Prescribed-time prescribed performance-based distributed formation control of surface vessels with system uncertainties

This paper puts forward a prescribed-time prescribed performance-based distributed formation control method for multiple vessels with system uncertainties. First, we design a prescribed-time disturbance observer to estimate the system uncertainties, which contain unmodeled dynamics, modeling uncertainties, and unknown environmental disturbances. Subsequently, a prescribed-time prescribed performance (PTPP) function, which has the advantages of shape-adaptability and prescribed-time convergence, is developed to improve the transient performance of system. The performance specification of the designed PTPP function is imposed on formation errors by introducing an error conversion. Then, a PTPP-based distributed formation controller is proposed for the multi-vessel formation system, which is proved to be prescribed-time stable. Finally, simulations and comparisons are given to verify the superiority of the proposed control strategy.