{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,11]],"date-time":"2025-06-11T08:40:02Z","timestamp":1749631202830,"version":"3.41.0"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"11","license":[{"start":{"date-parts":[[2016,10,10]],"date-time":"2016-10-10T00:00:00Z","timestamp":1476057600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci. China Inf. Sci."],"published-print":{"date-parts":[[2016,11]]},"DOI":"10.1007\/s11432-015-0096-3","type":"journal-article","created":{"date-parts":[[2016,10,12]],"date-time":"2016-10-12T14:10:52Z","timestamp":1476281452000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Optimal control on special Euclidean group via natural gradient algorithm","\u6b27\u51e0\u91cc\u5fb7\u7fa4\u7684\u6700\u4f18\u63a7\u5236\u95ee\u9898"],"prefix":"10.1007","volume":"59","author":[{"given":"Chunhui","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erchuan","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Jiu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huafei","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,10,10]]},"reference":[{"key":"96_CR1","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1007\/s10208-008-9025-1","volume":"8","author":"A M Bloch","year":"2008","unstructured":"Bloch A M, Crouch P E, Marsden J E. Optimal control and geodesics on quadratic matrix Lie groups. Found Comput Math, 2008, 8: 469\u2013500","journal-title":"Found Comput Math"},{"key":"96_CR2","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1109\/TASL.2010.2066266","volume":"19","author":"A Cont","year":"2011","unstructured":"Cont A, Dubnov S, Assayag G. On the information geometry of audio streams with applications to similarity computing. IEEE Trans Audio Speech Lang Process, 2011, 19: 837\u2013846","journal-title":"IEEE Trans Audio Speech Lang Process"},{"key":"96_CR3","first-page":"1","volume-title":"Proceedings of IEEE International Radar Conference","author":"F Barbaresco","year":"2008","unstructured":"Barbaresco F, Roussigny H. Innovative tools for Radar signal processing based on Cartan\u2019s geometry of SPD matrices and information geometry. In: Proceedings of IEEE International Radar Conference, Rome, 2008. 1\u20136"},{"key":"96_CR4","doi-asserted-by":"crossref","first-page":"790","DOI":"10.1109\/34.709572","volume":"20","author":"U Grenander","year":"1998","unstructured":"Grenander U, Miller M I, Srivastava A. Hilbert-Schmidt lower bounds for estimators on matrix Lie groups for ATR. IEEE Trans Patt Anal Mach Intell, 1998, 20: 790\u2013802","journal-title":"IEEE Trans Patt Anal Mach Intell"},{"key":"96_CR5","first-page":"244","volume-title":"Departmental Papers (MEAM)","author":"M Zefran","year":"1998","unstructured":"Zefran M, Kumar V, Croke C. On the generation of smooth three-dimensional rigid body motions. Departmental Papers (MEAM), 1998. 244"},{"key":"96_CR6","first-page":"1213","volume":"2","author":"S Amari","year":"1998","unstructured":"Amari S, Douglas S C. Why natural gradient? In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Seattle, 1998. 2: 1213\u20131216","journal-title":"Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing"},{"key":"96_CR7","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1162\/089976698300017746","volume":"10","author":"S Amari","year":"1998","unstructured":"Amari S. Natural gradient works efficiently in learning. Neural Comput, 1998, 10: 251\u2013276","journal-title":"Neural Comput"},{"key":"96_CR8","doi-asserted-by":"crossref","first-page":"9899","DOI":"10.1016\/j.amc.2013.03.119","volume":"219","author":"X M Duan","year":"2013","unstructured":"Duan X M, Sun H F, Peng L Y, et al. A natural gradient descent algorithm for the solution of discrete algebraic Lyapunov equations based on the geodesic distance. Appl Math Comput, 2013, 219: 9899\u20139905","journal-title":"Appl Math Comput"},{"key":"96_CR9","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1002\/oca.874","volume":"30","author":"Z N Zhang","year":"2009","unstructured":"Zhang Z N, Sun H F, Zhong F W. Natural gradient-projection algorithm for distribution control. Optim Contr Appl Met, 2009. 