Distributed predefined-time control for time-varying formation of multi-AUVs with input quantizers

A predefined-time tracking control is synchronized for three-dimensional time-varying formation of multiple underactuated autonomous underwater vehicles(AUVs) with the effects of hysteresis quantized input, where the upper bound of settling-time is less conservative. An innovative predefined-time tracking differentiators are constructed to estimate the differentiation of the virtual inputs, resolving the adverse effect of explosion of complexity inherent in traditional backstepping method. Then, a predefined-time time-varying formation control law is proposed in the backstepping framework. Rigorous stability analysis can prove that all signals of the closed-loop systems are uniformly ultimately bounded and the formation tracking error can be steered to an arbitrarily small neighborhood of the origin within the predefined time. Simulation results on a group of AUVs validate that the proposed control scheme is capable of ensuring the remarkable performance even under the input quantization.