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 proceedingConference 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 languageEnglish (US)
Title of host publication2019 IEEE 58th Conference on Decision and Control, CDC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4292-4297
Number of pages6
ISBN (Electronic)9781728113982
DOIs
StatePublished - Dec 2019
Event58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France
Duration: Dec 11 2019Dec 13 2019

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2019-December
ISSN (Print)0743-1546

Conference

Conference58th IEEE Conference on Decision and Control, CDC 2019
CountryFrance
CityNice
Period12/11/1912/13/19

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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  • 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). [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