A collocation-based approach to solve the finite horizon Hamilton-Jacobi-Bellman equation

Michael Mercurio, Nagavenkat Adurthi, Puneet Singla, Manoranjan Majji

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

This paper presents an approach to derive the optimal feedback control laws by solving the finite time Hamilton Jacobi Ballman equation. Conventional methods to solve the HJB equation suffer from curse of dimensionality as the number of spatial variables is equal to the state dimension, which is twice the number of degrees of freedom of a mechanical system. The presented approach exploits the recently developed non-product quadrature method known as Conjugate Unscented Transformation (CUT) in conjunction with sparse approximation tools to devise a collocation method to solve the HJB equation in a computationally efficient manner. Numerical simulation results are presented to assess the efficacy of the proposed ideas.

Original languageEnglish (US)
Title of host publication2016 American Control Conference, ACC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3322-3327
Number of pages6
ISBN (Electronic)9781467386821
DOIs
StatePublished - Jul 28 2016
Event2016 American Control Conference, ACC 2016 - Boston, United States
Duration: Jul 6 2016Jul 8 2016

Publication series

NameProceedings of the American Control Conference
Volume2016-July
ISSN (Print)0743-1619

Other

Other2016 American Control Conference, ACC 2016
CountryUnited States
CityBoston
Period7/6/167/8/16

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All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

Mercurio, M., Adurthi, N., Singla, P., & Majji, M. (2016). A collocation-based approach to solve the finite horizon Hamilton-Jacobi-Bellman equation. In 2016 American Control Conference, ACC 2016 (pp. 3322-3327). [7525430] (Proceedings of the American Control Conference; Vol. 2016-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2016.7525430