Robust predefined-time target surrounding control for multiple underactuated unmanned surface vessels

Abstract

A robust predefined-time targeted surrounding fault-tolerant controller is proposed in this paper for multiple underactuated unmanned surface vessels (USVs) to rotate uniformly around a target vessel with all errors converging in a predefined time. First, a predefined-time distributed state observer (PTDSO) is designed to observe the states of the target USV, which are passed to other USVs through the communication topology. Second, the case of input saturation is considered, a saturation function is constructed to constrain the control signals, and a predefined-time auxiliary dynamic system is constructed to compensate for the controller. Similarly, the velocities of the USVs are indirectly constrained by constraining the virtual control signals. Third, to enhance the robustness of the controller, the disturbances to which the USV is subjected are divided into two parts: general disturbances and strong disturbances. A predefined-time adaptive fuzzy neural network (FNN) is designed to approximate general environmental disturbances and model uncertainties and actuator faults, and a predefined-time $H_{\infty }$ algorithm is designed to suppress strong disturbances. Finally, the stability analysis proves that all the signals within the closed-loop system can converge within a predefined time. Numerical simulations demonstrate the effectiveness of the proposed algorithm.