{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T08:09:09Z","timestamp":1761293349964},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,12,9]],"date-time":"2015-12-09T00:00:00Z","timestamp":1449619200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Control Signals Syst."],"published-print":{"date-parts":[[2016,3]]},"DOI":"10.1007\/s00498-015-0151-4","type":"journal-article","created":{"date-parts":[[2015,12,9]],"date-time":"2015-12-09T14:13:11Z","timestamp":1449670391000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Global sensitivity analysis for the boundary control of an open channel"],"prefix":"10.1007","volume":"28","author":[{"given":"Alexandre","family":"Janon","sequence":"first","affiliation":[]},{"given":"Ma\u00eblle","family":"Nodet","sequence":"additional","affiliation":[]},{"given":"Christophe","family":"Prieur","sequence":"additional","affiliation":[]},{"given":"Cl\u00e9mentine","family":"Prieur","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,12,9]]},"reference":[{"issue":"6","key":"151_CR1","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","volume":"19","author":"H Akaike","year":"1974","unstructured":"Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):716\u2013723","journal-title":"IEEE Trans Autom Control"},{"issue":"1","key":"151_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00498-013-0112-8","volume":"26","author":"F Alabau-Boussouira","year":"2014","unstructured":"Alabau-Boussouira F (2014) Insensitizing exact controls for the scalar wave equation and exact controllability of 2-coupled cascade systems of PDE\u2019s by a single control. Math Control Signals Syst 26(1):1\u201346","journal-title":"Math Control Signals Syst"},{"key":"151_CR3","unstructured":"Bastin G, Coron J-M, d\u2019Andr\u00e9a Novel B (2008) Using hyperbolic systems of balance laws for modeling, control and stability analysis of physical networks. In: 17th IFAC world congress. Lecture notes for the pre-congress workshop on complex embedded and networked control systems, Seoul"},{"issue":"2","key":"151_CR4","doi-asserted-by":"crossref","first-page":"177","DOI":"10.3934\/nhm.2009.4.177","volume":"4","author":"G Bastin","year":"2009","unstructured":"Bastin G, Coron J-M, d\u2019Andr\u00e9a Novel B (2009) On Lyapunov stability of linearised Saint-Venant equations for a sloping channel. Netw Heterog Media 4(2):177\u2013187","journal-title":"Netw Heterog Media"},{"key":"151_CR5","doi-asserted-by":"crossref","first-page":"658","DOI":"10.1006\/jmaa.1995.1382","volume":"195","author":"O Bodart","year":"1995","unstructured":"Bodart O, Fabre C (1995) Controls insensitizing the norm of the solution of a semilinear heat equation in unbounded domains. J Math Anal Appl 195:658\u2013683","journal-title":"J Math Anal Appl"},{"issue":"7\u20138","key":"151_CR6","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1081\/PDE-200033749","volume":"29","author":"O Bodart","year":"2004","unstructured":"Bodart O, Gonz\u00e1lez-Burgos M, P\u00e9rez-Garc\u00eda R (2004) Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity. Commun Partial Differ Equ 29(7\u20138):1017\u20131050","journal-title":"Commun Partial Differ Equ"},{"key":"151_CR7","unstructured":"Coron J-M (2007) Control and nonlinearity. In: Mathematical surveys and monographs, vol 136. American Mathematical Society, Providence"},{"issue":"3","key":"151_CR8","doi-asserted-by":"crossref","first-page":"1460","DOI":"10.1137\/070706847","volume":"47","author":"J-M Coron","year":"2008","unstructured":"Coron J-M, Bastin G, d\u2019Andr\u00e9a Novel B (2008) Dissipative boundary conditions for one-dimensional nonlinear hyperbolic systems. SIAM J Control Optim 47(3):1460\u20131498","journal-title":"SIAM J Control Optim"},{"issue":"1","key":"151_CR9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0021-9991(78)90097-9","volume":"26","author":"RI Cukier","year":"1978","unstructured":"Cukier RI, Levine HB, Shuler KE (1978) Nonlinear sensitivity analysis of multiparameter model systems. J Comput Phys 26(1):1\u201342","journal-title":"J Comput Phys"},{"issue":"5","key":"151_CR10","doi-asserted-by":"crossref","first-page":"1758","DOI":"10.1137\/060654372","volume":"45","author":"R D\u00e1ger","year":"2006","unstructured":"D\u00e1ger R (2006) Insensitizing controls for