Global fixed-time position-constrained guidance and adaptive fuzzy prescribed performance control using novel shift function for multiple unmanned surface vehicles formation

Guidance and control of multiple unmanned surface vehicles (Multi-USVs) present many challenges due to their under-actuation and the unknown environmental disturbance. This research addresses the formation guidance and control problems of multi-USVs by designing a global fixed-time constrained guidance and control formation approach. First, a global fixed-time control Lyapunov function (GFCLF) is proposed using an innovative shift function to deal with the fixed-time output partial constraint. Subsequently, a fixed-time asymmetric position-constrained guidance algorithm for multi-USVs formation is designed by combining the line-of-sight guidance principle, the leader-follower structure, and the suggested GFCLF. Second, a global fixed-time prescribed performance function (GFPPF) is designed to solve the global tracking error performance constraint problem. Then, global fixed-time adaptive fuzzy prescribed performance control laws are developed to achieve the tracking control for the multi-USVs formation task, in which a fixed-time adaptive fuzzy logic system is designed to approximate the unknown disturbance of USVs. Furthermore, the closed-loop control system stability analysis is proven to support that all tracking error signals are bounded in a fixed time. Finally, simulations and comparative cases using the physical USV model are studied to demonstrate the practicality and superiority of theoretical results.