Fast Fixed-Time Output Multi-Formation Tracking of Networked Autonomous Surface Vehicles: A Mathematical Induction Method

In this paper, we aim to exploit an effective way to solve the output multi-formation tracking problem of the networked autonomous surface vehicles (ASVs) in a fast fixed time manner. Specifically, addressing the output multi-formation tracking problem implies that 1) the networked ASVs are divided into multiple interconnected subnetworks with respect to multiple targets; 2) for each subnetwork, the outputs of the networked ASVs form a desired geometric formation with exchanging the local interactions. Besides, solving the fast fixed-time tracking problem in this paper implies that 1) the convergence time is independent of the initial conditions; 2) the system states are forced to reach the employed nonsingular fixed-time sliding surface in a prescribed time, which thus called fast fixed-time control. Then, based on a time-related function and a nonsingular fixed-time sliding surface, a hierarchical fast fixed-time control algorithm is proposed to solve the aforementioned problem within a fast fixed time being independent of the initial conditions. Furthermore, by employing the Lyapunov argument and mathematical induction, we present the sufficient conditions for fast fixed-time convergence of the tracking errors with respect to multiple targets. Finally, numerous simulation examples are presented to demonstrate the effectiveness of the proposed control algorithm.

Automated summary

In this paper, a fast fixed-time control algorithm is proposed to solve the output multi-formation tracking problem of networked autonomous surface vehicles. The algorithm divides the vehicles into interconnected subnetworks and ensures that the outputs form desired geometric formations through local interactions. By using a time-related function and a nonsingular fixed-time sliding surface, the algorithm achieves fast fixed-time convergence independent of initial conditions.