Fixed-time formation control of fully-actuated surface vessels with input saturation and complex unknowns*

This paper focuses on fixed-time formation control of a crowd of fully actuated surface vessels with input constraint and complex unknowns. First, an adaptive auxiliary system is introduced for each vessel to conquer the harmful effects caused by input saturation. Second, so as to enhance the robustness and anti-interference ability, the predictor-based neural network is utilized to estimate the unknowns, and adaptive laws are designed to evaluate bounds of neural network errors. Third, considering the timing requirement, a fixed-time formation protocol is proposed by using a novel fixed-time convergence nonsingular terminal sliding mode. Not only the trajectory tracking errors of single vessel and cooperative errors between vessels, but also the relationship between position and velocity errors is considered in the sliding mode. It can be proved that the proposed protocol can make the above-mentioned errors converge to a tiny neighborhood near zero in a fixed time. Simulation studies based on four supply vessels are comprehensively provided to confirm the effectiveness of the proposed protocol.