the 1-D wave equation. SIAM J Control Optim 45(5):1758\u20131768","journal-title":"SIAM J Control Optim"},{"key":"151_CR11","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1051\/cocv:1997106","volume":"2","author":"L Teresa de","year":"1997","unstructured":"de Teresa L (1997) Controls insensitizing the norm of the solution of a semilinear heat equation in unbounded domains. ESAIM Control Optim Calc Var 2:125\u2013149","journal-title":"ESAIM Control Optim Calc Var"},{"issue":"1\u20132","key":"151_CR12","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1080\/03605300008821507","volume":"25","author":"L Teresa de","year":"2000","unstructured":"de Teresa L (2000) Insensitizing controls for a semilinear heat equation. Commun Partial Differ Equ 25(1\u20132):39\u201372","journal-title":"Commun Partial Differ Equ"},{"issue":"1","key":"151_CR13","doi-asserted-by":"crossref","first-page":"457","DOI":"10.3934\/cpaa.2009.8.457","volume":"8","author":"L Teresa de","year":"2009","unstructured":"de Teresa L, Zuazua E (2009) Identification of the class of initial data for the insensitizing control of the heat equation. Commun Pure Appl Anal 8(1):457\u2013471","journal-title":"Commun Pure Appl Anal"},{"issue":"6","key":"151_CR14","doi-asserted-by":"crossref","first-page":"1252","DOI":"10.1109\/TCST.2008.919418","volume":"16","author":"V Santos Dos","year":"2008","unstructured":"Dos Santos V, Prieur C (2008) Boundary control of open channels with numerical and experimental validations. IEEE Trans Control Syst Technol 16(6):1252\u20131264","journal-title":"IEEE Trans Control Syst Technol"},{"issue":"3","key":"151_CR15","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1214\/aos\/1176345462","volume":"9","author":"B Efron","year":"1981","unstructured":"Efron B, Stein C (1981) The jackknife estimate of variance. Ann Stat 9(3):586\u2013596","journal-title":"Ann Stat"},{"key":"151_CR16","doi-asserted-by":"crossref","DOI":"10.1201\/9781420034899","volume-title":"Design and modeling for computer experiments","author":"K-T Fang","year":"2005","unstructured":"Fang K-T, Li R, Sudjianto A (2005) Design and modeling for computer experiments. CRC Press, New York"},{"issue":"4","key":"151_CR17","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/S1631-073X(03)00334-0","volume":"337","author":"E Fern\u00e1ndez-Cara","year":"2003","unstructured":"Fern\u00e1ndez-Cara E, Garcia GC, Osses A (2003) Insensitizing controls for a large-scale ocean circulation model. Comptes Rendus Math 337(4):265\u2013270","journal-title":"Comptes Rendus Math"},{"key":"151_CR18","doi-asserted-by":"crossref","unstructured":"Gamboa F, Janon A, Klein T, Lagnoux-Renaudie A, Prieur C (2016) Statistical inference for Sobol pick freeze Monte Carlo method. Statistics (to appear)","DOI":"10.1080\/02331888.2015.1105803"},{"issue":"3","key":"151_CR19","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1051\/m2an:2007031","volume":"41","author":"MA Grepl","year":"2007","unstructured":"Grepl MA, Maday Y, Nguyen NC, Patera AT (2007) Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations. Math Model Numer Anal 41(3):575\u2013605","journal-title":"Math Model Numer Anal"},{"issue":"1","key":"151_CR20","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1051\/m2an:2005006","volume":"39","author":"MA Grepl","year":"2005","unstructured":"Grepl MA, Patera AT (2005) A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. Mathl Model Numer Anal 39(1):157\u2013181","journal-title":"Mathl Model Numer Anal"},{"issue":"6","key":"151_CR21","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1016\/j.anihpc.2006.11.001","volume":"24","author":"S Guerrero","year":"2007","unstructured":"Guerrero S (2007) Controllability of systems of Stokes equations with one control force: existence of insensitizing controls. Ann de l\u2019Inst Henri Poincare (C) Non Linear Anal 24(6):1029\u20131054","journal-title":"Ann de l\u2019Inst Henri Poincare (C) Non Linear Anal"},{"issue":"5","key":"151_CR22","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1016\/j.anihpc.2012.09.005","volume":"30","author":"M Gueye","year":"2013","unstructured":"Gueye M (2013) Insensitizing controls for the Navier\u2013Stokes equations. Ann de l\u2019Inst Henri Poincare (C) Non Linear Anal 30(5):825\u2013844","journal-title":"Ann