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Grüne, Lars ; Sperl, Mario:
Decaying Sensitivity of the Zero Solution for a Class of Nonlinear Optimal Control Problems.
Bayreuth
,
2026
. - 6 S.
DOI: https://doi.org/10.48550/arXiv.2602.05020
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| Projekttitel: |
Offizieller Projekttitel Projekt-ID Nichtlineare optimale Feedback-Regelung mit tiefen neuronalen Netzen ohne den Fluch der Dimension: Räumlich abnehmende Sensitivität und nichtglatte Probleme 463912816 |
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| Projektfinanzierung: |
Deutsche Forschungsgemeinschaft |
Abstract
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.