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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.13354 |
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Table of 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.