This paper addresses the problem of containment control strategy for a fleet of follower underactuated surface vessels (USVs) for avoiding obstacles safely and efficiently if the leader USVs are well equipped with high precision sensors. Therefore, within in this framework, we present a constructive method to design totally new prescribed-time performances for formation containment control problem for multiple underactuated surface vehicles (USVs) with unavailable velocity information, uncertainties and subject to inputs and outputs constraints, under directed communication graphs. First, in order to reconstruct the unavailable velocity information as well as to estimate unknown USVs dynamics, induced by unmodeled dynamics, and environmental disturbances, a fuzzy-adaptive observer is designed for the state estimation using only global position information and local measurement of the USVs orientation angle. Next, relying on the backstepping method with anti-windup compensators, new robust output feedback distributed controllers for the follower USVs are designed. Unlike some existing results, based on the use of a speed function, the devised controllers are able to drive the USVs to a neighborhood of the convex hull formed by the leaders in a given finite time at a controllable rate of convergence that can be prescribed by the user. Furthermore, to address the containment error constraints requirement, a universal barrier function approach with a new state transformation is introduced to deal with such constraints. It is shown that all the signals are bounded by an arbitrarily positive constant after a prescribed time. The benefits of the proposed control scheme are validated through computer simulations.
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