Regularization in Data-driven Predictive Control: A Convex Relaxation Perspective
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917412437229568 |
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| author | Shang, Xu Zheng, Yang |
| author_facet | Shang, Xu Zheng, Yang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09027 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularization in Data-driven Predictive Control: A Convex Relaxation Perspective Shang, Xu Zheng, Yang Optimization and Control Systems and Control 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. |
| title | Regularization in Data-driven Predictive Control: A Convex Relaxation Perspective |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2509.09027 |