{"ID":2872802,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.09027","arxiv_id":"2509.09027","title":"Regularization in Data-driven Predictive Control: A Convex Relaxation Perspective","abstract":"This paper explores the role of regularization in data-driven predictive control (DDPC) through the lens of convex relaxation. Using a bi-level optimization framework, we model system identification as an inner problem and predictive control as an outer problem. Within this framework, we show that several regularized DDPC formulations, including l1-norm penalties, projection-based regularizers, and a newly introduced causality-based regularizer, can be viewed as convex relaxations of their respective bi-level problems. This perspective clarifies the conceptual links between direct and indirect data-driven control and highlights how regularization implicitly enforces system identification. We further propose an optimality-based variant, A-DDPC, which approximately solves the inner problem with all identification constraints via an iterative algorithm. Numerical experiments demonstrate that A-DDPC outperforms existing regularized DDPC by reducing both bias and variance errors. These results indicate that further benefits may be obtained by applying system identification techniques to pre-process the trajectory library in nonlinear settings. Overall, our analysis contributes to a unified convex relaxation view of regularization in DDPC and sheds light on its strong empirical performance beyond linear time-invariant systems.","short_abstract":"This paper explores the role of regularization in data-driven predictive control (DDPC) through the lens of convex relaxation. Using a bi-level optimization framework, we model system identification as an inner problem and predictive control as an outer problem. Within this framework, we show that several regularized D...","url_abs":"https://arxiv.org/abs/2509.09027","url_pdf":"https://arxiv.org/pdf/2509.09027v2","authors":"[\"Xu Shang\",\"Yang Zheng\"]","published":"2025-09-10T21:54:13Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}