Adaptive fixed-time fuzzy formation control for multiple AUV systems considering time-varying tracking error constraints and asymmetric actuator saturation

In this study, the fixed-time formation control problem for multiple autonomous underwater vehicle (AUV) systems (MAUVS) subject to time-varying tracking error constraints and asymmetric actuator saturation is addressed. First, a novel formation control strategy is proposed, which utilizes some virtual leaders to transform the formation problem into a trajectory tracking problem. Then, a fuzzy logic system (FLS) is used to adaptively approximate the unknown modeling uncertainty and time-varying external disturbances. Subsequently, a smooth saturation function and a novel signal compensation mechanism are utilized to address asymmetric input saturations with respect to amplitude and rate. Furthermore, an adaptive fixed-time fuzzy control (AFTFC) strategy is proposed based on the tan-type barrier Lyapunov function (TT-BLF) to achieve precise tracking and guarantee tracking errors among the follower AUVs and the virtual leaders within the prescribed constraint range during operations. Finally, a theoretical analysis demonstrates that MAUVS can complete the formation task within a fixed time and that all the signals can be bounded. Simulations are used to illustrate the effectiveness of the proposed methodology.