Deep Lyapunov-Based Physics-Informed Neural Networks (DeLb-PINN) for Adaptive Control Design

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

Abstract: Physics-informed learning is an emerging machine learning technique driven by the desire to leverage known physical principles in machine learning algorithms. Recent developments have produced physics-informed neural networks (PINNs) which are neural networks designed to be constrained by known physical principles. However, developing real-time adaptive control methods with stability guarantees for PINNs remains an open problem. This paper develops the first result for a deep Lyapunov-based physics-informed neural network (DeLb-PINN) architecture to adaptively control uncertain Euler-Lagrange systems. Lyapunov-derived weight adaptation laws provide continuous, online learning using the DeLb-PINN architecture without the need for offline training. A nonsmooth desired compensation adaptation law (DCAL) Lyapunov-based analysis is provided to guarantee global asymptotic tracking error convergence.