A variable structure controller for a class of uncertain systems with unknown uncertainty bounding function
Bibliographic record
Abstract
In designing variable structure controllers when the upper bounding function for the matched system uncertainty is not known, the controller design remains to be a challenge. The main purpose of this paper is to solve this problem for a class of uncertain systems with matched uncertainties. To this end, a variable structure controller is proposed whose novelty lies in the form of the controller structure and also the mechanism introduced to update the controller's gain. Unlike most existing variable structure controllers, the new design does not require the upper bounding function for the uncertainty to be exactly known (for the bounded uncertainty case, the knowledge of the upper bound is not needed). It is proved that asymptotic stability of closed-loop systems can be guaranteed globally. One drawback for this controller is that the controller gain may go unbounded if the noises or other system uncertainties are not considered and are present. The other drawback is the well known controller chattering problem. To deal with these drawbacks, we modify the controller's gain update law and replace its discontinuous term with a continuous approximation, and hence propose a modified variable structure controller. With the modified variable structure controller, all the closed-loop signals are guaranteed to be bounded and the states can be driven to an arbitrarily small neighborhood of the origin. The price paid for this is the loss of asymptotic stability. Inspired by the equivalent control concept, a method for estimating the uncertainty is also derived when the modified variable structure controller is applied. Simulation examples are given to show the effectiveness of the controller and uncertainty estimation scheme
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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 | 0.001 | 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".