Resilient Distributed Linear Equation Solver under Secure Lightweight Protocol

This paper proposes a resilient distributed linear equation flow with lightweight communication against asynchronous Denial-of-Service (DoS) attacks. Unlike studies that focus on synchronous attacks targeting all channels simultaneously, our work considers asynchronous attacks to simulate a more realistic scenario, where multiple attackers operate in a distributed manner on different communication channels. To address the energy consumption challenge posed by communication for high-dimensional state vectors, we propose a "compression-expansion" mechanism to facilitate lightweight communication. Specifically, the current solution state vector is compressed into a scalar for communication among neighboring agents and subsequently expanded within each subsystem for local computation. Furthermore, we introduce a set of equivalent decay rates across the attacked channels to establish sufficient conditions for system stability. A distinct feature of the proposed approach is the integration of attack characteristics into the persistent excitation (PE) condition, which fully captures the dynamic behavior of the attacked system. Finally, a numerical example is presented to validate the effectiveness and advantages of the proposed flow.