{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T17:10:11Z","timestamp":1761844211678,"version":"3.40.4"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2012,10,1]],"date-time":"2012-10-01T00:00:00Z","timestamp":1349049600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Autom. Comput."],"published-print":{"date-parts":[[2012,10]]},"DOI":"10.1007\/s11633-012-0669-6","type":"journal-article","created":{"date-parts":[[2012,10,10]],"date-time":"2012-10-10T12:55:56Z","timestamp":1349873756000},"page":"474-479","source":"Crossref","is-referenced-by-count":2,"title":["Model reduction and controller design for a nonlinear heat conduction problem using finite element method"],"prefix":"10.1007","volume":"9","author":[{"given":"Paramita","family":"Guha","sequence":"first","affiliation":[]},{"given":"Mashuq Un","family":"Nabi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,10,11]]},"reference":[{"key":"669_CR1","doi-asserted-by":"crossref","first-page":"1056","DOI":"10.1109\/CDC.1997.657586","volume-title":"Proceedings of the 36th Conference on Decision and Control","author":"B. Bamieh","year":"1997","unstructured":"B. Bamieh. The structure of optimal controllers of spatiallyinvariant distributed parameter systems. In Proceedings of the 36th Conference on Decision and Control, IEEE, San Diego, USA, pp. 1056\u20131061, 1997."},{"key":"669_CR2","volume-title":"An Introduction to the Finite Element Method","author":"J. N. Reddy","year":"1993","unstructured":"J. N. Reddy. An Introduction to the Finite Element Method. 2nd ed., New York, USA: McGraw-Hill Science, 1993.","edition":"2nd ed."},{"key":"669_CR3","volume-title":"Numerical Methods in Electromagnetism","author":"M. V. K. Chari","year":"2000","unstructured":"M. V. K. Chari, S. J. Salon. Numerical Methods in Electromagnetism. New York, USA: Academic Press, 2000."},{"key":"669_CR4","first-page":"1040","volume-title":"Proceedings of the American Control Conference","author":"A. Armaou","year":"2002","unstructured":"A. Armaou, P. D. Christofides. Dynamic optimization of dissipative PDE systems using empirical eigenfunctions. In Proceedings of the American Control Conference, IEEE, USA, Anchorage AK, USA, vol. 2, pp. 1040\u20131048, 2002."},{"issue":"3","key":"669_CR5","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1007\/s11633-009-0234-0","volume":"6","author":"N. Duan","year":"2009","unstructured":"N. Duan, F. N. Hu, X. Yu. An improved control algorithm for high-order nonlinear systems with unmodelled dynamics. International Journal of Automation and Computing, vol. 6, no. 3, pp. 234\u2013239, 2009.","journal-title":"International Journal of Automation and Computing"},{"issue":"3","key":"669_CR6","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/s11633-006-0215-5","volume":"3","author":"K. Alimhan","year":"2006","unstructured":"K. Alimhan, H. Inaba. Output feedback control for a class of nonlinear systems. International Journal of Automation and Computing, vol. 3, no. 3, pp. 215\u2013221, 2006.","journal-title":"International Journal of Automation and Computing"},{"key":"669_CR7","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1109\/MED.2009.5164560","volume-title":"Proceedings of the 17th Mediterranean Conference on Control and Automation","author":"M. Nabi","year":"2009","unstructured":"M. Nabi, P. Guha. A control law for a nonlinear heat conduction problem on nontrivial domains using FEM. In Proceedings of the 17th Mediterranean Conference on Control and Automation, IEEE, Washington, DC, USA, pp. 320\u2013323, 2009."},{"key":"669_CR8","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1137\/1.9780898717525.ch4","volume-title":"Research Directions in Distributed Parameter Systems","author":"R. F. Curtain","year":"2003","unstructured":"R. F. Curtain. Model reduction for control design for distributed parameter systems. In Research Directions in Distributed Parameter Systems, SIAM, Philadelphia, PA, pp. 95\u2013121, 2003."