Universal Approximation of Flows of Control Systems by Recurrent Neural Networks

Miguel Aguiar; Amritam Das; Karl H. Johansson

doi:10.1109/CDC49753.2023.10383457

Universal Approximation of Flows of Control Systems by Recurrent Neural Networks

Miguel Aguiar
, Amritam Das
, Karl H. Johansson

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

4 Citaten (Scopus)

35 Downloads (Pure)

Samenvatting

We consider the problem of approximating flow functions of continuous-time dynamical systems with inputs. It is well-known that continuous-time recurrent neural networks are universal approximators of this type of system. In this paper, we prove that an architecture based on discrete-time recurrent neural networks universally approximates flows of continuous-time dynamical systems with inputs. The required assumptions are shown to hold for systems whose dynamics are well-behaved ordinary differential equations and with practically relevant classes of input signals. This enables the use of off-the-shelf solutions for learning such flow functions in continuous-time from sampled trajectory data.

Originele taal-2	Engels
Titel	2023 62nd IEEE Conference on Decision and Control, CDC 2023
Uitgeverij	Institute of Electrical and Electronics Engineers
Pagina's	2320-2327
Aantal pagina's	8
ISBN van elektronische versie	979-8-3503-0124-3
DOI's	https://doi.org/10.1109/CDC49753.2023.10383457
Status	Gepubliceerd - 19 jan. 2024
Evenement	2023 62nd IEEE Conference on Decision and Control (CDC) - Singapore, Singapore Duur: 13 dec. 2023 → 15 dec. 2023 Congresnummer: 62

Publicatie series

Naam	Proceedings of the IEEE Conference on Decision and Control
ISSN van geprinte versie	0743-1546
ISSN van elektronische versie	2576-2370

Congres

Congres	2023 62nd IEEE Conference on Decision and Control (CDC)
Verkorte titel	CDC 2023
Land/Regio	Singapore
Stad	Singapore
Periode	13/12/23 → 15/12/23

Toegang tot document

10.1109/CDC49753.2023.10383457

pdfDefinitieve gepubliceerde versie, 525 KBLicentie: TAVERNE

Andere bestanden en links

Link naar publicatie in Scopus

Citeer dit

Aguiar, M., Das, A., & Johansson, K. H. (2024). Universal Approximation of Flows of Control Systems by Recurrent Neural Networks. In 2023 62nd IEEE Conference on Decision and Control, CDC 2023 (blz. 2320-2327). Artikel 10383457 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC49753.2023.10383457

@inproceedings{09555f759cfb48ef8837558575ea56bb,

title = "Universal Approximation of Flows of Control Systems by Recurrent Neural Networks",

abstract = "We consider the problem of approximating flow functions of continuous-time dynamical systems with inputs. It is well-known that continuous-time recurrent neural networks are universal approximators of this type of system. In this paper, we prove that an architecture based on discrete-time recurrent neural networks universally approximates flows of continuous-time dynamical systems with inputs. The required assumptions are shown to hold for systems whose dynamics are well-behaved ordinary differential equations and with practically relevant classes of input signals. This enables the use of off-the-shelf solutions for learning such flow functions in continuous-time from sampled trajectory data.",

keywords = "Machine learning, Neural networks, Nonlinear systems",

author = "Miguel Aguiar and Amritam Das and Johansson, \{Karl H.\}",

year = "2024",

month = jan,

day = "19",

doi = "10.1109/CDC49753.2023.10383457",

language = "English",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers",

pages = "2320--2327",

booktitle = "2023 62nd IEEE Conference on Decision and Control, CDC 2023",

address = "United States",

note = "62nd IEEE Conference on Decision and Control, CDC 2023, CDC 2023 ; Conference date: 13-12-2023 Through 15-12-2023",

}

Aguiar, M, Das, A & Johansson, KH 2024, Universal Approximation of Flows of Control Systems by Recurrent Neural Networks. in 2023 62nd IEEE Conference on Decision and Control, CDC 2023., 10383457, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers, blz. 2320-2327, 2023 62nd IEEE Conference on Decision and Control (CDC), Singapore, Singapore, 13/12/23. https://doi.org/10.1109/CDC49753.2023.10383457

Universal Approximation of Flows of Control Systems by Recurrent Neural Networks. / Aguiar, Miguel; Das, Amritam; Johansson, Karl H.
2023 62nd IEEE Conference on Decision and Control, CDC 2023. Institute of Electrical and Electronics Engineers, 2024. blz. 2320-2327 10383457 (Proceedings of the IEEE Conference on Decision and Control).

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

TY - GEN

T1 - Universal Approximation of Flows of Control Systems by Recurrent Neural Networks

AU - Aguiar, Miguel

AU - Das, Amritam

AU - Johansson, Karl H.

N1 - Conference code: 62

PY - 2024/1/19

Y1 - 2024/1/19

N2 - We consider the problem of approximating flow functions of continuous-time dynamical systems with inputs. It is well-known that continuous-time recurrent neural networks are universal approximators of this type of system. In this paper, we prove that an architecture based on discrete-time recurrent neural networks universally approximates flows of continuous-time dynamical systems with inputs. The required assumptions are shown to hold for systems whose dynamics are well-behaved ordinary differential equations and with practically relevant classes of input signals. This enables the use of off-the-shelf solutions for learning such flow functions in continuous-time from sampled trajectory data.

AB - We consider the problem of approximating flow functions of continuous-time dynamical systems with inputs. It is well-known that continuous-time recurrent neural networks are universal approximators of this type of system. In this paper, we prove that an architecture based on discrete-time recurrent neural networks universally approximates flows of continuous-time dynamical systems with inputs. The required assumptions are shown to hold for systems whose dynamics are well-behaved ordinary differential equations and with practically relevant classes of input signals. This enables the use of off-the-shelf solutions for learning such flow functions in continuous-time from sampled trajectory data.

KW - Machine learning

KW - Neural networks

KW - Nonlinear systems

UR - https://www.scopus.com/pages/publications/85184831372

U2 - 10.1109/CDC49753.2023.10383457

DO - 10.1109/CDC49753.2023.10383457

M3 - Conference contribution

AN - SCOPUS:85184831372

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 2320

EP - 2327

BT - 2023 62nd IEEE Conference on Decision and Control, CDC 2023

PB - Institute of Electrical and Electronics Engineers

T2 - 62nd IEEE Conference on Decision and Control, CDC 2023

Y2 - 13 December 2023 through 15 December 2023

ER -

Universal Approximation of Flows of Control Systems by Recurrent Neural Networks

Samenvatting

Publicatie series

Congres

Toegang tot document

Andere bestanden en links

Vingerafdruk

Citeer dit