Distributed fixed-time cooperative tracking control of networked uncertain underactuated surface vessels with unmeasured velocity and input saturation

• A novel distributed fixed-time observer is proposed to rapidly estimate the leader’s trajectory with synchronous convergence. • A hierarchical fixed-time cooperative tracking controller is proposed, simplifying design over traditional coupled formation controllers. • A fixed-time composite observer estimates unmeasured velocity and disturbance in USVs, with an auxiliary signal mitigating input saturation. This article proposes a distributed fixed-time cooperative tracking control scheme based on a hierarchical design framework, consisting of a distributed cooperative estimation layer and a decentralized control layer, to address cooperative tracking control of networked uncertain underactuated surface vessels (USVs) with unmeasured velocity and input saturation. Firstly, in the distributed cooperative estimation layer, a novel distributed fixed-time cooperative observer is designed to rapidly estimate the reference trajectory of the leader. Then, in the decentralized tracking control layer, a fixed-time compound disturbance and velocity observer is designed to address the unmeasured velocity and the compound disturbance (including external environmental disturbances, model parameter uncertainties, and unknown dynamic coupling) for the follower vessel. Furthermore, to address the complexity and error accumulation caused by the repeated differentiation of the virtual velocity control law, a non-smooth filter is designed to enhance system stability. Meanwhile, to avoid the inaccurate estimation of the leader’s reference trajectory at the initial moment, which could result in large control input and trigger input saturation, a fixed-time saturation tracking controller with an auxiliary system signal is designed to rapidly track the leader. Finally, Lyapunov stability analysis and simulation are performed to verify the effectiveness of the proposed cooperative tracking control scheme.