Resilient Distributed Control for Uncertain Nonlinear Interconnected Systems under Replay Cyber-Attacks

We address a distributed adaptive control methodology for nonlinear interconnected systems possibly affected by replay cyber-attacks. In the framework of adaptive approximation, the distributed controller and parameter estimator are designed by exploiting a backstepping approach. The stability of the attacked distributed control system is analyzed, where both the local replay attack and neighboring attack propagation effects are simultaneously considered. To quantify the resilience of the interconnected system under the action of replay attacks, we derive bounds on the duration of each cyber-attack and the resting time between two consecutive cyber-attacks. Specifically, when each attack duration is smaller than our designed upper bound, the interconnected system controlled by the distributed approximation-based controller remains asymptotically stable. Moreover, if the resting time between two consecutive attacks is larger than the proposed bound, then all signals of the control system are guaranteed to be bounded. In this article, we show that under the action of the proposed distributed adaptive controller, the interconnected system remains stable in the presence of replay attacks with both the qualitative and quantitative resilient conditions. Extensive simulation results show the effectiveness of our theoretical results.