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A continuous-time fundamental lemma and its application in data-driven optimal control

A continuous-time fundamental lemma and its application in data-driven optimal control
A continuous-time fundamental lemma and its application in data-driven optimal control
Data-driven control of discrete-time and continuous-time systems is of tremendous research interest. In this paper, we explore data-driven optimal control of continuous-time linear systems using input-output data. Based on a density result, we rigorously derive error bounds for finite-order polynomial approximations of elements of the system behavior. To this end, we leverage a link between latent variables and flat outputs of controllable systems. Combined with a continuous-time counterpart of Willems et al.’s fundamental lemma, we characterize the suboptimality resulting from polynomial approximations in data-driven linear-quadratic optimal control. Finally, we draw upon a numerical example to illustrate our results.
Continuous time, Data-driven control, Differential flatness, Identifiable, Persistency of excitation, Polynomial approximation
0167-6911
Schmitz, Phillip
d324d4bb-065c-4b32-9a9d-1ae86b90cd09
Faulwasser, Timm
145bd776-a976-4709-81c9-0d531655e184
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Worthmann, Karl
fc9e0546-9839-47ee-8816-8504756c3eef
Schmitz, Phillip
d324d4bb-065c-4b32-9a9d-1ae86b90cd09
Faulwasser, Timm
145bd776-a976-4709-81c9-0d531655e184
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Worthmann, Karl
fc9e0546-9839-47ee-8816-8504756c3eef

Schmitz, Phillip, Faulwasser, Timm, Rapisarda, Paolo and Worthmann, Karl (2024) A continuous-time fundamental lemma and its application in data-driven optimal control. Systems & Control Letters, 194, [105950]. (doi:10.1016/j.sysconle.2024.105950).

Record type: Article

Abstract

Data-driven control of discrete-time and continuous-time systems is of tremendous research interest. In this paper, we explore data-driven optimal control of continuous-time linear systems using input-output data. Based on a density result, we rigorously derive error bounds for finite-order polynomial approximations of elements of the system behavior. To this end, we leverage a link between latent variables and flat outputs of controllable systems. Combined with a continuous-time counterpart of Willems et al.’s fundamental lemma, we characterize the suboptimality resulting from polynomial approximations in data-driven linear-quadratic optimal control. Finally, we draw upon a numerical example to illustrate our results.

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More information

Accepted/In Press date: 12 October 2024
e-pub ahead of print date: 30 October 2024
Published date: 30 October 2024
Keywords: Continuous time, Data-driven control, Differential flatness, Identifiable, Persistency of excitation, Polynomial approximation

Identifiers

Local EPrints ID: 495252
URI: http://eprints.soton.ac.uk/id/eprint/495252
ISSN: 0167-6911
PURE UUID: 700e2931-57d1-44f5-815c-dc89830f38c2

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Date deposited: 04 Nov 2024 17:37
Last modified: 04 Nov 2024 17:40

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Contributors

Author: Phillip Schmitz
Author: Timm Faulwasser
Author: Paolo Rapisarda
Author: Karl Worthmann

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