Explainable LP-MPC: Shadow Price Contributions Reveal MV-CV Pairings
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917503989448704 |
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| author | Siang, Lim C. O'Connor, Daniel L. |
| author_facet | Siang, Lim C. O'Connor, Daniel L. |
| contents | In the process industries, MPC (Model Predictive Control) is typically implemented as a two-stage controller with a Linear Program (LP) steady-state optimizer that generates economically optimal targets for the MPC algorithm. Abnormal behaviors in industrial LP optimizers are often difficult to rationalize, especially when a large number of manipulated variables (MVs) and controlled variables (CVs) are involved. We introduce a novel, post-hoc LP explainability method by recasting the role of shadow prices in the LP solution as an attribution mechanism for MV-CV relationships. The core idea is that the shadow price of a constrained CV is not just an intrinsic property of the LP solution, but can be split into contributions from individual unconstrained MVs and resolved into one-to-one MV-CV pairings using a linear sum assignment algorithm. The proposed MV-CV pairing framework serves as a practical explainability tool for online LP-MPC systems, enabling practitioners to diagnose suboptimal constraints and verify alignment of the controller's behavior with its original design. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06194 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explainable LP-MPC: Shadow Price Contributions Reveal MV-CV Pairings Siang, Lim C. O'Connor, Daniel L. Systems and Control In the process industries, MPC (Model Predictive Control) is typically implemented as a two-stage controller with a Linear Program (LP) steady-state optimizer that generates economically optimal targets for the MPC algorithm. Abnormal behaviors in industrial LP optimizers are often difficult to rationalize, especially when a large number of manipulated variables (MVs) and controlled variables (CVs) are involved. We introduce a novel, post-hoc LP explainability method by recasting the role of shadow prices in the LP solution as an attribution mechanism for MV-CV relationships. The core idea is that the shadow price of a constrained CV is not just an intrinsic property of the LP solution, but can be split into contributions from individual unconstrained MVs and resolved into one-to-one MV-CV pairings using a linear sum assignment algorithm. The proposed MV-CV pairing framework serves as a practical explainability tool for online LP-MPC systems, enabling practitioners to diagnose suboptimal constraints and verify alignment of the controller's behavior with its original design. |
| title | Explainable LP-MPC: Shadow Price Contributions Reveal MV-CV Pairings |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2512.06194 |