},{"key":"669_CR9","doi-asserted-by":"crossref","unstructured":"E. B. Rudnyi, J. G. Korvink. Model order reduction for large scale finite element engineering models. In Proceedings of European Conference on Computational Fluid Dynamics, Delft, The Netherlands, 2006.","DOI":"10.1007\/11558958_41"},{"issue":"7","key":"669_CR10","first-page":"808","volume":"78","author":"A. Chatterjee","year":"2000","unstructured":"A. Chatterjee. An introduction to the proper orthogonal decomposition. Current Science, vol. 78, no. 7, pp. 808\u2013817, 2000.","journal-title":"Current Science"},{"issue":"3","key":"669_CR11","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1142\/S0218127405012429","volume":"15","author":"C. W. Rowley","year":"2005","unstructured":"C. W. Rowley. Model reduction for fluids, using balanced proper orthogonal decomposition. International Journal of Bifurcation and Chaos, vol. 15, no. 3, pp. 997\u20131013, 2005.","journal-title":"International Journal of Bifurcation and Chaos"},{"key":"669_CR12","first-page":"267","volume-title":"Proceedings of American Control Conference","author":"J. R. Singler","year":"2008","unstructured":"J. R. Singler. Approximate low rank solutions of Lyapunov equations via proper orthogonal decomposition. In Proceedings of American Control Conference, IEEE, Seattle, USA, pp. 267\u2013272, 2008."},{"issue":"5","key":"669_CR13","doi-asserted-by":"crossref","first-page":"1888","DOI":"10.1109\/TMAG.2007.892691","volume":"33","author":"Y. Zhai","year":"2007","unstructured":"Y. Zhai, L. Vu-Quoc. Analysis of power magnetic components with nonlinear static hysteresis: Proper orthogonal decomposition and model reduction. IEEE Transactions on Magnetics, vol. 33, no. 5, pp. 1888\u20131897, 2007.","journal-title":"IEEE Transactions on Magnetics"},{"issue":"2","key":"669_CR14","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1016\/j.apnum.2008.02.004","volume":"59","author":"M. A. Singer","year":"2009","unstructured":"M. A. Singer, W. H. Green. Using adaptive proper orthogonal decomposition to solve the reaction-diffusion equation. Applied Numerical Mathematics, vol. 59, no. 2, pp. 272\u2013279, 2009.","journal-title":"Applied Numerical Mathematics"},{"issue":"1\u20132","key":"669_CR15","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/S0377-0427(00)00396-4","volume":"123","author":"R. W. Freund","year":"2000","unstructured":"R. W. Freund. Krylov-subspace methods for reduced-order modeling in circuit simulation. Journal for Computational and Applied Mathematics, vol. 123, no. 1\u20132, pp. 395\u2013421, 2000.","journal-title":"Journal for Computational and Applied Mathematics"},{"issue":"7","key":"669_CR16","doi-asserted-by":"crossref","first-page":"1253","DOI":"10.1016\/S0167-739X(03)00050-5","volume":"19","author":"B. N. Datta","year":"2003","unstructured":"B. N. Datta. Krylov subspace methods for large-scale matrix problems in control. Future Generation Computer Systems, vol. 19, no. 7, pp. 1253\u20131263, 2003.","journal-title":"Future Generation Computer Systems"},{"key":"669_CR17","volume-title":"Krylov Projection Methods for Model Reduction","author":"E. J. Grimme","year":"1997","unstructured":"E. J. Grimme. Krylov Projection Methods for Model Reduction, Ph. D. dissertation, University of Illinios at Urbana Champaign, Urbana IL, USA, 1997."},{"issue":"2","key":"669_CR18","doi-asserted-by":"crossref","first-page":"888","DOI":"10.1109\/TPWRS.2005.846109","volume":"20","author":"D. Chaniotis","year":"2006","unstructured":"D. Chaniotis, M. A. Pai. Model reduction in power systems using Krylov subspace methods. IEEE Transactions on Power Systems, vol. 20, no. 2, pp. 888\u2013894, 2006.","journal-title":"IEEE Transactions on Power Systems"},{"issue":"12","key":"669_CR19","doi-asserted-by":"crossref","first-page":"2022","DOI":"10.1109\/9.975513","volume":"46","author":"D. M. Bo\u0161skovi\u0107","year":"2001","unstructured":"D. M. Bo\u0161skovi\u0107, M. Krsti\u0107 W. Liu. Boundary control of an unstable heat equation via measurement of domainaveraged temperature. IEEE Transactions on Automatic Control, vol. 46, no. 12, pp. 2022\u20132028, 2001.","journal-title":"IEEE Transactions on Automatic Control"}],"container-title":["International Journal of Automation and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11633-012-0669-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11633-012-0669-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11633-012-0669-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,10]],"date-time":"2025-04-10T10:19:29Z","timestamp":1744280369000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11633-012-0669-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,10]]},"references-count":19,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2012,10]]}},"alternative-id":["669"],"URL":"https:\/\/doi.org\/10.1007\/s11633-012-0669-6","relation":{},"ISSN":["1476-8186","1751-8520"],"issn-type":[{"type":"print","value":"1476-8186"},{"type":"electronic","value":"1751-8520"}],"subject":[],"published":{"date-parts":[[2012,10]]}}}