Adaptive dynamic surface control for cooperative path following of underactuated marine surface vehicles via fast learning

This study presents a solution to the problem of cooperative path following of multiple underactuated marine surface vehicles subject to dynamical uncertainties and ocean disturbances. The dedicated control designs are categorised into two envelopes. One is to steer individual underactuated marine surface vehicle to track a given spatial path; and the other is to synchronise the along-path speeds and path variables under the constraints of an underlying communication network in order to hold a desired formation pattern. Within these two formulations, a robust adaptive path-following controller is first designed for individual vehicle based on neural networks and a dynamic surface control (DSC) technique. Then, the along-path speeds and path variables are synchronised to each vehicle owing to the proposed decentralised synchronisation control law building on graph theory and Lyapunov theory. The key features of the developed controllers are that, first, the DSC technique simplifies the controller design by introducing first-order filters and avoids the calculation of derivatives of virtual control signals. Second, the developed controllers with filtering adaptive laws allow for fast learning without generating high-frequency oscillations in control signals. Rigorous theoretical analysis demonstrates that all signals in the closed-loop system are uniformly ultimately bounded. Simulation results are provided to show the efficacy of the proposed method.