Adaptive synchronization with disturbance rejection for under-actuated ships with disturbances under thruster saturation

An adaptive synchronization control scheme with the disturbance estimation and rejection is proposed for the under-actuated ships with unknown time-varying disturbances under thruster saturation effects without leader ship’s velocities. The unknown time-varying disturbances are described as the sinusoidal disturbances whose amplitudes, frequencies and phases are uncertain. The disturbances are expressed by using an unknown parametric exogenous system which is converted into a canonical model with the disturbances as inputs. A disturbance filter is constructed to estimate the state vector in the canonical model such that the disturbances are represented by the parametric equations with exponentially decaying errors. The main highlights lie in that the anti-disturbance problem is transformed into the adaptive control problem based on parametric disturbance representations. This enables that the additional control filters are constructed to generate the filtered signals of the control deviations to on-line correct feedback control errors such that the adaptive disturbance rejection control would be workable under thruster saturation effects. The proposed adaptive synchronization scheme achieves the disturbance rejection and the thruster saturation attenuation simultaneously. Simulations with comparisons demonstrate the effectiveness and the superiority of the control scheme.