Secure formation-containment control for multi-agent systems subject to denial-of-service attacks

This paper investigates the problem of secure formation-containment control under denial-of-service (DoS) attacks. It is assumed that each attack period of DoS consists of an active period and a dormant period. The jammer attacks only part or all of the links in the communication network during active periods, and supplements energy during dormancy periods without attacking the communication network. With this setting of DoS attacks, an effective distributed update rule based on the abandonment strategy is proposed. Relying on the product properties of sub-stochastic matrices, it is theoretically proven that the proposed distributed update rule can effectively ensure the realization of formation-containment control, i.e., the followers finally reach the desired formation states within the convex hull of the leaders under DoS attacks. At last, the proposed distributed update rule is confirmed to be effective through simulation examples.