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
8 April 2026
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).
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.
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- Accepted Manuscript
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
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Date deposited: 29 Apr 2026 16:39
Last modified: 30 Apr 2026 01:40
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Contributors
Author:
Philipp Schmitz
Author:
Karl Worthmann
Author:
Timm Faulwasser
Author:
Paolo Rapisarda
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