{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:37:37Z","timestamp":1740141457832,"version":"3.37.3"},"reference-count":33,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2021,6,3]],"date-time":"2021-06-03T00:00:00Z","timestamp":1622678400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11471036"],"award-info":[{"award-number":["11471036"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,8,28]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper is concerned with the optimal boundary control for the one-dimensional Saint-Venant equations with arbitrary friction and space-varying slope. By the Dubovitskii and Milyutin functional analytical approach, the Pontryagin maximum principles of the optimal control systems equipped with two boundary control variables are investigated and the first-order necessary optimality conditions are presented in both the fixed and the free final horizon cases, respectively. Finally, a remark on numerical solution is made for illustrating how to apply the obtained results to the investigational optimal boundary control problem.<\/jats:p>","DOI":"10.1093\/imamci\/dnab016","type":"journal-article","created":{"date-parts":[[2021,5,13]],"date-time":"2021-05-13T11:23:09Z","timestamp":1620904989000},"page":"881-907","source":"Crossref","is-referenced-by-count":1,"title":["Optimal boundary control of Saint-Venant equations with arbitrary friction and space-varying slope"],"prefix":"10.1093","volume":"38","author":[{"given":"Yang-Yang","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R. China"}]},{"given":"Bing","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R. China"},{"name":"Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 100081, P.R. China"}]}],"member":"286","published-online":{"date-parts":[[2021,6,3]]},"reference":[{"key":"2021083004505564200_ref1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-32062-5","article-title":"Progress in Nonlinear Differential Equations and Their Applications: Subseries in Control","volume-title":"Stability and Boundary Stabilization of 1-D Hyperbolic Systems","author":"Bastin","year":"2016"},{"key":"2021083004505564200_ref2","doi-asserted-by":"crossref","first-page":"100026","DOI":"10.1016\/j.ifacsc.2019.100026","article-title":"Boundary feedback stabilization of hydraulic jumps","volume":"7","author":"Bastin","year":"2019","journal-title":"IFAC J. Syst. Control"},{"key":"2021083004505564200_ref3","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1016\/S1631-073X(02)02610-9","article-title":"On viscous shallow-water equations (Saint-Venant model) and the quasi-geostrophic limit","volume":"335","author":"Bresch","year":"2002","journal-title":"C. R. Math. Acad. Sci. Paris"},{"key":"2021083004505564200_ref4","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1134\/S0965542514010047","article-title":"Analytical and numerical Riemann solutions of the Saint Venant equations for forward- and backward-facing step flows","volume":"54","author":"Bulatov","year":"2014","journal-title":"Comput. Math. Math. Phys."},{"key":"2021083004505564200_ref5","first-page":"4313","article-title":"Nonlinear optimal control of an open-channel hydraulic system based on an infinite-dimensional model","volume-title":"Proceedings of the 38th IEEE Conference on Decision and Control (CDC)","author":"Chen","year":"1999"},{"key":"2021083004505564200_ref6","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1002\/apj.1944","article-title":"Computational optimal control of the Saint-Venant PDE model using the time-scaling technique","volume":"11","author":"Chen","year":"2015","journal-title":"Asia-Pac. J. Chem. Eng."},{"key":"2021083004505564200_ref7","doi-asserted-by":"crossref","first-page":"273","DOI":"10.4171\/IFB\/424","article-title":"Optimal control problem for viscous systems of conservation laws, with geometric parameter, and application to the shallow-water equations","volume":"21","author":"Court","year":"2019","journal-title":"Interfaces Free Bound."},{"key":"2021083004505564200_ref8","doi-asserted-by":"crossref","first-page":"1365","DOI":"10.1016\/S0005-1098(03)00109-2","article-title":"Boundary feedback control in networks of open channels","volume":"39","author":"de Halleux","year":"2003","journal-title":"Automatica J. IFAC"},{"key":"2021083004505564200_ref9","first-page":"147","article-title":"Th\u00e9orie du mouvement nonpermanent des eaux, avec applications aux crues des rivi\u00e8res et \u00e0 l\u2019introduction des mar\u00e9es dans leur lit (Theory of unsteady water flow, with application to river floods and to propagation of tides in river channels)","volume":"73","author":"de Saint-Venant","year":"1871","journal-title":"C. R. Math. Acad. Sci. Paris"},{"key":"2021083004505564200_ref10","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.arcontrol.2017.09.003","article-title":"Control of shallow waves of two unmixed fluids by backstepping","volume":"44","author":"Diagne","year":"2017","journal-title":"Annu. Rev. Control"},{"key":"2021083004505564200_ref11","doi-asserted-by":"crossref","first-page":"1215","DOI":"10.1061\/(ASCE)0733-9429(2006)132:11(1215)","article-title":"Optimal control of open-channel flow using adjoint sensitivity analysis","volume":"132","author":"Ding","year":"2006","journal-title":"J. Hydraul. Eng."},{"volume-title":"Linear Operators, Part I: General Theory","year":"1958","author":"Dunford","key":"2021083004505564200_ref12"},{"key":"2021083004505564200_ref13","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1016\/j.apnum.2005.09.002","article-title":"CWENO-type central-upwind schemes for multidimensional Saint-Venant system of shallow water equations","volume":"56","author":"Feng","year":"2006","journal-title":"Appl. Numer. Math."},{"key":"2021083004505564200_ref14","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1093\/imamci\/dnq001","article-title":"Dubovitskii\u2013Milyutin formalism applied to optimal control problems with constraints given by the heat equation with final data","volume":"27","author":"Gayte","year":"2010","journal-title":"IMA J. Math. Control Inform."