Time‐Varying Formation‐Containment Control of Underactuated Surface Vehicles: A Matrix‐Weighted Consensus Approach

ABSTRACT This paper studies the time‐varying formation‐containment control problem for multiple underactuated unmanned surface vehicles (USVs). A novel matrix‐weighted consensus control strategy is proposed for multiple underactuated USVs to achieve time‐varying formation containment. The area of the convex hull formed by the group leaders can scale down or up, which relies only on the motions of the first leader. Moreover, a series of dynamic matrix‐value weights enables the group leaders to achieve a time‐varying formation shape, and all followers ultimately converge into the convex hull formed by the group leaders. The proposed formation‐containment control laws can be implementable in an arbitrarily local coordinate frame only using relative position measurements, which are favorable for many practical applications. Barrier Lyapunov functions and adaptive backstepping procedure are incorporated into the formation‐containment controller design such that formation‐containment errors can converge to a small neighborhood of zero in a prescribed time, where the convergence time can be specified in advance by the user. Simulation studies are performed to show the performance of the proposed formation‐containment control laws.