On the robustness of Riccati flows to complete model misspecification

Bishop, AN; Del Moral, P

On the robustness of Riccati flows to complete model misspecification

Bishop, AN

Del Moral, P

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Publication Type:: Journal Article
Citation:: Journal of the Franklin Institute, 2018, 355 (15), pp. 7178 - 7200
Issue Date:: 2018-10-01

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Field	Value	Language
dc.contributor.author	Bishop, AN https://orcid.org/0000-0001-8581-8562	en_US
dc.contributor.author	Del Moral, P	en_US
dc.date.issued	2018-10-01	en_US
dc.identifier.citation	Journal of the Franklin Institute, 2018, 355 (15), pp. 7178 - 7200	en_US
dc.identifier.issn	0016-0032	en_US
dc.identifier.uri	http://hdl.handle.net/10453/132392
dc.description.abstract	© 2018 The Franklin Institute Consider the continuous-time matrix Riccati operator Ricc(Q)=AQ+QA′−QSQ+R. In this work, we consider the robustness of this operator to direct perturbations of the matrices (A, R, S) and, in particular, the flow robustness of the corresponding Riccati differential equation. For a given class of perturbation, we show that the corresponding differential equation is well defined in the sense it is bounded above and below, it has a well-defined fixed point, and it converges to this fixed point exponentially fast. Moreover, the flow of the perturbed Riccati flow is close to the nominal Riccati flow when the perturbation is small; i.e. we prove a continuity-type condition in the size of the perturbation.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DE120102873
dc.relation.ispartof	Journal of the Franklin Institute	en_US
dc.relation.isbasedon	10.1016/j.jfranklin.2018.06.042	en_US
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject.classification	Industrial Engineering & Automation	en_US
dc.title	On the robustness of Riccati flows to complete model misspecification	en_US
dc.type	Journal Article
utslib.citation.volume	15	en_US
utslib.citation.volume	355	en_US
utslib.for	0101 Pure Mathematics	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0906 Electrical and Electronic 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	closed_access	*
pubs.issue	15	en_US
pubs.publication-status	Published	en_US
pubs.volume	355	en_US

Abstract:

© 2018 The Franklin Institute Consider the continuous-time matrix Riccati operator Ricc(Q)=AQ+QA′−QSQ+R. In this work, we consider the robustness of this operator to direct perturbations of the matrices (A, R, S) and, in particular, the flow robustness of the corresponding Riccati differential equation. For a given class of perturbation, we show that the corresponding differential equation is well defined in the sense it is bounded above and below, it has a well-defined fixed point, and it converges to this fixed point exponentially fast. Moreover, the flow of the perturbed Riccati flow is close to the nominal Riccati flow when the perturbation is small; i.e. we prove a continuity-type condition in the size of the perturbation.

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http://hdl.handle.net/10453/132392