at Google ScholarTitle data
Grüne, Lars ; Sperl, Mario:
Decaying Sensitivity of the Zero Solution for a Class of Nonlinear Optimal Control Problems.
Bayreuth
,
2026
. - 6 p.
DOI: https://doi.org/10.48550/arXiv.2602.05020
Project information
| Project title: |
Project's official title Project's id Nichtlineare optimale Feedback-Regelung mit tiefen neuronalen Netzen ohne den Fluch der Dimension: Räumlich abnehmende Sensitivität und nichtglatte Probleme 463912816 |
|---|---|
| Project financing: |
Deutsche Forschungsgemeinschaft |
Abstract in another language
We study spatial decay properties of sensitivities in a nonlinear optimal control problem with a graph-structured interaction topology. For a problem with nonlinear decoupled dynamics and quadratic cost, we show that a localized perturbation of the zero reference leads to an optimal trajectory that decays exponentially with the graph distance. The analysis, based on a nonlinear controllability condition, provides a first step toward extending known spatial decay results from linear–quadratic to nonlinear systems. A numerical example illustrates the theoretical findings.