},{"key":"2021083004505564200_ref15","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1080\/00207177408932654","article-title":"A predictive min-H method to improve convergence to optimal solutions","volume":"19","author":"Gibson","year":"1974","journal-title":"Internat. J. Control"},{"key":"2021083004505564200_ref16","article-title":"Lecture Notes in Economics and Mathematical Systems","volume-title":"Lectures on Mathematical Theory of Extremum Problems","author":"Girsanov","year":"1972"},{"key":"2021083004505564200_ref17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0294-1449(02)00004-5","article-title":"Global boundary controllability of the de St. Venant equations between steady states","volume":"20","author":"Gugat","year":"2003","journal-title":"Ann. Inst. H. Poincar\u00e9 Anal. Non Lin\u00e9aire"},{"key":"2021083004505564200_ref18","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.automatica.2018.10.035","article-title":"A quadratic Lyapunov function for Saint-Venant equations with arbitrary friction and space-varying slope","volume":"100","author":"Hayat","year":"2019","journal-title":"Automatica J. IFAC"},{"key":"2021083004505564200_ref19","first-page":"231","article-title":"Necessary optimality conditions and a semi-smooth Newton approach for an optimal control problem of a coupled system of Saint-Venant equations and ordinary differential equations","volume":"1","author":"Kimmerle","year":"2016","journal-title":"Pure Appl. Funct. Anal."},{"volume-title":"Some Problem of Optimal and Pareto Optimal Control for Distributed Parameter Systems","year":"1997","author":"Kotarski","key":"2021083004505564200_ref20"},{"key":"2021083004505564200_ref21","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1137\/100789798","article-title":"Persistence of generalized roll-waves under viscous perturbation","volume":"45","author":"Le Blanc","year":"2013","journal-title":"SIAM J. Math. Anal."},{"key":"2021083004505564200_ref22","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1137\/S0363012900375664","article-title":"On the modelling and stabilization of flows in networks of open canals","volume":"41","author":"Leugering","year":"2002","journal-title":"SIAM J. Control Optim."},{"key":"2021083004505564200_ref23","doi-asserted-by":"crossref","first-page":"1089","DOI":"10.1002\/mma.488","article-title":"Exact controllability for quasilinear hyperbolic systems and its application to unsteady flows in a network of open canals","volume":"27","author":"Li","year":"2004","journal-title":"Math. Methods Appl. Sci."},{"key":"2021083004505564200_ref24","doi-asserted-by":"crossref","first-page":"243","DOI":"10.3934\/dcds.2010.28.243","article-title":"Exact boundary controllability and observability for first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions","volume":"28","author":"Li","year":"2010","journal-title":"Discrete Contin. Dyn. Syst."},{"key":"2021083004505564200_ref25","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1016\/j.automatica.2006.02.002","article-title":"Boundary control of linearized Saint-Venant equations oscillating modes","volume":"42","author":"Litrico","year":"2006","journal-title":"Automatica J. IFAC"},{"key":"2021083004505564200_ref26","first-page":"338","article-title":"PILOTE: optimal control of irrigation canals","volume-title":"Proceedings of the First International Conference on Water Resources Engineering, Irrigation and Drainage","author":"Malaterre","year":"1995"},{"key":"2021083004505564200_ref27","doi-asserted-by":"crossref","first-page":"2413","DOI":"10.23919\/ECC.2003.7085328","article-title":"Robust optimal control of one-reach open-channels","volume-title":"Proceedings of the 2003 European Control Conference (ECC)","author":"Ouarit","year":"2003"},{"key":"2021083004505564200_ref28","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.automatica.2017.11.028","article-title":"Boundary feedback control of linear hyperbolic systems: application to the Saint-Venant\u2013Exner equations","volume":"89","author":"Prieur","year":"2018","journal-title":"Automatica J. IFAC"},{"key":"2021083004505564200_ref29","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1080\/00207729508929029","article-title":"Multivariate optimal control for on-demand operation of irrigation canals","volume":"26","author":"Sawadogo","year":"1995","journal-title":"Internat. J. Systems Sci."},{"article-title":"Shallow water equations","year":"2020","author":"Wikipedia","key":"2021083004505564200_ref30"},{"key":"2021083004505564200_ref31","first-page":"2596","article-title":"Optimal control of irrigation canals based on control vector parametrization","volume-title":"Proceedings of the 35th Chinese Control Conference (CCC)","author":"Wu","year":"2016"},{"key":"2021083004505564200_ref32","doi-asserted-by":"crossref","first-page":"4001","DOI":"10.5194\/hess-24-4001-2020","article-title":"A new form of the Saint-Venant equations for variable topography","volume":"24","author":"Yu","year":"2020","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"2021083004505564200_ref33","doi-asserted-by":"crossref","first-page":"1957","DOI":"10.1016\/j.camwa.2011.06.039","article-title":"On numerical stabilization in the solution of Saint-Venant equations using the finite element method","volume":"62","author":"Zarmehi","year":"2011","journal-title":"Comput. Math. Appl."}],"container-title":["IMA Journal of Mathematical Control and Information"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/imamci\/article-pdf\/38\/3\/881\/40076684\/dnab016.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/imamci\/article-pdf\/38\/3\/881\/40076684\/dnab016.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,30]],"date-time":"2021-08-30T04:52:07Z","timestamp":1630299127000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/imamci\/article\/38\/3\/881\/6291510"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,3]]},"references-count":33,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,6,3]]},"published-print":{"date-parts":[[2021,8,28]]}},"URL":"https:\/\/doi.org\/10.1093\/imamci\/dnab016","relation":{},"ISSN":["0265-0754","1471-6887"],"issn-type":[{"type":"print","value":"0265-0754"},{"type":"electronic","value":"1471-6887"}],"subject":[],"published-other":{"date-parts":[[2021,9]]},"published":{"date-parts":[[2021,6,3]]}}}