Control-Oriented Learning of Lagrangian and Hamiltonian Systems

Mohamadreza Ahmadi; Ufuk Topcu; Clarence Rowley

doi:10.23919/ACC.2018.8431726

Control-Oriented Learning of Lagrangian and Hamiltonian Systems

Mohamadreza Ahmadi, Ufuk Topcu, Clarence Rowley

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

3 Scopus citations

Abstract

We propose a method based on quadratic programming for learning control-oriented models of physical systems for which limited data from only one trajectory is available. To this end, we take advantage of the principle of least action from physics. We propose two methods based on quadratic programming to approximate either the Lagrangian or the Hamiltonian of the system from the data. We show how the learning methods based on convex optimization can accommodate symmetries about the underlying system if they are known a priori. Furthermore, we incorporate the error in the approximation to build a data-driven differential inclusion, that is suitable for control purposes. We illustrate the results by an example.

Original language	English (US)
Title of host publication	2018 Annual American Control Conference, ACC 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	520-525
Number of pages	6
ISBN (Print)	9781538654286
DOIs	https://doi.org/10.23919/ACC.2018.8431726
State	Published - Aug 9 2018
Event	2018 Annual American Control Conference, ACC 2018 - Milwauke, United States Duration: Jun 27 2018 → Jun 29 2018

Publication series

Name	Proceedings of the American Control Conference
Volume	2018-June
ISSN (Print)	0743-1619

Other

Other	2018 Annual American Control Conference, ACC 2018
Country	United States
City	Milwauke
Period	6/27/18 → 6/29/18

All Science Journal Classification (ASJC) codes

Electrical and Electronic Engineering

Access to Document

10.23919/ACC.2018.8431726

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Ahmadi, M., Topcu, U., & Rowley, C. (2018). Control-Oriented Learning of Lagrangian and Hamiltonian Systems. In 2018 Annual American Control Conference, ACC 2018 (pp. 520-525). [8431726] (Proceedings of the American Control Conference; Vol. 2018-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC.2018.8431726

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title = "Control-Oriented Learning of Lagrangian and Hamiltonian Systems",

abstract = "We propose a method based on quadratic programming for learning control-oriented models of physical systems for which limited data from only one trajectory is available. To this end, we take advantage of the principle of least action from physics. We propose two methods based on quadratic programming to approximate either the Lagrangian or the Hamiltonian of the system from the data. We show how the learning methods based on convex optimization can accommodate symmetries about the underlying system if they are known a priori. Furthermore, we incorporate the error in the approximation to build a data-driven differential inclusion, that is suitable for control purposes. We illustrate the results by an example.",

author = "Mohamadreza Ahmadi and Ufuk Topcu and Clarence Rowley",

year = "2018",

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Ahmadi, M, Topcu, U & Rowley, C 2018, Control-Oriented Learning of Lagrangian and Hamiltonian Systems. in 2018 Annual American Control Conference, ACC 2018., 8431726, Proceedings of the American Control Conference, vol. 2018-June, Institute of Electrical and Electronics Engineers Inc., pp. 520-525, 2018 Annual American Control Conference, ACC 2018, Milwauke, United States, 6/27/18. https://doi.org/10.23919/ACC.2018.8431726

Control-Oriented Learning of Lagrangian and Hamiltonian Systems. / Ahmadi, Mohamadreza; Topcu, Ufuk; Rowley, Clarence.

2018 Annual American Control Conference, ACC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 520-525 8431726 (Proceedings of the American Control Conference; Vol. 2018-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AB - We propose a method based on quadratic programming for learning control-oriented models of physical systems for which limited data from only one trajectory is available. To this end, we take advantage of the principle of least action from physics. We propose two methods based on quadratic programming to approximate either the Lagrangian or the Hamiltonian of the system from the data. We show how the learning methods based on convex optimization can accommodate symmetries about the underlying system if they are known a priori. Furthermore, we incorporate the error in the approximation to build a data-driven differential inclusion, that is suitable for control purposes. We illustrate the results by an example.

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