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arXiv · 2512.15725

Generative design of stabilizing controllers with diffusion models: the Youla approach

Matteo Cercola·Donatello Materassi·Simone Formentin
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Abstract

Designing controllers that simultaneously achieve strong performance and provable closed-loop stability remains a central challenge in control engineering. This work introduces a diffusion-based generative framework for linear controller synthesis grounded in the Youla-Kucera parameterization, enabling the construction of stabilizing controllers by design. The diffusion model learns a conditional mapping from plant dynamics and desired performance metrics to feasible Youla parameters, guaranteeing internal stability while flexibly accommodating user-specified targets. Trained on synthetically generated stable SISO plants with fixed-order Youla parameters, the proposed approach reliably synthesizes controllers that meet prescribed sensitivity and settling-time specifications on previously unseen systems. To the best of our knowledge, this work provides the first demonstration that diffusion models can generate stabilizing controllers, combining rigorous control-theoretic guarantees with the versatility of modern generative modeling.

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Matteo Cercola, Donatello Materassi, Simone Formentin. 2025-12-04. Generative design of stabilizing controllers with diffusion models: the Youla approach. https://arxiv.org/abs/2512.15725

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