A noise-resilient distributed recurrent neural network for multi-agent consensus control and acoustic source localization.

In multi-agent systems (MASs), consensus control and acoustic source localization are fundamental yet noise-sensitive tasks. While recurrent neural networks (RNNs) have shown strong potential in these domains due to their dynamic modeling capabilities, their control accuracy degrades notably under noise interference, and RNN-based control for disturbed multi-agent scenarios has received limited attention. To address this challenge, we design a noise-resilient distributed RNN (NDRNN) within the multi-agent consensus framework and develop a corresponding consensus control protocol, termed NDRNN-CP. The NDRNN incorporates a time-delay mechanism to adaptively learn noise variation patterns and employs an optimized activation function for accelerated convergence. Rigorous theoretical analyses prove that NDRNN-CP ensures global stability, robustness against periodic and stochastic disturbances, and predefined-time convergence. Furthermore, building on the NDRNN design principle, we propose NDRNN-S, a distributed acoustic source localization solver capable of maintaining high accuracy in noisy multi-agent environments. Extensive simulations on multi-agent consensus and distributed acoustic source localization demonstrate that, compared with conventional DRNN-based methods, the proposed NDRNN-CP and NDRNN-S achieve faster convergence and significantly lower steady-state errors under various noise signal conditions, confirming the effectiveness and broad applicability of the proposed approach.