Bibliographic record
Abstract
Just as an explicit parameterisation of system dynamics by state, i.e., a choice of coordinates, can impede the identification of general structure, so it is too with an explicit parameterisation of system dynamics by control. However, such explicit and fixed parameterisation by control is commonplace in control theory, leading to definitions, methodologies, and results that depend in unexpected ways on control parameterisation. In this paper a framework is presented for modelling systems in geometric control theory in a manner that does not make any choice of parameterisation by control; the systems are called "tautological control systems." For the framework to be coherent, it relies in a fundamental way on topologies for spaces of vector fields. As such, classes of systems are considered possessing a variety of degrees of regularity: finitely differentiable; Lipschitz; smooth; real analytic. In each case, explicit geometric seminorms are provided for the topologies of spaces of vector fields that enable straightforward descriptions of time-varying vector fields and control systems. As part of the development, theorems are proved for regular (including real analytic) dependence on initial conditions of flows of vector fields depending measurably on time. Classes of "ordinary" control systems are characterised that interact with the regularity under consideration in a comprehensive way. In this framework, for example, the statement that "a smooth or real analytic control-affine system is a smooth or real analytic control system" becomes a theorem. Correspondences between ordinary control systems and tautological control systems are carefully examined, and trajectory correspondence between the two classes is proved for control-affine systems and for systems with general control dependence when the control set is compact.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.011 | 0.002 |
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".