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

TL;DR

A diffusion-based generative framework for linear controller synthesis grounded in the Youla-Kucera parameterization is introduced, enabling the construction of stabilizing controllers by design, providing the first demonstration that diffusion models can generate stabilizing controllers.

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.