Distributed event-triggered adaptive finite-time formation control for multiple under-actuated AUVs using command filtered backstepping technique with prescribed performance

This study proposes an event-triggered adaptive finite time formation control for multiple under-actuated autonomous underwater vehicles (AUVs) with prescribed performance regarding to time-varying external disturbances and model uncertainties. Firstly, a state transformation is performed as to rectify the under-actuated issue of the vehicle and streamline the subsequent procedure for designing the controller. The distributed formation tracking error is then determined by applying the graph theory. Also, a mapping function is implemented to convert the constrained errors into new unconstrained variables as to achieve the prescribed performance. Second, the control law is formulated utilizing the finite time backstepping approach and event-triggering conditions, where the finite-time filter is adopted to reduce computational complexity. An adaptive strategy is developed to deal with model uncertainties and external disturbances using the universal approximation ability of radial basis function neural networks (RBFNNs). This strategy permits updating only two parameters per follower. The problem of control input saturation is also considered and resolved with the design of the finite-time auxiliary system. Consequently, all signals of the closed-loop system exhibit stability and achieve finite-time convergence while successfully avoiding the Zeno behavior. Eventually, case study using numerical simulations demonstrates the feasibility, superiority and effectiveness of the proposed controller.