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

2025/12/04 by Matteo Cercola, Cercola, Matteo, Donatello Materassi +3
Engineering · Physics and Astronomy · #Control Systems and Identification #Control and Stability of Dynamical Systems #FOS: Electrical engineering #Model Reduction and Neural Networks #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2512.15725

openalex publication_date 2025/12/04 · openalex created_date 2025/12/21 · openalex updated_date 2026/07/28

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.

Citations

• Diffusion State-Guided Projected Gradient for Inverse Problems
• Diffusion Models are Minimax Optimal Distribution Estimators
• Diffusion Posterior Sampling for General Noisy Inverse Problems
• Convergence of score-based generative modeling for general data distributions
• Classifier-Free Diffusion Guidance
• Elucidating the Design Space of Diffusion-Based Generative Models
• Planning with Diffusion for Flexible Behavior Synthesis
• Riemannian Score-Based Generative Modelling
• Diffusion Models Beat GANs on Image Synthesis
• Score-Based Generative Modeling through Stochastic Differential Equations
• Denoising Diffusion Probabilistic Models
• Deep Unsupervised Learning using Nonequilibrium Thermodynamics

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• Score Matching Diffusion Based Feedback Control and Planning of Nonlinear Systems
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• System Level Synthesis