A multilevel approach for stochastic nonlinear optimal control

Jasra, A; Heng, J; Xu, Y; Bishop, AN

A multilevel approach for stochastic nonlinear optimal control

Jasra, A Heng, J Xu, Y Bishop, AN

Permalink

Publisher:: Taylor and Francis
Publication Type:: Journal Article
Citation:: International Journal of Control, 2022, 95, (5), pp. 1290-1304
Issue Date:: 2022-01-01

Open Access

Copyright Clearance Process

Recently Added
In Progress
Open Access

This item is open access.

Adobe PDF

Download Accepted versionAdobe PDF (551.41 kB)

View on publisher's site

View statistics

Full metadata record

Field	Value	Language
dc.contributor.author	Jasra, A
dc.contributor.author	Heng, J
dc.contributor.author	Xu, Y
dc.contributor.author	Bishop, AN
dc.date.accessioned	2023-03-09T23:04:58Z
dc.date.available	2023-03-09T23:04:58Z
dc.date.issued	2022-01-01
dc.identifier.citation	International Journal of Control, 2022, 95, (5), pp. 1290-1304
dc.identifier.issn	0020-7179
dc.identifier.issn	1366-5820
dc.identifier.uri	http://hdl.handle.net/10453/166914
dc.description.abstract	We consider a class of finite-time horizon nonlinear stochastic optimal control problem. Although the optimal control admits a path integral representation for this class of control problems, efficient computation of the associated path integrals remains a challenging task. We propose a new Monte Carlo approach that significantly improves upon existing methodology. We tackle the issue of exponential growth in variance with the time horizon by casting optimal control estimation as a smoothing problem for a state-space model, and applying smoothing algorithms based on particle Markov chain Monte Carlo. To further reduce the cost, we then develop a multilevel Monte Carlo method which allows us to obtain an estimator of the optimal control with (Formula presented.) mean squared error with a cost of (Formula presented.). In contrast, a cost of (Formula presented.) is required for the existing methodology to achieve the same mean squared error. Our approach is illustrated on two numerical examples.
dc.language	en
dc.publisher	Taylor and Francis
dc.relation.ispartof	International Journal of Control
dc.relation.isbasedon	10.1080/00207179.2020.1849805
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	“This is an Accepted Manuscript of an article published by Taylor & Francis in A multilevel approach for stochastic nonlinear optimal control on 03 Dec 2020 , available online: https://www.tandfonline.com/doi/full/10.1080/00207179.2020.1849805
dc.subject	0102 Applied Mathematics, 0906 Electrical and Electronic Engineering, 0913 Mechanical Engineering
dc.subject.classification	Industrial Engineering & Automation
dc.title	A multilevel approach for stochastic nonlinear optimal control
dc.type	Journal Article
utslib.citation.volume	95
utslib.for	0102 Applied Mathematics
utslib.for	0906 Electrical and Electronic Engineering
utslib.for	0913 Mechanical Engineering
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - CHT - Health Technologies
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Biomedical Engineering
pubs.organisational-group	/University of Technology Sydney/Centre for Health Technologies (CHT)
utslib.copyright.status	open_access	*
pubs.consider-herdc	true
dc.date.updated	2023-03-09T23:04:57Z
pubs.issue	5
pubs.publication-status	Published
pubs.volume	95
utslib.citation.issue	5

Abstract:

We consider a class of finite-time horizon nonlinear stochastic optimal control problem. Although the optimal control admits a path integral representation for this class of control problems, efficient computation of the associated path integrals remains a challenging task. We propose a new Monte Carlo approach that significantly improves upon existing methodology. We tackle the issue of exponential growth in variance with the time horizon by casting optimal control estimation as a smoothing problem for a state-space model, and applying smoothing algorithms based on particle Markov chain Monte Carlo. To further reduce the cost, we then develop a multilevel Monte Carlo method which allows us to obtain an estimator of the optimal control with (Formula presented.) mean squared error with a cost of (Formula presented.). In contrast, a cost of (Formula presented.) is required for the existing methodology to achieve the same mean squared error. Our approach is illustrated on two numerical examples.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/166914