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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2511.13595 |
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| _version_ | 1866914512080207872 |
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| author | Mengozzi, Sebastiano Esposito, Giovanni B. Bin, Michelangelo Acquaviva, Andrea Bartolini, Andrea Marconi, Lorenzo |
| author_facet | Mengozzi, Sebastiano Esposito, Giovanni B. Bin, Michelangelo Acquaviva, Andrea Bartolini, Andrea Marconi, Lorenzo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13595 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Physics-Informed Neural Networks for Nonlinear Output Regulation Mengozzi, Sebastiano Esposito, Giovanni B. Bin, Michelangelo Acquaviva, Andrea Bartolini, Andrea Marconi, Lorenzo Systems and Control Artificial Intelligence 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. |
| title | Physics-Informed Neural Networks for Nonlinear Output Regulation |
| topic | Systems and Control Artificial Intelligence |
| url | https://arxiv.org/abs/2511.13595 |