Lyapunov-Based Long Short-Term Memory (Lb-LSTM) Neural Network-Based Adaptive Observer

Abstract

Long short-term memory (LSTM) neural networks excel at capturing short- and long-term dependencies, making them powerful tools for system identification and state estimation. Their unique design improves memory capabilities by retaining important information and discarding irrelevant data over time. However, due to mathematical challenges involved in developing adaptive control methods for LSTMs, their training is predominantly limited to offline methods. This letter develops a Lyapunov-based (Lb-) LSTM observer for state estimation in nonlinear systems. The Lb-LSTM weights adapt in real-time using Lyapunov-based stability-driven adaptation laws. A nonsmooth Lyapunov-based stability analysis ensures state estimation error convergence and stability of the overall Lb-LSTM architecture. To validate the developed observer design, simulations were performed to estimate the unknown angular velocity states of a two-link robot manipulator. The developed method yielded a 41.13% improvement in the root mean square estimation error when compared to an adaptive RNN observer.