Adaptive Output Feedback Control Using Lyapunov-Based Deep Recurrent Neural Networks (Lb-DRNNs)

Unlike traditional feedforward neural networks, recurrent neural networks (RNNs) possess a recurrent connection that allows them to retain past information. This internal memory enables RNNs to effectively model and capture time-varying and accumulative effects observed in dynamic systems, which cannot be achieved by static feedforward neural networks, making RNNs more suitable for tasks such as state estimation and output feedback control. Motivated by the dynamic behavior of RNNs, this paper develops an adaptive Lyapunov-based deep RNN (Lb-DRNN) output feedback controller for uncertain nonlinear systems. Specifically, an Lb-DRNN observer is designed to adaptively estimate the unknown states of the system and is integrated into an output feedback control framework. To ensure real-time adaptation and online learning, the DRNN weights are dynamically adjusted using Lyapunov-based adaptation laws. A Lyapunov-based stability analysis proves asymptotic estimation and tracking error convergence. Validation simulation experiments on an unmanned underwater vehicle system yielded a 31.85% and 86.21% improvement in normalized linear and angular tracking error, respectively, when compared to the shallow RNN-based OFB controller.