Bilevel MPC for Linear Systems: A Tractable Reduction and Continuous Connection to Hierarchical MPC
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911556534534144 |
|---|---|
| author | Moriyasu, Ryuta Alonso, Carmen Amo Pavone, Marco |
| author_facet | Moriyasu, Ryuta Alonso, Carmen Amo Pavone, Marco |
| contents | Model predictive control (MPC) has been widely used in many fields, often in hierarchical architectures that combine controllers and decision-making layers at different levels. However, when such architectures are cast as bilevel optimization problems, standard KKT-based reformulations often introduce nonconvex and potentially nonsmooth structures that are undesirable for real-time verifiable control. In this paper, we study a bilevel MPC architecture composed of (i) an upper layer that selects the reference sequence and (ii) a lower-level linear MPC that tracks such reference sequence. We propose a smooth single-level reduction that does not degrade performance under a verifiable block-matrix nonsingularity condition. In addition, when the problem is convex, its solution is unique and equivalent to a corresponding centralized MPC, enabling the inheritance of closed-loop properties. We further show that bilevel MPC is a natural extension of standard hierarchical MPC, and introduce an interpolation framework that continuously connects the two via move-blocking. This framework reveals optimal-value ordering among the resulting formulations and provides inexpensive a posteriori degradation certificates, thereby enabling a principled performance-computational efficiency trade-off. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29265 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bilevel MPC for Linear Systems: A Tractable Reduction and Continuous Connection to Hierarchical MPC Moriyasu, Ryuta Alonso, Carmen Amo Pavone, Marco Systems and Control Optimization and Control Model predictive control (MPC) has been widely used in many fields, often in hierarchical architectures that combine controllers and decision-making layers at different levels. However, when such architectures are cast as bilevel optimization problems, standard KKT-based reformulations often introduce nonconvex and potentially nonsmooth structures that are undesirable for real-time verifiable control. In this paper, we study a bilevel MPC architecture composed of (i) an upper layer that selects the reference sequence and (ii) a lower-level linear MPC that tracks such reference sequence. We propose a smooth single-level reduction that does not degrade performance under a verifiable block-matrix nonsingularity condition. In addition, when the problem is convex, its solution is unique and equivalent to a corresponding centralized MPC, enabling the inheritance of closed-loop properties. We further show that bilevel MPC is a natural extension of standard hierarchical MPC, and introduce an interpolation framework that continuously connects the two via move-blocking. This framework reveals optimal-value ordering among the resulting formulations and provides inexpensive a posteriori degradation certificates, thereby enabling a principled performance-computational efficiency trade-off. |
| title | Bilevel MPC for Linear Systems: A Tractable Reduction and Continuous Connection to Hierarchical MPC |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2603.29265 |