Distributed finite-time fault-tolerant containment control for multiple ocean Bottom Flying node systems with error constraints

The Ocean Bottom Flying Node (OBFN) belongs to Autonomous Underwater Vehicle (AUV) designed for detecting seabed resources. When considering model uncertainties, external disturbances, and thruster faults, by applying the nonsingular fast terminal sliding-mode technique, a distributed finite-time fault-tolerant error constraint containment control method for multiple OBFN systems is proposed under directed communication topology. Besides, only a part of follower OBFNs can get the information of leader OBFNs. First, the error constraint strategy is considered to improve the system performance while the defined error variable of containment control was converted into a suitable form. Then, by choosing the appropriate nonsingular fast terminal sliding surface, the systems states can reach the sliding surface in finite time such that the follower OBFNs could converge to the convex hull formed by the leader OBFNs in finite time. Neural Network (NN) is employed to estimate and compensate the general disturbances consisting of model uncertainties, external disturbances, and thruster faults. An adaptive law is designed to compensate the upper bound of the estimation errors. The finite-time stability of the systems and the boundedness of containment errors are proved by utilizing graph theory, finite time theory, and Lyapunov technique. Numerical simulations under different types of thruster faults are given to show the effectiveness of the proposed methods.