studies dual-rate consensus in multi-agent systems with fixed transmission delays, identifying conditions for convergence, and optimizing measurement sampling rates to enhance convergence speed.

Contribution

It introduces a comprehensive analysis of dual-rate consensus with delays, including conditions for convergence and an optimization framework for sampling rates.

Findings

Consensus is achieved if the communication graph is connected and the control gain is within a specific interval.

There exists an optimal sampling rate that can improve the convergence speed.

Numerical simulations verify the theoretical results.

Abstract

In this paper, we investigate the problem of dual-rate consensus under transmission delays, where the control updates happen at a faster rate than the measurements being received. We assume that the measurements are delayed by a fixed delay and show that for all delays and rates, the system reaches a consensus if and only if the communication graph of the agents is connected and the control gain is chosen in a specific interval. Based on these results we dive deeper into the convergence properties and investigate how the convergence changes when we change the rate for sending measurements. We observe that in certain cases there exists a sweet spot for choosing the sampling rate of the measurements, which can improve the convergence to the consensus point. We then formulate an optimization problem to find a sampling rate to improve the convergence speed and provide a necessary and sufficient condition for the existence of a finite optimizer of this problem. Our results are verified with numerical simulations.