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Introduction
In the past few years, the field of the cooperative control for multiple autonomous surface vehicles (ASVs) is of increasing interest to the motion control community. This is due to the fact that a group of ships can be used to complete a specific task, where it contributes greater robustness, lower cost, and better performance. Some typical applications include environmental monitoring, rescue, and reconnaissance operations.1–5 To achieve these objectives, an increasing number of studies have focused on the cooperative control of a group of ASVs.
Recently, the cooperative control problem of multiple ASVs has been studied by many researches. For instance, a design is presented for distributed maneuvering of multiple ASVs with the aid of neurodynamic optimization and fuzzy approximation in Peng et al.6 The authors in the study of Fahimi7 design a nonlinear model predictive formation control (NMPFC) law based on an underactuated model to stabilize the relative distances and orientations between the follower and the leader; in the study of Kyrkjebø et al.,8 a leader–follower (L-F) synchronization output feedback controller has been proposed for the ship replenishment problem using an nonlinear observer; in the study of Dong,9 continuous time-varying cooperative control laws are designed to perform a geometric pattern using suitable transformations while assuming that the yaw velocity is nonzero; to cope with the uncertainties of the ASV model, a robust adaptive formation control law is developed that combines neural network (NN) with dynamic surface control (DSC) technique in the study of Peng et al.;2 in the study of Shojaei,3 a L-F formation tracking controller has been proposed to force a group of ASVs to maintain the desired orientations and positions relative to one leading ship, considering the input saturation; in the study of Peng et al.,10 a robust cooperative control method has also been applied to form a desired geometric pattern with the aid of NN, backstepping (BP) method, and graph theory. A common trait in these designs is that only one leader exists in the group.
In practical applications, there might exist multiple leaders in the group, which can be called as the containment control problem.11 In this case, the control objective is containment of the followers in the convex...