30: 495\u2013504","journal-title":"Optim Contr Appl Met"},{"key":"96_CR10","doi-asserted-by":"crossref","first-page":"682","DOI":"10.1016\/j.difgeo.2013.07.004","volume":"31","author":"Z N Zhang","year":"2013","unstructured":"Zhang Z N, Sun H F, Peng L Y. Natural gradient algorithm for stochastic distribution systems with output feedback. Differ Geom Appl, 2013, 31: 682\u2013690","journal-title":"Differ Geom Appl"},{"key":"96_CR11","doi-asserted-by":"crossref","first-page":"292787","DOI":"10.1155\/2013\/292787","volume":"2013","author":"X M Duan","year":"2013","unstructured":"Duan X M, Sun H F, Peng L Y. Riemannian means on special Euclidean group and unipotent matrices group. Sci World J, 2013, 2013: 292787","journal-title":"Sci World J"},{"key":"96_CR12","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-0093-9","volume-title":"Matrix Groups","author":"M L Curtis","year":"1979","unstructured":"Curtis M L. Matrix Groups. New York: Springer-Verlag, 1979"},{"key":"96_CR13","volume-title":"Matrix Analysis and Application","author":"X D Zhang","year":"2004","unstructured":"Zhang X D. Matrix Analysis and Application. Beijing: Springer, 2004"},{"key":"96_CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-04672-2","volume-title":"Riemannian Geometry and Geometric Analysis","author":"J Jost","year":"2002","unstructured":"Jost J. Riemannian Geometry and Geometric Analysis. 3rd ed. Berlin: Springer, 2002"},{"key":"96_CR15","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1137\/S0895479803436937","volume":"26","author":"M Moakher","year":"2005","unstructured":"Moakher M. A differential geometric approch to the geometric mean of symmetric positive-definite matrices. SIAM J Matrix Anal Appl, 2005, 26: 735\u2013747","journal-title":"SIAM J Matrix Anal Appl"},{"key":"96_CR16","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1049\/ip-cta:20030143","volume":"150","author":"H Wang","year":"2003","unstructured":"Wang H. Control of conditional output probability density functions for general nonlinear and non-Gaussian dynamic stochastic systems. IEE Proc-Control Theory Appl, 2003, 150: 55\u201360","journal-title":"IEE Proc-Control Theory Appl"},{"key":"96_CR17","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1109\/9.983388","volume":"47","author":"H Wang","year":"2002","unstructured":"Wang H. Minimum entropy control of non-Gaussian dynamic stochastic systems. IEEE Trans Automat Control, 2002, 47: 398\u2013403","journal-title":"IEEE Trans Automat Control"},{"key":"96_CR18","doi-asserted-by":"crossref","first-page":"2103","DOI":"10.1109\/9.802925","volume":"44","author":"H Wang","year":"1999","unstructured":"Wang H. Robust control of the output probability density functions for multivariable stochastic systems with guaranteed stability. IEEE Trans Automat Control, 1999, 44: 2103\u20132107","journal-title":"IEEE Trans Automat Control"},{"key":"96_CR19","doi-asserted-by":"crossref","first-page":"407497","DOI":"10.1155\/2011\/407497","volume":"2011","author":"M R Bastian","year":"2011","unstructured":"Bastian M R, Gunther J H, Moon T K. A simplified natural gradient learning algorithm. Adv Artif Neural Syst, 2011, 2011: 407497","journal-title":"Adv Artif Neural Syst"},{"key":"96_CR20","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1109\/RAICS.2011.6069406","volume-title":"Proceedings of 2011 IEEE Recent Advances in Intelligent Computational Systems (RAICS)","author":"N Das","year":"2011","unstructured":"Das N, Dash P K, Routray A. A constrained sequential algorithm for source separation in a non-stationary environment using natural gradient. In: Proceedings of 2011 IEEE Recent Advances in Intelligent Computational Systems (RAICS), Trivandrum, 2011. 729\u2013734"}],"container-title":["Science China Information Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11432-015-0096-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11432-015-0096-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11432-015-0096-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,11]],"date-time":"2025-06-11T08:14:49Z","timestamp":1749629689000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11432-015-0096-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,10]]},"references-count":20,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2016,11]]}},"alternative-id":["96"],"URL":"https:\/\/doi.org\/10.1007\/s11432-015-0096-3","relation":{},"ISSN":["1674-733X","1869-1919"],"issn-type":[{"type":"print","value":"1674-733X"},{"type":"electronic","value":"1869-1919"}],"subject":[],"published":{"date-parts":[[2016,10,10]]},"article-number":"112203"}}