Near-Optimal Control Strategy in Leader-Follower Networks: A Case Study\n for Linear Quadratic Mean-Field Teams
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Bibliographic record
Abstract
In this paper, a decentralized stochastic control system consisting of one\nleader and many homogeneous followers is studied. The leader and followers are\ncoupled in both dynamics and cost, where the dynamics are linear and the cost\nfunction is quadratic in the states and actions of the leader and followers.\nThe objective of the leader and followers is to reach consensus while\nminimizing their communication and energy costs. The leader knows its local\nstate and each follower knows its local state and the state of the leader. The\nnumber of required links to implement this decentralized information structure\nis equal to the number of followers, which is the minimum number of links for a\ncommunication graph to be connected. In the special case of leaderless, no link\nis required among followers, i.e., the communication graph is not even\nconnected. We propose a near-optimal control strategy that converges to the\noptimal solution as the number of followers increases. One of the salient\nfeatures of the proposed solution is that it provides a design scheme, where\nthe convergence rate \\edit{as well as} the collective behavior of the followers\ncan be designed by choosing appropriate cost functions. In addition, the\ncomputational complexity of the proposed solution does not depend on the number\nof followers. Furthermore, the proposed strategy can be computed in a\ndistributed manner, where the leader solves one Riccati equation and each\nfollower solves two Riccati equations to calculate their strategies. Two\nnumerical examples are provided to demonstrate the effectiveness of the results\nin the control of multi-agent systems.\n
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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