ON UNIQUENESS OF FILIPPOV’S SOLUTIONS FOR NON-SMOOTH SYSTEMS HAVING MULTIPLE DISCONTINUITY SURFACES WITH APPLICATIONS TO ROBOTIC CONTROL SYSTEMS
Bibliographic record
Abstract
Analysis of the uniqueness of Filippov's solutions to non-smooth robotic control systems is important before the solutions can be sought. Such an analysis is extremely challenging when the discontinuity surface is the intersection of multiple discontinuity surfaces. The key step is to study the intersections of the convex sets from Filippov's inclusions and their associated sets containing vectors tangent to the discontinuity surfaces. For practical non-smooth robotic systems, due to their complexities, the determination of the intersections of these sets symbolically is extremely difficult if not impossible. In this paper, we propose a method such that the determinations of the intersections become feasible. Two examples of practical non-smooth robotic control systems are presented to demonstrate the efficacy of the method. The work contributes significantly to the analysis of non-smooth systems where the proof of the uniqueness of Filippov’s solution is crucial to keep the mathematical model relevant to physical systems and to ensure the numerical solutions can be sought.
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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 | 0.002 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".