This paper studies the distributed cooperative control problem for multiple surface vessels (MSVs) subject to unknown environmental disturbances, model uncertainties, unavailable velocities and prescribed performance constraints. Firstly, a fixed-time extended state observer (FxESO) is designed to provide the estimations of velocities and lumped disturbances (including unknown environmental disturbances and model uncertainties). Secondly, to improve the convergence performance of the MSVs, a hyperbolic cosecant prescribed performance function is incorporated into the cooperative control algorithm. Thirdly, a fixed-time event-triggered control law with prescribed performance constraint is applied to cooperative control based on a fixed-time nonsingular terminal sliding mode manifold (FxNTSMM), and the cooperative errors can converge within fixed time. Finally, by employing Lyapunov function theory, the stability of the closed-loop system is analyzed. Simulation results are given to demonstrate the effectiveness of the proposed control scheme.INDEX TERMS multiple surface vessels, fixed-time extended state observer, prescribed performance, fixed-time sliding mode control, event-triggered controller

In this paper, a fixed-time distributed cooperative control under actuator faults with input saturation scheme is designed for multiple surface vessels (MSVs). Firstly, a fixed-time disturbance observer (FxDO) is introduced to observe unknown environmental disturbances and actuator faults (AF). Secondly, to deal with the actuator saturation, an improved nonlinear antiwindup compensator is introduced to compensate for the saturation effect of the actuator. Thirdly, a fixed-time fault-tolerant event-triggered control law with the actuator saturation is applied to cooperative control based on a fixed-time nonsingular terminal sliding mode manifold (FxNTSMM), and their cooperative errors can converge within fixed time. At the same time, the upper bound of convergence time is independent of the initial state. Finally, the stability analysis of the cooperative control system is given to prove that the system can realize the practical fixed time stability, and Zeno phenomenon is avoided by theoretical proof. Simulation results are given to demonstrate the effectiveness of the proposed control scheme.INDEX TERMS Multiple surface vessels, disturbance observer, fixed-time sliding mode control, eventtriggered controller, input saturation, actuator faults.

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Aiming at the problems of cooperative control for multiple surface vessels (MSVs), such as unknown environmental disturbances, unavailable velocities, model uncertainties, actuator saturation, and limited action times of the actuator, an event-triggered fixed-time distributed output feedback sliding mode cooperative control method with input saturation is proposed. The scheme ensures the practical fixed-time stability of the cooperative control system. First, a fixed-time extended state observer (FxESO) is designed to provide the estimations of velocities and lumped disturbances including unknown environmental disturbances and model uncertainties. Second, to deal with the actuator saturation, a fixed-time auxiliary dynamic system is designed. Third, a fixed-time non-singular terminal sliding mode manifold (FxNTSMM) is introduced to effectively eliminate singularity and improve chattering of the system. Finally, an event-triggered distributed controller based on FxNTSMM and FxESO is proposed. An event-triggered condition can avoid unnecessary actions of the actuator, and Zeno phenomenon is avoided by theoretical proof. In addition, the upper bound of the convergence time is independent of the initial state. Simulation results are given to demonstrate the effectiveness of the proposed control scheme.