Secure and Privacy-Preserving Formation Control for Networked Marine Surface Vehicles with Sampled-Data Interactions

This paper proposes a cyber-physical framework consisting of the secure and privacy-preserving distributed impulsive-based estimator (DIE) algorithm and the local nonlinear control (LNC) algorithm to solve the cooperative formation tracking problem of networked marine surface vehicles (NMSVs) with sampled-data interactions and external disturbances. In the cyber layer, a secure and privacy-preserving information exchange scheme is proposed based on the Paillier cryptosystem such that the states of the virtual leader can be estimated in a secure and privacy-preserving way. In the physical layer, the LNC algorithm is designed with the utilization of the estimators in the cyber layer to achieve the formation tracking for the NMSVs with disturbance rejection ability. Sufficient conditions for guaranteeing the convergence and the stability of the closed-loop system are derived based on systematic analysis. Finally, numerical simulations are performed on Cyber-Ships II to verify the effectiveness of the main results.