Computing control invariant set using reinforcement learning by leveraging default value function
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Bibliographic record
Abstract
This paper presents a framework for computing the control invariant set (CIS) of a general nonlinear system using reinforcement learning (RL). By formulating the CIS problem as an RL task with a specially tailored reward design and value initialization, the proposed approach identifies safe states as those converging to a nonnegative value function, while states leading to constraint violation accumulate negative values. This distinction allows for a straightforward classification of the safe region without requiring complex set-based operations or assumptions on the shape of the invariant set. The paper provides a theoretical analysis showing that, in the absence of disturbances, states lying within the CIS converge to an optimal value of zero, whereas any trajectory that eventually violates the constraint attains strictly negative values. Leveraging standard RL algorithms, ranging from value iteration to Q-learning and deep Q-learning, this method is readily applicable to both low-dimensional and relatively high-dimensional systems with discrete or continuous state spaces. Numerical demonstrations on continuously stirred tank reactors illustrate that the proposed RL-based framework achieves results comparable to existing graph-based methods. These findings highlight the potential of RL, with only minimal modifications, as a data-driven tool to approximate and certify control invariant sets for complex process 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 | 0.000 | 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