Hierarchical Nash equilibrium seeking for optimal fault-tolerant formation control of networked MSVs in aggregative games

This paper investigates the optimal fault-tolerant formation control problem of networked marine surface vehicles (NMSVs) in aggregative games, where each MSV suffers from external disturbances, actuator faults and failures. The hierarchical Nash equilibrium seeking algorithm is proposed to solve this control problem, including the decentralized decision layer and the local control layer. In the decentralized decision layer, the Nash equilibrium of the aggregative game for each MSV can be estimated in a decentralized manner, by constructing the cost function based on both its individual decision and the aggregative impacts of the decision of all the other MSVs. In the control layer, the fault-tolerant local controller is designed to stabilize the positions of the networked MSVs to the desired formation based on the estimated Nash equilibrium generated from the decision layer under the influences of actuator faults and failures. Then, based on the game theory and Lyapunov argument, the sufficient conditions on the selection of the algorithm parameters are presented for guaranteeing the convergence of the seeking algorithm. Finally, the practical simulation example is provided to demonstrate the effectiveness of the presented theoretical results.