A linear-quadratic partially observed Stackelberg stochastic differential game with multiple followers and its application to multi-agent formation control
Bibliographic record
Abstract
In this paper, we study a linear-quadratic partially observed Stackelberg stochastic differential game problem in which a single leader and multiple followers are involved. We consider more practical formulation for partial information that none of them can observed the complete information and the followers know more than the leader. Some completely different methods including a novel state decomposition and orthogonal decomposition are applied to overcome the difficulties caused by partially observability which improves the tools and relaxes the constraint condition imposed on admissible control in the existing literature. More precisely, the followers encounter the standard linear-quadratic partially observed optimal control problems, however, a kind of forward-backward indefinite linear-quadratic partially observed optimal control problem is considered by the leader. Instead of maximum principle of forward-backward control systems, inspired by the existing work related to definite case and classical forward control system, some distinct forward-backward linear-quadratic decoupling techniques including the method of completion of squares are applied to solve the leader's problem. More interestingly, we develop the deterministic formation control in multi-agent system with a framework of Stackelberg differential game and extend it to the stochastic case. The optimal strategies are obtained by our theoretical result suitably.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".