de l\u2019Inst Henri Poincare (C) Non Linear Anal"},{"key":"151_CR23","doi-asserted-by":"crossref","unstructured":"Hastie T (2014) GAM: generalized additive models. R package version 1.09.1","DOI":"10.1002\/9781118445112.stat03141"},{"issue":"10\u201311","key":"151_CR24","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.1016\/j.ress.2005.11.017","volume":"91","author":"JC Helton","year":"2006","unstructured":"Helton JC, Johnson JD, Sallaberry CJ, Storlie CB (2006) Survey of sampling-based methods for uncertainty and sensitivity analysis. Reliab Eng Syst Saf 91(10\u201311):1175\u20131209","journal-title":"Reliab Eng Syst Saf"},{"key":"151_CR25","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1214\/aoms\/1177730196","volume":"19","author":"WF Hoeffding","year":"1948","unstructured":"Hoeffding WF (1948) A class of statistics with asymptotically normal distributions. Ann Math Stat 19:293\u2013325","journal-title":"Ann Math Stat"},{"issue":"1","key":"151_CR26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0951-8320(96)00002-6","volume":"52","author":"T Homma","year":"1996","unstructured":"Homma T, Saltelli A (1996) Importance measures in global sensitivity analysis of nonlinear models. Reliab Engi Syst Saf 52(1):1\u201317","journal-title":"Reliab Engi Syst Saf"},{"issue":"8","key":"151_CR27","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1016\/j.crma.2007.09.019","volume":"345","author":"DBP Huynh","year":"2007","unstructured":"Huynh DBP, Rozza G, Sen S, Patera AT (2007) A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants. Comptes Rendus Mathematique 345(8):473\u2013478","journal-title":"Comptes Rendus Mathematique"},{"key":"151_CR28","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1051\/ps\/2013040","volume":"18","author":"A Janon","year":"2014","unstructured":"Janon A, Klein T, Lagnoux A, Nodet M, Prieur C (2014) Asymptotic normality and efficiency of two Sobol index estimators. ESAIM Probab Stat 18:342\u2013364","journal-title":"ESAIM Probab Stat"},{"issue":"2","key":"151_CR29","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1051\/m2an\/2012029","volume":"47","author":"A Janon","year":"2013","unstructured":"Janon A, Nodet M, Prieur C (2013) Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values. ESAIM Math Model Numer Anal 47(2):317\u2013348","journal-title":"ESAIM Math Model Numer Anal"},{"issue":"1","key":"151_CR30","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1615\/Int.J.UncertaintyQuantification.2012004291","volume":"4","author":"A Janon","year":"2014","unstructured":"Janon A, Nodet M, Prieur C (2014) Uncertainties assessment in global sensitivity indices estimation from metamodels. Int J Uncertain Quantif 4(1):21\u201336","journal-title":"Int J Uncertain Quantif"},{"key":"151_CR31","doi-asserted-by":"crossref","unstructured":"Janon A, Nodet M, Prieur C (2015) Goal-oriented error estimation for reduced basis method, with application to certified sensitivity analysis. J Sci Comput (to appear)","DOI":"10.1007\/s10915-015-0127-z"},{"key":"151_CR32","doi-asserted-by":"crossref","unstructured":"Janon A, Nodet M, Prieur Ch., Prieur Cl. (2014) Global sensitivity analysis for the boundary control of an open channel. In: 53rd IEEE conference on decision and control, Los Angeles, pp 589\u2013594","DOI":"10.1109\/CDC.2014.7039445"},{"key":"151_CR33","unstructured":"Li T-T (1994) Global classical solutions for quasilinear hyperbolic systems. In: RAM: research in applied mathematics, vol 32. Masson, Paris"},{"issue":"8","key":"151_CR34","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1016\/j.aml.2003.10.006","volume":"17","author":"S Micu","year":"2004","unstructured":"Micu S, Ortega JH, de Teresa L (2004) An example of $$\\epsilon $$ \u03f5 -insensitizing controls for the heat equation with no intersecting observation and control regions. Appl Math Lett 17(8):927\u2013932","journal-title":"Appl Math Lett"},{"key":"151_CR35","unstructured":"Monod H, Naud C, Makowski D (2006 ) Uncertainty and sensitivity analysis for crop models. In: Wallach D, Makowski D, Jones JW (eds) Working with dynamic crop models: evaluation, analysis, parameterization, and applications, chapter\u00a04. Elsevier, Amsterdam, pp 55\u201399"},{"key":"151_CR36","unstructured":"Nguyen NC, Veroy