Privacy-preserving secure control for nonlinear multi-agent systems under hybrid attacks

In the paper, the privacy-preserving secure bipartite consensus is discussed for nonlinear multi-agent systems within the framework of periodic event-triggered control, where agents suffer from replay attacks and deception attacks. Firstly, draw support from the gain control technique, a compensator-based secure control strategy is designed to effectively resist replay attacks, moreover, a periodic event-triggered mechanism is employed to update the control strategy. Then, to compensate for the effect of hybrid attacks, a novel auxiliary system and an extended observer are constructed. Meanwhile, a time-varying mask function is introduced into the output signal and compensator/observer to realize privacy protection of the initial information. Further, the secure bipartite consensus issue is successfully solved by combining secure control strategies with Lyapunov function method. Particularly, the proposed control strategies are capable of ensuring intermittent communication, removing sampling period limitation and naturally avoiding Zeno behaviour. Finally, the effectiveness of the main results is confirmed via simulation examples.