Consensus of multi-agent systems under variable denial-of-service attacks: Noise-based event-triggered protocols

This paper unveils the consensus of multi-agent systems (MSs) with noise under variable denial-of-service attacks (VDoSA). Instead of the current continuous observation noise, a noise-based dynamic event-triggered protocol (NDETP) is raised to assure the consensus. It is worth emphasizing that we focus on almost sure consensus, that is, noise plays a constructive role in achieving consensus, which protests about the present results regarding stochastic MSs with event-triggered strategy. Owing to the distinctiveness of the problem, a novel comparison method integrating Lyapunov method are adopted since directly using the Lyapunov method is no longer applicable. By analyzing the convergence of the solution in small order moments for the system with continuous-time consensus protocol, an almost sure consensus criterion of MSs is derived directly that removes the prerequisite of mean square consensus. The criterion is closely associated with topological structure, attack successful probability, average attacks rate, and noise magnitude. Based on the established consensus criterion, an algorithm is given to settle the solutions of related parameters in event-triggering mechanisms while ensuring the consensus. Eventually, the theoretical results are used to investigate a class of robot arms system with a numerical example being shown.