Consistent approximation of optimal control problems using Bernstein polynomials

Venanzio Cichella; Isaac Kaminer; Claire Walton; Naira Hovakimyan; Antonio M. Pascoal

doi:10.1109/CDC40024.2019.9029677

Consistent approximation of optimal control problems using Bernstein polynomials

Venanzio Cichella, Isaac Kaminer, Claire Walton, Naira Hovakimyan, Antonio M. Pascoal

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

Abstract

We present a direct method for the solution of nonlinear optimal control problems based on Bernstein polynomial approximations. We show, using a rigorous setting, that the proposed method yields consistent approximations of time continuous optimal control problems. We demonstrate that the method can also be used for the estimation of optimal control problems costates. This result leads to the formulation of the Covector Mapping Theorem for Bernstein polynomial approximation. Finally, we exploit the numerical and geometric properties of Bernstein polynomials, and illustrate the advantages of the method through numerical examples.

Original language	English (US)
Title of host publication	2019 IEEE 58th Conference on Decision and Control, CDC 2019
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4292-4297
Number of pages	6
ISBN (Electronic)	9781728113982
DOIs	https://doi.org/10.1109/CDC40024.2019.9029677
State	Published - Dec 2019
Event	58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France Duration: Dec 11 2019 → Dec 13 2019

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2019-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	58th IEEE Conference on Decision and Control, CDC 2019
Country/Territory	France
City	Nice
Period	12/11/19 → 12/13/19

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Online availability

10.1109/CDC40024.2019.9029677

Library availability

Discover UIUC Full Text

Cite this

Cichella, V., Kaminer, I., Walton, C., Hovakimyan, N., & Pascoal, A. M. (2019). Consistent approximation of optimal control problems using Bernstein polynomials. In 2019 IEEE 58th Conference on Decision and Control, CDC 2019 (pp. 4292-4297). Article 9029677 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC40024.2019.9029677

Consistent approximation of optimal control problems using Bernstein polynomials. / Cichella, Venanzio; Kaminer, Isaac; Walton, Claire et al.
2019 IEEE 58th Conference on Decision and Control, CDC 2019. Institute of Electrical and Electronics Engineers Inc., 2019. p. 4292-4297 9029677 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December).

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

Cichella, V, Kaminer, I, Walton, C, Hovakimyan, N & Pascoal, AM 2019, Consistent approximation of optimal control problems using Bernstein polynomials. in 2019 IEEE 58th Conference on Decision and Control, CDC 2019., 9029677, Proceedings of the IEEE Conference on Decision and Control, vol. 2019-December, Institute of Electrical and Electronics Engineers Inc., pp. 4292-4297, 58th IEEE Conference on Decision and Control, CDC 2019, Nice, France, 12/11/19. https://doi.org/10.1109/CDC40024.2019.9029677

Cichella V, Kaminer I, Walton C, Hovakimyan N, Pascoal AM. Consistent approximation of optimal control problems using Bernstein polynomials. In 2019 IEEE 58th Conference on Decision and Control, CDC 2019. Institute of Electrical and Electronics Engineers Inc. 2019. p. 4292-4297. 9029677. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC40024.2019.9029677

@inproceedings{6fa3175bae824e9f8d8a553c23539c9d,

title = "Consistent approximation of optimal control problems using Bernstein polynomials",

abstract = "We present a direct method for the solution of nonlinear optimal control problems based on Bernstein polynomial approximations. We show, using a rigorous setting, that the proposed method yields consistent approximations of time continuous optimal control problems. We demonstrate that the method can also be used for the estimation of optimal control problems costates. This result leads to the formulation of the Covector Mapping Theorem for Bernstein polynomial approximation. Finally, we exploit the numerical and geometric properties of Bernstein polynomials, and illustrate the advantages of the method through numerical examples.",

author = "Venanzio Cichella and Isaac Kaminer and Claire Walton and Naira Hovakimyan and Pascoal, {Antonio M.}",

note = "Publisher Copyright: {\textcopyright} 2019 IEEE.; 58th IEEE Conference on Decision and Control, CDC 2019 ; Conference date: 11-12-2019 Through 13-12-2019",

year = "2019",

month = dec,

doi = "10.1109/CDC40024.2019.9029677",

language = "English (US)",

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

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "4292--4297",

booktitle = "2019 IEEE 58th Conference on Decision and Control, CDC 2019",

address = "United States",

}

TY - GEN

T1 - Consistent approximation of optimal control problems using Bernstein polynomials

AU - Cichella, Venanzio

AU - Kaminer, Isaac

AU - Walton, Claire

AU - Hovakimyan, Naira

AU - Pascoal, Antonio M.

PY - 2019/12

Y1 - 2019/12

N2 - We present a direct method for the solution of nonlinear optimal control problems based on Bernstein polynomial approximations. We show, using a rigorous setting, that the proposed method yields consistent approximations of time continuous optimal control problems. We demonstrate that the method can also be used for the estimation of optimal control problems costates. This result leads to the formulation of the Covector Mapping Theorem for Bernstein polynomial approximation. Finally, we exploit the numerical and geometric properties of Bernstein polynomials, and illustrate the advantages of the method through numerical examples.

AB - We present a direct method for the solution of nonlinear optimal control problems based on Bernstein polynomial approximations. We show, using a rigorous setting, that the proposed method yields consistent approximations of time continuous optimal control problems. We demonstrate that the method can also be used for the estimation of optimal control problems costates. This result leads to the formulation of the Covector Mapping Theorem for Bernstein polynomial approximation. Finally, we exploit the numerical and geometric properties of Bernstein polynomials, and illustrate the advantages of the method through numerical examples.

UR - http://www.scopus.com/inward/record.url?scp=85082461132&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85082461132&partnerID=8YFLogxK

U2 - 10.1109/CDC40024.2019.9029677

DO - 10.1109/CDC40024.2019.9029677

M3 - Conference contribution

AN - SCOPUS:85082461132

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 4292

EP - 4297

BT - 2019 IEEE 58th Conference on Decision and Control, CDC 2019

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 58th IEEE Conference on Decision and Control, CDC 2019

Y2 - 11 December 2019 through 13 December 2019

ER -

Consistent approximation of optimal control problems using Bernstein polynomials

Abstract

Publication series

Conference

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this