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Article: Nonlinear dynamical system modeling via recurrent neural networks and a weighted state space search algorithm

TitleNonlinear dynamical system modeling via recurrent neural networks and a weighted state space search algorithm
Authors
KeywordsNonlinear Dynamical System
Recurrent Neural Network
State Space Search
Issue Date2011
PublisherAmerican Institute of Mathematical Sciences. The Journal's web site is located at http://aimsciences.org/journals/jimo/description.htm
Citation
Journal Of Industrial And Management Optimization, 2011, v. 7 n. 2, p. 385-400 How to Cite?
AbstractGiven a task of tracking a trajectory, a recurrent neural network may be considered as a black-box nonlinear regression model for tracking un-known dynamic systems. An error function is used to measure the difference between the system outputs and the desired trajectory that formulates a non-linear least square problem with dynamical constraints. With the dynamical constraints, classical gradient type methods are dificult and time consuming due to the involving of the computation of the partial derivatives along the trajectory. We develop an alternative learning algorithm, namely the weighted state space search algorithm, which searches the neighborhood of the target trajectory in the state space instead of the parameter space. Since there is no computation of partial derivatives involved, our algorithm is simple and fast. We demonstrate our approach by modeling the short-term foreign exchange rates. The empirical results show that the weighted state space search method is very promising and effective in solving least square problems with dynam-ical constraints. Numerical costs between the gradient method and our the proposed method are provided.
Persistent Identifierhttp://hdl.handle.net/10722/155942
ISSN
2015 Impact Factor: 0.776
2015 SCImago Journal Rankings: 0.639
ISI Accession Number ID
Funding AgencyGrant Number
Hong Kong Polytechnic UniversityPolyU A-SA63
RGC5365/09E
Funding Information:

The first author is supported by the Hong Kong Polytechnic University (PolyU A-SA63). The third author is supported by RGC Grant PolyU. (5365/09E). The paper was presented in the 4th International Conference on Optimization and Control with Applications (OCA2009), 6-11 June, 2009 in Harbin, China. A brief version of this paper was published in the Conference Proceedings.

References

 

DC FieldValueLanguage
dc.contributor.authorLi, LKen_US
dc.contributor.authorShao, Sen_US
dc.contributor.authorYiu, KFCen_US
dc.date.accessioned2012-08-08T08:38:31Z-
dc.date.available2012-08-08T08:38:31Z-
dc.date.issued2011en_US
dc.identifier.citationJournal Of Industrial And Management Optimization, 2011, v. 7 n. 2, p. 385-400en_US
dc.identifier.issn1547-5816en_US
dc.identifier.urihttp://hdl.handle.net/10722/155942-
dc.description.abstractGiven a task of tracking a trajectory, a recurrent neural network may be considered as a black-box nonlinear regression model for tracking un-known dynamic systems. An error function is used to measure the difference between the system outputs and the desired trajectory that formulates a non-linear least square problem with dynamical constraints. With the dynamical constraints, classical gradient type methods are dificult and time consuming due to the involving of the computation of the partial derivatives along the trajectory. We develop an alternative learning algorithm, namely the weighted state space search algorithm, which searches the neighborhood of the target trajectory in the state space instead of the parameter space. Since there is no computation of partial derivatives involved, our algorithm is simple and fast. We demonstrate our approach by modeling the short-term foreign exchange rates. The empirical results show that the weighted state space search method is very promising and effective in solving least square problems with dynam-ical constraints. Numerical costs between the gradient method and our the proposed method are provided.en_US
dc.languageengen_US
dc.publisherAmerican Institute of Mathematical Sciences. The Journal's web site is located at http://aimsciences.org/journals/jimo/description.htmen_US
dc.relation.ispartofJournal of Industrial and Management Optimizationen_US
dc.subjectNonlinear Dynamical Systemen_US
dc.subjectRecurrent Neural Networken_US
dc.subjectState Space Searchen_US
dc.titleNonlinear dynamical system modeling via recurrent neural networks and a weighted state space search algorithmen_US
dc.typeArticleen_US
dc.identifier.emailYiu, KFC:cedric@hkucc.hku.hken_US
dc.identifier.authorityYiu, KFC=rp00206en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.3934/jimo.2011.7.385en_US
dc.identifier.scopuseid_2-s2.0-79955046602en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-79955046602&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume7en_US
dc.identifier.issue2en_US
dc.identifier.spage385en_US
dc.identifier.epage400en_US
dc.identifier.isiWOS:000290616900006-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridLi, LK=7501447410en_US
dc.identifier.scopusauthoridShao, S=7102636557en_US
dc.identifier.scopusauthoridYiu, KFC=24802813000en_US

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