A graph-informed regret metric for optimal distributed control
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915625593470976 |
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| author | Martinelli, Daniele Martin, Andrea Ferrari-Trecate, Giancarlo Furieri, Luca |
| author_facet | Martinelli, Daniele Martin, Andrea Ferrari-Trecate, Giancarlo Furieri, Luca |
| contents | We consider the optimal control of large-scale systems using distributed controllers with a network topology that mirrors the coupling graph between subsystems. In this work, we introduce spatial regret, a graph-informed metric that measures the worst-case performance gap between a distributed controller and an oracle which is assumed to have access to additional sensor information. The oracle's graph is a user-specified augmentation of the available information graph, resulting in a benchmark policy that highlights disturbances for which additional sensor information would significantly improve performance. Minimizing spatial regret yields distributed controllers-respecting the nominal information graph-that emulate the oracle's response to disturbances that are characteristic of large-scale networks, such as localized perturbations. We show that minimizing spatial regret admits a convex reformulation as an infinite program with a finite-dimensional approximation. To scale to large networks, we derive a computable upper bound on the spatial regret metric whose minimization problem can be solved in a distributed way. Numerical experiments on power-system models demonstrate that the resulting controllers mitigate localized disturbances more effectively than controllers optimized using classical metrics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_14280 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A graph-informed regret metric for optimal distributed control Martinelli, Daniele Martin, Andrea Ferrari-Trecate, Giancarlo Furieri, Luca Systems and Control Optimization and Control We consider the optimal control of large-scale systems using distributed controllers with a network topology that mirrors the coupling graph between subsystems. In this work, we introduce spatial regret, a graph-informed metric that measures the worst-case performance gap between a distributed controller and an oracle which is assumed to have access to additional sensor information. The oracle's graph is a user-specified augmentation of the available information graph, resulting in a benchmark policy that highlights disturbances for which additional sensor information would significantly improve performance. Minimizing spatial regret yields distributed controllers-respecting the nominal information graph-that emulate the oracle's response to disturbances that are characteristic of large-scale networks, such as localized perturbations. We show that minimizing spatial regret admits a convex reformulation as an infinite program with a finite-dimensional approximation. To scale to large networks, we derive a computable upper bound on the spatial regret metric whose minimization problem can be solved in a distributed way. Numerical experiments on power-system models demonstrate that the resulting controllers mitigate localized disturbances more effectively than controllers optimized using classical metrics. |
| title | A graph-informed regret metric for optimal distributed control |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2511.14280 |