Adaptive Fixed-Time Control for High-Order Stochastic Nonlinear Time-Delay Systems: An Improved Lyapunov–Krasovskii Function
Bibliographic record
Abstract
In this article, the adaptive tracking control problem is considered for high-order stochastic nonlinear time-delay systems in fixed-time. Being different from existing results, an improved Lyapunov-Krasovskii function is designed, which can not only compensate for the time-delay term but also remove the obstacle from the high-order term. Due to the introduction of the Lyapunov-Krasovskii function into the total Lyapunov function, it makes it difficult to stabilize the controlled system within a fixed-time interval. L'Hopital's rule is used to determine the boundedness of the Lyapunov-Krasovskii function, and the fixed-time boundedness of the integral functions can be inferred. By utilizing the fixed-time Lyapunov stability theorem, it is proved that the controlled system is semi-globally practical fixed-time stable (SGPFS), all the closed-loop signals (CLSs) are bounded within the fixed-time interval, and the tracking error converges into a small region around zero. The validity of the designed scheme is substantiated via simulation results.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 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) | 0.001 | 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".