Mean-Square Consensus of Second-Order Multi-agent Systems with Semi-Markov Switching for Non-periodic DoS Attacks

Denial of service (DoS) attacks can disrupt communication channels between agents, rendering them unable to cooperate to achieve consensus. The second-order multi-agent system (SMAS) as a high-dimensional MAS composed of multiple different formation models emerges as a popular MAS that has wide deployability in numerous modern applications such as auto driving, robotics and UAV flying. How to reduce the impact of DoS attacks on SMAS with semi-Markov switching (SMS) of ultra-high ability for random connections is a crucial problem encountered in various applications. Currently, most research in SMAS consensus with a switching process is based on the Markov switching (MS). No result based on SMS is known because of the increased difficulty in its analysis due to the more general distribution of SMS than MS and the higher computational complexity of SMAS than MAS due to its higher-dimensional state spaces. This paper proposes an effective consensus algorithm that adopts a dynamic event-triggering strategy to reduce the control frequency required for SMAS to achieve consensus under DoS attacks. We conduct both rigid theoretical analyses to show the performance of our algorithm and extensive simulation experiments to verify its effectiveness. Particularly, through constructing different Lyapunov functions at different stages using random techniques, we derive the sufficient conditions to attain SMAS mean-square consensus in the presence of non-periodic DoS attacks for which no result is known at present.