Q‐Learning‐Based Controller Design for Logarithmic Quantised Input Systems
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Bibliographic record
Abstract
ABSTRACT This paper explores the design of optimal controllers for systems with logarithmic quantised inputs, using reinforcement learning. We introduce a novel method that ensures global optimality in Guaranteed Cost Control (GCC) while achieving quadratic stabilisation through the selection of an optimal scaling gain. By transforming the uncertain system into an control framework, we derive the optimal solution using a Zero‐Sum Dynamical Game (ZSDG). We then reformulate the problem using a virtual input, eliminating reliance on the scaling gain. Based on the introduced virtual input, we develop a novel model‐free Q ‐function and an algorithm for controller synthesis that is independent of the scaling gain. The proposed Q ‐function matches the dimension of a standard Q ‐function, minimising the number of decision variables. Simulation results on real‐world systems demonstrate that the proposed approach consistently outperforms both model‐free and model‐based methods, delivering superior optimality and computational efficiency.
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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) | 0.000 | 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 | 0.001 | 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