Distributed dual-loop event-triggered formation control for underactuated AUVs under directed topology

Objectives This paper investigates a distributed dual-loop event-triggered control method for the formation tracking problem of multiple autonomous underwater vehicles (AUVs) under directed asymmetric topology, locally reachable leader information, unknown dynamics, and actuator saturation. Methods The outer loop integrates distributed observation, adaptive formation control, and dynamic event-triggered communication to generate desired velocity commands. The inner-loop dynamics are formulated as a ten-dimensional augmented model incorporating command-filter states. A nonquadratic cost function is employed to characterize input constraints, and the filtered input is incorporated into the Hamilton–Jacobi–Isaacs (HJI) robust envelope. An offline Actor–Critic policy-improvement method is adopted, with the network weights fixed during closed-loop execution. Results Under the relevant assumptions, the outer-loop error satisfies conditional local p-ISS with respect to the inner-loop velocity error, command-filtering error, and communication sampling error; the inner loop satisfies local p-ISS and ultimate boundedness, and the communication and control event sequences are Zeno-free. Simulation results show that the proposed method achieves position and velocity IAEs of 30.34 and 4.51, respectively. The outer-loop communication count is 1432, which is 71.4% lower than that of 10 Hz time-triggered communication. The inner-loop control updates are 10226; compared with the 100 Hz fixed Actor, the position and velocity IAEs are reduced by 0.08% and increased by 3.65%, respectively, while the control updates are reduced by 74.44%. Conclusions The proposed method provides a distributed control framework that balances formation-tracking performance with communication and control-update costs for multi-AUV systems under directed topologies and unknown dynamics, and offers a methodological reference for cooperative AUV operations in underwater environments.