Target Controllability Scores for Actuation-Constrained Network Intervention
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917430707617792 |
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| author | Sato, Kazuhiro |
| author_facet | Sato, Kazuhiro |
| contents | We introduce the target controllability score (TCS), a concept for evaluating node importance under actuator constraints and designated target objectives, formulated within a virtual system setting. The TCS consists of the target volumetric controllability score (VCS) and the target average energy controllability score (AECS), each defined as an optimal solution to a convex optimization problem associated with the output controllability Gramian. We establish existence and uniqueness (for almost all time horizons), develop a projected gradient method for computation, and show that target VCS/AECS can behave qualitatively differently from their standard full-state counterparts because projection onto the target nodes changes the underlying Gramian structure. To enable scalability, we construct a target-only reduced virtual system and derive non-asymptotic bounds showing that weak cross-coupling and a low or negative logarithmic norm of the system matrix yield accurate approximations of target VCS/AECS, particularly over short or moderate time horizons. Experiments on human brain networks reveal a clear trade-off: at short horizons, both target VCS and target AECS are well approximated by their reduced formulations, while at long horizons, target AECS remains robust but target VCS deteriorates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13354 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Target Controllability Scores for Actuation-Constrained Network Intervention Sato, Kazuhiro Optimization and Control We introduce the target controllability score (TCS), a concept for evaluating node importance under actuator constraints and designated target objectives, formulated within a virtual system setting. The TCS consists of the target volumetric controllability score (VCS) and the target average energy controllability score (AECS), each defined as an optimal solution to a convex optimization problem associated with the output controllability Gramian. We establish existence and uniqueness (for almost all time horizons), develop a projected gradient method for computation, and show that target VCS/AECS can behave qualitatively differently from their standard full-state counterparts because projection onto the target nodes changes the underlying Gramian structure. To enable scalability, we construct a target-only reduced virtual system and derive non-asymptotic bounds showing that weak cross-coupling and a low or negative logarithmic norm of the system matrix yield accurate approximations of target VCS/AECS, particularly over short or moderate time horizons. Experiments on human brain networks reveal a clear trade-off: at short horizons, both target VCS and target AECS are well approximated by their reduced formulations, while at long horizons, target AECS remains robust but target VCS deteriorates. |
| title | Target Controllability Scores for Actuation-Constrained Network Intervention |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.13354 |