Optimal control of network-coupled subsystems: Spectral decomposition and low-dimensional solutions
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Bibliographic record
Abstract
In this paper, we investigate optimal control of network-coupled subsystems where the dynamics and the cost couplings depend on an underlying undirected weighted graph. The graph coupling matrix in the dynamics may be the adjacency matrix, the Laplacian matrix, or any other symmetric matrix corresponding to the underlying graph. The cost couplings can be any polynomial function of the underlying coupling matrix. We use the spectral decomposition of the graph coupling matrix to decompose the overall system into (L+1) systems with decoupled dynamics and cost, where L is the rank of the coupling matrix. Furthermore, the optimal control input at each subsystem can be computed by solving (Ldist + 1) decoupled Riccati equations where Ldist (Ldist \leq L) is the number of distinct non-zero eigenvalues of the coupling matrix. A salient feature of the result is that the solution complexity depends on the number of distinct eigenvalues of the coupling matrix rather than the size of the network. Therefore, the proposed solution framework provides a scalable method for synthesizing and implementing optimal control laws for large-scale network-coupled subsystems.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it