DYNAMIC SLIDING MANIFOLDS FOR REALIZATION OF HIGH INDEX DIFFERENTIAL‐ALGEBRAIC SYSTEMS
Bibliographic record
Abstract
ABSTRACT Differential‐algebraic equation (DAE) systems present a number of difficult problems in nonlinear simulation and control. One of the key difficulties is that DAEs are not expressed in an explicit state space form required by many simulation and control design methods. In this paper, the problem is addressed using a new approach that constructs an explicit state space approximation of the DAEs using a sliding controller. The state space model can in turn be used with existing nonlinear control and simulation methods. This procedure, known as realization, is achieved by developing a boundary layer sliding controller with a dynamic sliding manifold. The approach builds on previous realization methods proposed by the author that employ a static sliding control surface. The approach is generalized by employing a dynamic sliding manifold which allows much greater freedom in determining optimality, robustness, and convergence of the realization than previous methods allow. The necessary criteria for key properties such as convergence, stability, and controllability of this new method are proven using a special type of sliding normal form. Furthermore, the important property of observability for sliding realizations is established for the first time by analyzing the convergence of local eigenvectors of the approximation. Together these results establish a new general framework for realization of a large class of nonlinear high index DAE systems.
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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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".