Linearization by Redundancy and Stabilization of Nonlinear Dynamical Systems: A State Transformation Approach
Bibliographic record
Abstract
This paper presents a new concept of linearization of nonlinear dynamical systems. The used approach relies on immersion and static state feedback transformations. As a first contribution, we show how we can make the transformed immersed system dynamics available for control. Therefore, the vector of control in the immersed system dynamics is now getting out of any premultiplying column matrix. The main stream of our approach is that the immersed system dynamics is regarded as the nonreduced-order dynamics of a mechanical constrained system that can be expressed in terms of an unconstrained (or initial) dynamics and a term of constraint. Further, a systematic way of expressing the immersed dynamics in terms of an initial dynamics and a term of constraint is discussed. At this point, our linearization approach consists of designing an immersion and a static state feedback which render the initial dynamics linear, however, the whole transformed immersed system dynamics is still nonlinear. In order to demonstrate the effectiveness of the presented linearization approach, we show that the stabilization problem for the original nonlinear system dynamics is reduced to a stabilization problem for a linear system dynamics that represents the initial dynamics of the transformed immersed system dynamics. We believe that our linearization approach may be very useful for the global output feedback tracking control problem of nonlinear 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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 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".