A Barrier Function-Based Integral Sliding Mode Control of Heart Rate During Treadmill Exercise
Bibliographic record
Abstract
The objective of this work is to design an Integral Sliding Mode Controller based on barrier function (ISMCbf) for a human Heart Rate (HR) during a treadmill exercise.ISMCbf commands the speed of the treadmill such that the individual HR follows a time-varying profile.This profile is pre specified as part of rehabilitation exercises for patients with cardiovascular diseases.ISMCbf is chosen due to its well-known robustness properties as well as to its simple design procedure as compared to classic SMC and ISMC.It does not require the upper bounds of the uncertainties and perturbations in its design.Moreover, it does not have discontinuous function, hence it is a chattering-free controller.ISMCbf designed in this work for the first time for this system and its performance is compared to Quasi SMC (QSMC) and Super Twisting SMC (STSMC) from previous studies.The simulated exercises were conducted on a nonlinear model describing HR response to the walking speed of a treadmill.For ISMCbf, the model parameters and their upper bound of uncertainties are considered unknown.During two different exercise scenarios, the three controllers guided HR to follow the time-varying reference profile.However, ISMCbf showed higher quantitative performance by recording less Integral Squared Error (ISE) and Integral Time Absolute Error (ITAE) indices as compared to the other controllers.
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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 | 0.000 | 0.001 |
| 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) | 0.001 | 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".