Regulation With Guaranteed Convergence Rate for Continuous-Time Systems With Completely Unknown Dynamics in the Presence of Disturbance
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Bibliographic record
Abstract
This paper presents the design of a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -based control framework for state regulation of continuous-time linear systems with completely unknown dynamics. The proposed method solves the regulation problem with the desired convergence rate and simultaneously seeks to attenuate the adverse effect of disturbance on the system. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> regulation problem assumes a cost function that considers regulation with a guaranteed rate of convergence as well as disturbance attenuation. The problem is then turned into a two-player zero-sum game optimization problem that can be solved by solving the associated algebraic Riccati equation (ARE), which provides a model-based solution. To solve this problem in a model-free way, a novel integral reinforcement learning (IRL) algorithm is designed to learn the solution online without requiring any prior knowledge of the system dynamics. It is shown that the model-free method (i.e., IRL-based method) provides the same solution as the model-based method (i.e., ARE). The effectiveness of the proposed method is ascertained through simulation examples; it is shown that the proposed method effectively addresses the problem for both stable and unstable systems.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 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