Nonlinear stochastic receding horizon control: stability, robustness and Monte Carlo methods for control approximation

Bertoli, F; Bishop, AN

Nonlinear stochastic receding horizon control: stability, robustness and Monte Carlo methods for control approximation

Bertoli, F Bishop, AN

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Publication Type:: Journal Article
Citation:: International Journal of Control, 2018, 91 (10), pp. 2387 - 2402
Issue Date:: 2018-10-03

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Field	Value	Language
dc.contributor.author	Bertoli, F	en_US
dc.contributor.author	Bishop, AN https://orcid.org/0000-0001-8581-8562	en_US
dc.date.issued	2018-10-03	en_US
dc.identifier.citation	International Journal of Control, 2018, 91 (10), pp. 2387 - 2402	en_US
dc.identifier.issn	0020-7179	en_US
dc.identifier.uri	http://hdl.handle.net/10453/132327
dc.description.abstract	© 2017, © 2017 Informa UK Limited, trading as Taylor & Francis Group. This work considers the stability of nonlinear stochastic receding horizon control when the optimal controller is only computed approximately. A number of general classes of controller approximation error are analysed including deterministic and probabilistic errors and even controller sample and hold errors. In each case, it is shown that the controller approximation errors do not accumulate (even over an infinite time frame) and the process converges exponentially fast to a small neighbourhood of the origin. In addition to this analysis, an approximation method for receding horizon optimal control is proposed based on Monte Carlo simulation. This method is derived via the Feynman–Kac formula which gives a stochastic interpretation for the solution of a Hamilton–Jacobi–Bellman equation associated with the true optimal controller. It is shown, and it is a prime motivation for this study, that this particular controller approximation method practically stabilises the underlying nonlinear process.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DE120102873
dc.relation.ispartof	International Journal of Control	en_US
dc.relation.isbasedon	10.1080/00207179.2017.1349340	en_US
dc.rights	info:eu-repo/semantics/openAccess
dc.subject.classification	Industrial Engineering & Automation	en_US
dc.title	Nonlinear stochastic receding horizon control: stability, robustness and Monte Carlo methods for control approximation	en_US
dc.type	Journal Article
utslib.citation.volume	10	en_US
utslib.citation.volume	91	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0906 Electrical and Electronic Engineering	en_US
utslib.for	0913 Mechanical Engineering	en_US
pubs.embargo.period	Not known	en_US
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/Faculty of Engineering and Information Technology/School of Biomedical Engineering
pubs.organisational-group	/University of Technology Sydney/Strength - CHT - Health Technologies
utslib.copyright.status	open_access	*
pubs.issue	10	en_US
pubs.publication-status	Published	en_US
pubs.volume	91	en_US

Abstract:

© 2017, © 2017 Informa UK Limited, trading as Taylor & Francis Group. This work considers the stability of nonlinear stochastic receding horizon control when the optimal controller is only computed approximately. A number of general classes of controller approximation error are analysed including deterministic and probabilistic errors and even controller sample and hold errors. In each case, it is shown that the controller approximation errors do not accumulate (even over an infinite time frame) and the process converges exponentially fast to a small neighbourhood of the origin. In addition to this analysis, an approximation method for receding horizon optimal control is proposed based on Monte Carlo simulation. This method is derived via the Feynman–Kac formula which gives a stochastic interpretation for the solution of a Hamilton–Jacobi–Bellman equation associated with the true optimal controller. It is shown, and it is a prime motivation for this study, that this particular controller approximation method practically stabilises the underlying nonlinear process.

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http://hdl.handle.net/10453/132327