Co-Design of Fault Detection and Consensus Control Protocol for Multi-Agent Systems Under Hidden DoS Attack

This article is concerned with the co-design of fault detection and consensus control protocol for a class of multi-agent systems (MASs) subject to Denial-of-Service attack, where the attack behavior is hidden to the defender as the adversary may launch the attack with different durations but the defender may not know the real situation at each time instant. Due to the complicated attack behavior, a hidden semi-Markov process is introduced where only the observed attack modes emitted by the inaccessible ones are available. The probability density functions of sojourn time and the semi-Markov kernel are adopted to help analyze the combined fault detection and consensus control system. Sufficient conditions on the <inline-formula> <tex-math notation="LaTeX">$\sigma $ </tex-math></inline-formula>-error mean square stability of MASs with mixed <inline-formula> <tex-math notation="LaTeX">${H_\infty }/{H_ {-} }$ </tex-math></inline-formula> performance are established by using a set of Lyapunov functions that depend on the hidden and the observed attack modes. Moreover, the gain matrices of controller and detector are obtained by solving an optimization problem with some matrix inequality constraints. Finally, the simulation of autonomous unmanned underwater vehicles is used to show the effectiveness of the proposed results.