Prescribed-time tracking control for nonlinear systems with linear time-varying state feedback
Bibliographic record
Abstract
In this article, the prescribed-time tracking control problem is taken into consideration for a class of strict feedback single-input-single-output(SISO) systems with unknown nonlinear items. A novel 3-segment piecewise parametric function is introduced in the prescribed time. By utilising the unique positive definite solution of the parametric Lyapunov equation (PLE), a linear state feedback controller with a time-varying gain is designed to achieve prescribed-time output tracking control with the impact of unknown nonlinear terms attenuated. The existing parametric function has a disadvantage that it is not differentiable in some time spots, therefore it is modified to be differentiable and bounded during the whole time span. It is proved that with the proposed linear time-varying controller, the Lyapunov-like function is bounded, which implies that all the state signals, control signals, and the output tracking error are bounded not only before the prescribed time but also beyond the prescribed time. Finally, the simulation results and simulation comparisons on a second-order nonlinear system verify the effectiveness of the proposed control mechanism. Moreover, the proposed controller is applied to control a tower crane, which demonstrates the feasibility of the proposed method in applications.
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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) | 0.000 | 0.000 |
| 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".