Virtual–Real-Based Distributed Neuro-Adaptive Control Design for 3-D Formation Tracking Motion of Underactuated Autonomous Underwater Vehicles

This article proposes a novel distributed neuro-adaptive 3-D formation tracking control framework of multiple autonomous underwater vehicles (multi-AUVs) subject to marine environmental disturbances. On the one hand, we assume that all AUVs can obtain the real-time states. By introducing a series of variable transformations, the multi-AUV system is transformed into an underactuated nonlinear system with virtual control input. Radial basis function neural networks (RBFNNs), whose weights are updated online, are utilized to approximate nonlinear functions. Considering environmental disturbances, a virtual controller is designed such that all AUVs track the leader while maintaining the desired formation geometry. Then, the actual controller is given as an adaptive form according to the virtual control signals. On the other hand, we assume that all AUVs can only obtain the sampling states of themselves and their neighbors under the predefined event-triggered conditions. Multi-AUV system is transformed into a second-order system with complex nonlinear dynamics, then their states are reconstructed via a neuro-adaptive state observer using sampling states, and a virtual controller is proposed such that all AUVs track the leader while maintaining the desired formation geometry under local communication with no Zeno behavior. Finally, numerical simulations are carried out to demonstrate the effectiveness of the proposed control design.