Lyapunov-Based Physics-Informed Long Short-Term Memory (LSTM) Neural Network-Based Adaptive Control

Rebecca G. Hart, Emily J. Griffis, Omkar Sudhir Patil, Warren E. Dixon

Abstract: Deep neural networks (DNNs) and long short-term memory networks (LSTMs) have grown in recent popularity due to their function approximation performance when compared to traditional NN architectures. However, the predictions that may result from these networks often do not align with physical principles. This letter introduces the first physics-informed LSTM (PI-LSTM) controller composed of DNNs and LSTMs, where the weight adaptation laws are designed from a Lyapunov-based analysis. The developed PI-LSTM combines DNNs and LSTMs for the purpose of function approximation and memory while respecting the underlying system physics. Simulations were performed to demonstrate feasibility and resulted in a root mean square tracking error of 0.0185 rad and a 33.76% improvement over the baseline method.