Resilient Containment Under Time-Varying Networks With Relaxed Graph Robustness

This paper investigates the resilient containment control problem for leader-follower MASs in time-invariant and time-varying digraphs. Despite the existence of some noncooperative agents in the network, the cooperative followers are expected to converge to the safety interval constructed by the cooperative leaders. Specifically, to defend against malicious attacks and achieve the objective of resilient containment, each cooperative follower disregards the most suspicious values in its in-neighbor set and utilizes the retained values for state update. However, resilient containment is usually achieved at the cost of stringent graph conditions. In our work, with the introduction of a novel graph-theoretic property, namely the strongly trusted robustness, a small subset of agents is set as trusted nodes and the graph robustness requirement for resilient containment is relaxed. The constraint on the minimum number of leaders is also relaxed through this operation. Moreover, this novel property is extended to time-varying networks, for which the notion of jointly and strongly trusted robustness is proposed. This notion further relaxes the requirement that the digraph should satisfy certain graph conditions at each time step, thus reducing the communication burden. Numerical simulations are provided to validate the theoretical results.