Bounded neural adaptive formation control of multiple underactuated AUVs under uncertain dynamics

This paper studies the leader-following formation control problem of multiple underactuated autonomous underwater vehicles (AUVs) under uncertain dynamics and limited control torques. A multi-layer neural network-based estimation model is designed to handle the unknown follower dynamics. The backstepping approach, a neural estimation model, as well as a saturation function, are employed to propose a bounded formation control law. Then, a Lyapunov-based stability analysis ensures a maximum bound for all the closed-loop system variables and guarantees that the formation errors between vehicles ultimately converge to a bounded compact set. The outstanding properties of the designed controller are highlighted as follows. First, only the leader position and given formation are required without any leader velocity information requirement. Second, update laws of the neural network weight are extracted using the estimation errors instead of tracking ones, which can effectively enhance the transient characteristics of the control system. Third, the control torques are bounded within predefined bounds. At the end, extensive simulations are given for a number of AUVs to verify the efficiency of the presented formation control scheme.