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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

1 Citation (Scopus)

3 Downloads (Pure)

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.

Original language	English
Title of host publication	2023 62nd IEEE Conference on Decision and Control, CDC 2023
Publisher	Institute of Electrical and Electronics Engineers
Pages	2320-2327
Number of pages	8
ISBN (Electronic)	979-8-3503-0124-3
DOIs	https://doi.org/10.1109/CDC49753.2023.10383457
Publication status	Published - 19 Jan 2024
Event	62nd IEEE Conference on Decision and Control, CDC 2023 - Singapore, Singapore Duration: 13 Dec 2023 → 15 Dec 2023 Conference number: 62

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	62nd IEEE Conference on Decision and Control, CDC 2023
Abbreviated title	CDC 2023
Country/Territory	Singapore
City	Singapore
Period	13/12/23 → 15/12/23

Keywords

Machine learning
Neural networks
Nonlinear systems

Access to Document

10.1109/CDC49753.2023.10383457

pdfFinal published version, 525 KBLicence: TAVERNE

Cite this

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 (pp. 2320-2327). Article 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, pp. 2320-2327, 62nd IEEE Conference on Decision and Control, CDC 2023, 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. p. 2320-2327 10383457 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › 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 - http://www.scopus.com/inward/record.url?scp=85184831372&partnerID=8YFLogxK

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

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this