Physics-Informed Neural Networks for Nonlinear Output Regulation

• URL: http://arxiv.org/abs/2511.13595v2
• Date: Tue, 18 Nov 2025 11:04:37 GMT
• Title: Physics-Informed Neural Networks for Nonlinear Output Regulation
• Abstract summary: We introduce a physics-informed neural network (PINN) approach that directly approximates $(w)$ and $c(w)$.<n>The framework is validated on a regulation task that synchronizes a helicopter's vertical dynamics with a harmonically oscillating platform.
• Score: 3.28594109710934
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This work addresses the full-information output regulation problem for nonlinear systems, assuming the states of both the plant and the exosystem are known. In this setting, perfect tracking or rejection is achieved by constructing a zero-regulation-error manifold $π(w)$ and a feedforward input $c(w)$ that render such manifold invariant. The pair $(π(w), c(w))$ is characterized by the regulator equations, i.e., a system of PDEs with an algebraic constraint. We focus on accurately solving the regulator equations introducing a physics-informed neural network (PINN) approach that directly approximates $π(w)$ and $c(w)$ by minimizing the residuals under boundary and feasibility conditions, without requiring precomputed trajectories or labeled data. The learned operator maps exosystem states to steady state plant states and inputs, enables real-time inference and, critically, generalizes across families of the exosystem with varying initial conditions and parameters. The framework is validated on a regulation task that synchronizes a helicopter's vertical dynamics with a harmonically oscillating platform. The resulting PINN-based solver reconstructs the zero-error manifold with high fidelity and sustains regulation performance under exosystem variations, highlighting the potential of learning-enabled solvers for nonlinear output regulation. The proposed approach is broadly applicable to nonlinear systems that admit a solution to the output regulation problem.

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