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Universal Approximation of Flows of Control Systems by Recurrent Neural Networks
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control). (Digital Futures)ORCID iD: 0009-0006-0657-4103
Eindhoven University of Technology, Control Systems Group, EE Dept., MB Eindhoven, The Netherlands.
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control). KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre. (Digital Futures)ORCID iD: 0000-0001-9940-5929
2023 (English)In: 2023 62nd IEEE Conference on Decision and Control, CDC 2023, Institute of Electrical and Electronics Engineers (IEEE) , 2023, p. 2320-2327Conference paper, Published paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE) , 2023. p. 2320-2327
Keywords [en]
Machine learning, Neural networks, Nonlinear systems
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-343710DOI: 10.1109/CDC49753.2023.10383457ISI: 001166433801150Scopus ID: 2-s2.0-85184831372OAI: oai:DiVA.org:kth-343710DiVA, id: diva2:1839905
Conference
62nd IEEE Conference on Decision and Control, CDC 2023, Singapore, Singapore, Dec 13 2023 - Dec 15 2023
Note

QC 20240222

Part of ISBN  979-8-3503-0124-3

Available from: 2024-02-22 Created: 2024-02-22 Last updated: 2024-03-26Bibliographically approved

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Aguiar, MiguelJohansson, Karl H.

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