NAPI-MPC: Neural Accelerated Physics-Informed MPC for Nonlinear PDE Systems

Abstract

The control of systems governed by nonlinear partial differential equations (PDEs) can present substantial challenges for traditional linear model predictive control (MPC) approaches. Data-driven MPC has emerged as a solution for dealing with unknown nonlinear dynamics, but issues regarding safety guarantees, accuracy, and data efficiency remain a concern. We propose NAPI-MPC: a novel physics-informed scenario-based MPC approach for control of nonlinear PDE systems with partially unknown dynamics. Unlike other physics-informed learning methods that require extensive knowledge on the governing equations, our NAPI-MPC leverages distributed Port-Hamiltonian systems as a generalized, energy-based representation of the PDE dynamics, in which the Hamiltonian is modeled and learned by a Gaussian process. The Bayesian nature of the Gaussian process enables the drawing of scenario samples that are used in scenario-based predictive control to determine the optimal control action for the PDE system. To ensure applicability in time-sensitive contexts, we leverage a neural network as proxy for the MPC controller, trained offline on states and optimal control actions to enable fast inference for real-time operation.