Vanishing Events and Regularity-Conditioned Reachability in Linear Stieltjes Systems
Abstract
We study linear Stieltjes control systems in which actuation is concentrated at finitely many temporal events, and we ask what happens when one of those events progressively loses its atomic weight in the associated Stieltjes measure. For constant coefficients, ordinary finite-atomic reachability is governed by a truncated Krylov space and is therefore insensitive to the positive values of the event weights. A different picture emerges once trajectory regularity is imposed. In the supercritical super-g-Hölder regime, we minimize the largest event-normalized state jump and characterize exactly the terminal directions for which this cost remains uniformly bounded as a prescribed event weight tends to zero. The characterization combines what can be reached before the vulnerable event, a drift-cancellability condition at that event, and the directions that remain available afterwards. Ordinary reachability of the deleted-event system can therefore be strictly larger than bounded-cost reachability in the singular limit. We also separate two mechanisms of divergence: loss of ordinary reachability after deletion and failure of the intermediate compatibility condition. For compatible targets, the minimum cost converges to a constrained deleted-event problem. A dimensionless position--velocity benchmark motivated by pulsed proximity maneuvers shows the distinction explicitly.
Related
- Reachability and exact controllability of linear Stieltjes differential systems
- Super-g-Hölder Regularity in Stieltjes Dynamics: Atomic Structure, Exact Extremal Values, and Recovery of the Stieltjes Clock
- Selections of Set-Valued Maps under Stieltjes Clocks: Regularity, Variation, and Atomic Structure
- Scalable Reachability Analysis of Linear Continuous Systems with Property-Driven Time-Step Adaptation
- Oleinik estimate for Temple systems via vanishing viscosity limit
BibTeX
@misc{fernandez2026vanishing,
title = {{Vanishing Events and Regularity-Conditioned Reachability in Linear Stieltjes Systems}},
author = {Francisco J. Fernández},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17345},
eprint = {2610.17345},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17345},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Vanishing Events and Regularity-Conditioned Reachability in Linear Stieltjes Systems
AU - Francisco J. Fernández
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17345
UR - https://arxiv.org/abs/2610.17345
AB - We study linear Stieltjes control systems in which actuation is concentrated at finitely many temporal events, and we ask what happens when one of those events progressively loses its atomic weight in the associated Stieltjes measure. For constant coefficients, ordinary finite-atomic reachability is governed by a truncated Krylov space and is therefore insensitive to the positive values of the event weights. A different picture emerges once trajectory regularity is imposed. In the supercritical super-g-Hölder regime, we minimize the largest event-normalized state jump and characterize exactly the terminal directions for which this cost remains uniformly bounded as a prescribed event weight tends to zero. The characterization combines what can be reached before the vulnerable event, a drift-cancellability condition at that event, and the directions that remain available afterwards. Ordinary reachability of the deleted-event system can therefore be strictly larger than bounded-cost reachability in the singular limit. We also separate two mechanisms of divergence: loss of ordinary reachability after deletion and failure of the intermediate compatibility condition. For compatible targets, the minimum cost converges to a constrained deleted-event problem. A dimensionless position--velocity benchmark motivated by pulsed proximity maneuvers shows the distinction explicitly.
ER -