Robust predefined fixed-time formation-containment control for multiple unmanned surface vehicles with input saturation

Abstract

The predefined fixed-time formation-containment (PFTFC) control problem for unmanned surface vehicles (USVs) under unknown disturbances and input saturation is investigated, where the leaders form a formation configuration and the followers converge to the predefined convex hull formed by the leaders within a fixed time. To address this issue, a two-layer framework is introduced, decomposing the problem into trajectory estimation and trajectory tracking components. In the first layer, a novel fixed-time trajectory estimator is proposed for the leaders and the followers to estimate the desired trajectory. In the second layer, to eliminate the effects of unknown disturbances and input saturation, a fixed-time disturbance observer and an auxiliary system are proposed. Then combining fixed-time Lyapunov stability and integral sliding mode control, fixed-time control laws are proposed for both the leaders and the followers, respectively. Finally, a numerical simulation example is presented to illustrate the effectiveness of the method introduced in this paper.