Exact compensation of communication delays for discrete-time heterogeneous multi-agent linear systems with applications to SIR epidemic model

TL;DR

This paper presents a prediction-based method to exactly compensate for communication delays in discrete-time heterogeneous multi-agent systems, ensuring output synchronization and demonstrating significant benefits in epidemic modeling.

Contribution

It introduces a novel prediction-based framework with distributed predictors and controllers to eliminate delays in multi-agent systems, validated through theoretical analysis and practical applications.

Findings

Delay compensation achieves exact synchronization after finite steps

Method reduces peak infections by over 200,000 in a large-scale epidemic model

Validated through numerical simulations and Koopman operator analysis

Abstract

This paper investigates the output synchronization problem for discrete-time heterogeneous multi-agent systems (MASs) subject to distinct communication delays. The presence of such delays prevents the instantaneous delivery of information from neighboring nodes, thereby severely degrading the performance of standard distributed control schemes. To overcome this, we propose a prediction-based framework for exact delay compensation. Specifically, we introduce predictors combined with a mechanism of distributed predictors, which enables the recursive reconstruction of future state information across the communication network. Building upon these predictors, we construct prediction-based distributed observers and formulate both prediction-based distributed state-feedback and dynamic output-feedback controllers. Theoretical analysis confirms that the proposed strategy eliminates the impact of delays after a finite number of steps, ensuring output synchronization. The effectiveness of the methods is validated through a numerical example and a Koopman operator-based linear Susceptible-Infected-Recovered (SIR) epidemic model. Notably, for a population of 4 million, the proposed delay compensation strategy achieves a reduction of over 200,000 infected individuals at the peak, underscoring its potential significance in epidemic mitigation.