Predefined-time sliding mode formation control for multiple autonomous underwater vehicles with uncertainties

In this paper, the follower-leader formation tracking control problem of multiple autonomous underwater vehicles (AUVs) with uncertainties is addressed. A predefined-time sliding-mode reaching law and a predefined-time sliding-mode surface are developed. Then, a novel predefined-time sliding-mode controller (SMC) is proposed. The newly proposed predefined-time SMC extends the recent finite-time and fixed-time schemes and exhibits the following attractive features: (i) The convergence time of finite-time SMC scheme is affected by the initial system conditions. Like the fixed-time SMC, the proposed control scheme can guarantee that the tracking error converges to zero in a finite time which is independent on the initial system conditions; (ii) Unlike the fixed-time SMC, the proposed scheme provides a new appealing advantage is that, the convergence time of proposed scheme is predefined, which means the proposed control scheme can directly achieve the desired convergence time without using the trial and error to choose control parameters. Finally, the numerical simulation demonstrates the effectiveness of the proposed method.