Extended Lagrangian-Informed Deep Learning and Control for Electro-mechanical Systems

In order to accurately model the dynamics of non-linear electro-mechanical systems, it is imperative to consider the contributions of coupling terms and dissipation. The Lagrangian formulation alone is insufficient to fully capture the holistic behavior of the system. Coupling and dissipation mechanisms play a pivotal role in shaping the system's response. Consequently, to effectively capture the dynamics of inter-coupled electro-mechanical systems with dissipation, we propose an extended Lagrangian-informed deep neural network framework in this paper. Our approach leverages the underlying physics-based knowledge of the system, incorporating it into the neural network architecture. By employing the Euler-Lagrange equations as constraints in the training process, we ensure that the learned dynamics conform to the true behavior of the system. To validate the theoretical framework, we conduct simulation experiments on a DC motor with a cart system, which serves as a representative model of dissipative nonlinear electro-mechanical systems. The experimental results demonstrate the efficacy of our approach in accurately capturing and integrating the dynamics to solve the reference tracking model predictive control design.