Recursive Input-Output Linearization for Slow-Fast Realization of Nonholonomic Hamiltonian Control Systems
Bibliographic record
Abstract
In this paper, we study a slow-fast realization of nonholonomic Hamiltonian control systems mediated by strong friction forces which is viewed as a singular perturbation of the nonholonomic system. We propose a systematic decomposition of the perturbed dynamics into slow and fast directions using the kinetic energy metric and the geometry of friction forces. The slow manifold is identified by a set of invariance conditions resulting in partial differential equations that generally do not have an analytic solution. We approximate the slow manifold along with the control inputs with power series and show that using this approximation the invariance conditions admit an inherent recursion. Accordingly, we develop a recursive procedure to perform dynamic input-output linearization of the approximated slow system. We consider the output trajectory tracking problem using a PD control law on the Nth order approximation of the slow manifold. Closed-loop stability analysis is performed on both the slow manifold and the full phase space of the system. We prove that if the internal dynamics of the nonholonomic system is exponentially stable, then the perturbed system remains asymptotically stable. Moreover, we prove that the output error dynamics is uniformly bounded when applying the approximated control law, with bounds dependent on the control gains and strength of the friction force. Our approach is illustrated through a numerical case study on a differential robot.
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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 | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 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".