Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Optimization and Control

arXiv:2210.06053 (math)
[Submitted on 12 Oct 2022]

Title:Sensitivity analysis of value functional of fractional optimal control problem with application to construction of optimal feedback control

Authors:Mikhail Gomoyunov
View PDF
Abstract:We consider an optimal control problem for a dynamical system described by a Caputo fractional differential equation and a terminal cost functional. We prove that, under certain assumptions, the (non-smooth, in general) value functional of this problem has a property of directional differentiability of order $\alpha$. As an application of this result, we propose a new method for constructing an optimal positional (feedback) control strategy.
Subjects: Optimization and Control (math.OC)
MSC classes: 49N35, 34A08, 49L12, 49J52
Cite as: arXiv:2210.06053 [math.OC]
  (or arXiv:2210.06053v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2210.06053
Journal reference: Appl. Math. Optim. 88, 41 (2023)
Related DOI: https://doi.org/10.1007/s00245-023-10022-4

Submission history

From: Mikhail Gomoyunov [view email]
[v1] Wed, 12 Oct 2022 09:46:29 UTC (42 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.OC
< prev   |   next >
new | recent | 2022-10
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)