Adaptive fixed-time containment control of uncertain underactuated underwater vehicles under dynamic event-driven mechanism

This paper presents a dynamic event-driven fixed-time design strategy for the three-dimensional containment control of underactuated underwater vehicles under a directed topology. Our main contribution is the development of a novel error transformation approach based on adaptive multi-leader estimation to address the fixed-time containment (FTC) control problem in the presence of underactuation input and unknown leaders' velocity. An adaptive FTC control law using stabilizing auxiliary variables and nonlinear filters is constructed based on event-driven conditions. The dynamic thresholds, which depend on containment errors, are presented to efficiently reduce communication resources required for implementing the FTC controller. According to Lyapunov theory, it is shown that the trajectories of the followers converge to the convex hull spanned by multiple leader signals within a fixed time while ensuring the avoidance of the Zeno phenomenon. Finally, the effectiveness of the suggested control approach is verified through simulation results.