The University of Southampton
University of Southampton Institutional Repository

Data-driven continuous-time optimal control: a unified framework using orthogonal functions

Data-driven continuous-time optimal control: a unified framework using orthogonal functions
Data-driven continuous-time optimal control: a unified framework using orthogonal functions
We study data-driven optimal control of continuous-time linear systems over
finite- and infinite-time horizons. Our approach builds on our continuous-time
version of Willems et al.’s fundamental lemma and on the use of orthogonal basis
functions to approximate system trajectories. We show that the solution to an
optimal control problem can be approximated by a finite linear combination of
basis functions and we establish error bounds for such approximations. Moreover,
we approximately solve the algebraic Riccati equation and the associated optimal
controller gain directly from data, opening up the possibility of optimal controller
design directly from data analogue devices.
Approximation error, Data-driven methods, Optimal Control, Orthogonal bases, Willems’ fundamental lemma
Schmitz, Philipp
63c851f6-1d4a-4c8d-8acf-cb799cf30fd4
Worthmann, Karl
9ff70f79-8aeb-47f1-a1b6-8a1c505b2495
Faulwasser, Timm
6ea4b017-0253-41a0-b68d-8a7cd4241720
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Schmitz, Philipp
63c851f6-1d4a-4c8d-8acf-cb799cf30fd4
Worthmann, Karl
9ff70f79-8aeb-47f1-a1b6-8a1c505b2495
Faulwasser, Timm
6ea4b017-0253-41a0-b68d-8a7cd4241720
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b

Schmitz, Philipp, Worthmann, Karl, Faulwasser, Timm and Rapisarda, Paolo (2026) Data-driven continuous-time optimal control: a unified framework using orthogonal functions. Mathematics of Control, Signals, and Systems. (doi:10.1007/s00498-026-00444-0).

Record type: Article

Abstract

We study data-driven optimal control of continuous-time linear systems over
finite- and infinite-time horizons. Our approach builds on our continuous-time
version of Willems et al.’s fundamental lemma and on the use of orthogonal basis
functions to approximate system trajectories. We show that the solution to an
optimal control problem can be approximated by a finite linear combination of
basis functions and we establish error bounds for such approximations. Moreover,
we approximately solve the algebraic Riccati equation and the associated optimal
controller gain directly from data, opening up the possibility of optimal controller
design directly from data analogue devices.

Text
main - Accepted Manuscript
Available under License Creative Commons Attribution.
Download (805kB)

More information

Accepted/In Press date: 19 March 2026
Published date: 8 April 2026
Additional Information: Publisher Copyright: © The Author(s) 2026.
Keywords: Approximation error, Data-driven methods, Optimal Control, Orthogonal bases, Willems’ fundamental lemma

Identifiers

Local EPrints ID: 511045
URI: http://eprints.soton.ac.uk/id/eprint/511045
PURE UUID: ec0699bd-9c48-4f1e-9c9f-5488cb78c4c2
ORCID for Paolo Rapisarda: ORCID iD orcid.org/0000-0001-9682-8977

Catalogue record

Date deposited: 29 Apr 2026 16:39
Last modified: 30 Apr 2026 01:40

Export record

Altmetrics

Contributors

Author: Philipp Schmitz
Author: Karl Worthmann
Author: Timm Faulwasser
Author: Paolo Rapisarda ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×