Practical fixed-time formation control with disturbance rejection for marine vehicles under input saturation

This paper addresses the practical fixed-time disturbance rejection formation control problem for marine vehicles under input saturation effects. First, a novel practical fixed-time stability lemma is established. A practical fixed-time disturbance observer which is independent of initial estimation errors is developed to estimate ocean disturbances within a fixed-time interval. Then, considering the susceptibility of control forces to saturation resulting from fixed-time control strategies, the input saturation effects are reduced by correcting the control error online through the state vector of the constructed practical fixed-time auxiliary dynamic filter. Furthermore, through the utilization of the vectorial backstepping, the practical fixed-time disturbance rejection anti-saturation formation controller is derived with the first-order filter being incorporated to overcome the differential explosion. Theoretical analysis demonstrates that the proposed control method enables the follower vehicle to effectively track the leader vehicle while ensuring stability in all states within a fixed settling time, independent of the follower's initial states. Finally, simulation results are presented to validate the effectiveness of our developed control scheme.