K, Patera AT (2005) Certified real-time solution of parametrized partial differential equations. In: Handbook of materials modeling, pp 1523\u20131558"},{"issue":"2","key":"151_CR37","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/s00498-008-0028-x","volume":"20","author":"C Prieur","year":"2008","unstructured":"Prieur C, Winkin J, Bastin G (2008) Robust boundary control of systems of conservation laws. Math Control Signals Syst 20(2):173\u2013197","journal-title":"Math Control Signals Syst"},{"key":"151_CR38","unstructured":"R Core Team (2014) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna"},{"key":"151_CR39","unstructured":"Saltelli A, Chan K, Scott EM (2000) Sensitivity analysis. In: Wiley series in probability and statistics. Wiley, Chichester"},{"key":"151_CR40","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3799-8","volume-title":"The design and analysis of computer experiments","author":"TJ Santner","year":"2003","unstructured":"Santner TJ, Williams B, Notz W (2003) The design and analysis of computer experiments. Springer, New York"},{"key":"151_CR41","doi-asserted-by":"crossref","unstructured":"Schaback R (2003) Mathematical results concerning kernel techniques. In: Prep. 13th IFAC symposium on system identification, Rotterdam. Citeseer, pp 1814\u20131819","DOI":"10.1016\/S1474-6670(17)35017-6"},{"issue":"3","key":"151_CR42","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1090\/qam\/910462","volume":"45","author":"L Sirovich","year":"1987","unstructured":"Sirovich L (1987) Turbulence and the dynamics of coherent structures. Part I\u2013II. Q Appl Math 45(3):561\u2013590","journal-title":"Q Appl Math"},{"key":"151_CR43","first-page":"407","volume":"1","author":"IM Sobol\u2019","year":"1993","unstructured":"Sobol\u2019 IM (1993) Sensitivity analysis for nonlinear mathematical models. Mathl Model Comput Exp 1:407\u2013414","journal-title":"Mathl Model Comput Exp"},{"issue":"1\u20133","key":"151_CR44","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/S0378-4754(00)00270-6","volume":"55","author":"IM Sobol\u2019","year":"2001","unstructured":"Sobol\u2019 IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul 55(1\u20133):271\u2013280","journal-title":"Math Comput Simul"},{"issue":"7","key":"151_CR45","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1016\/j.ress.2007.04.002","volume":"93","author":"B Sudret","year":"2008","unstructured":"Sudret B (2008) Global sensitivity analysis using polynomial chaos expansions. Reliab Eng Syst Saf 93(7):964\u2013979","journal-title":"Reliab Eng Syst Saf"},{"issue":"7","key":"151_CR46","doi-asserted-by":"crossref","first-page":"1358","DOI":"10.1080\/00949655.2014.971799","volume":"85","author":"J-Y Tissot","year":"2015","unstructured":"Tissot J-Y, Prieur C (2015) A randomized orthogonal array-based procedure for the estimation of first- and second-order Sobol\u2019 indices. J Stat Comput Simul 85(7):1358\u20131381","journal-title":"J Stat Comput Simul"},{"issue":"8\u20139","key":"151_CR47","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1002\/fld.867","volume":"47","author":"K Veroy","year":"2005","unstructured":"Veroy K, Patera AT (2005) Certified real-time solution of the parametrized steady incompressible Navier\u2013Stokes equations: rigorous reduced-basis a posteriori error bounds. Int J Numer Methods Fluids 47(8\u20139):773\u2013788","journal-title":"Int J Numer Methods Fluids"}],"container-title":["Mathematics of Control, Signals, and Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00498-015-0151-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00498-015-0151-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00498-015-0151-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,2]],"date-time":"2019-09-02T08:39:02Z","timestamp":1567413542000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00498-015-0151-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,9]]},"references-count":47,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,3]]}},"alternative-id":["151"],"URL":"https:\/\/doi.org\/10.1007\/s00498-015-0151-4","relation":{},"ISSN":["0932-4194","1435-568X"],"issn-type":[{"value":"0932-4194","type":"print"},{"value":"1435-568X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,12,9]]},"article-number":"6"}}