{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:46:30Z","timestamp":1740123990016,"version":"3.37.3"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,6,20]],"date-time":"2020-06-20T00:00:00Z","timestamp":1592611200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,6,20]],"date-time":"2020-06-20T00:00:00Z","timestamp":1592611200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100012740","name":"Gruppo Nazionale per l\u2019Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni","doi-asserted-by":"publisher","award":["Metodi di analisi reale per l\u2019approssimazione attraverso operatori discreti e applicazioni"],"award-info":[{"award-number":["Metodi di analisi reale per l\u2019approssimazione attraverso operatori discreti e applicazioni"]}],"id":[{"id":"10.13039\/100012740","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2020,7]]},"DOI":"10.1007\/s10957-020-01700-2","type":"journal-article","created":{"date-parts":[[2020,6,20]],"date-time":"2020-06-20T05:02:24Z","timestamp":1592629344000},"page":"24-49","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Strong Local Optimality for a Bang\u2013Bang\u2013Singular Extremal: General Constraints"],"prefix":"10.1007","volume":"186","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5493-6013","authenticated-orcid":false,"given":"Laura","family":"Poggiolini","sequence":"first","affiliation":[]},{"given":"Gianna","family":"Stefani","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,6,20]]},"reference":[{"issue":"3","key":"1700_CR1","doi-asserted-by":"publisher","first-page":"2274","DOI":"10.1137\/17M1140248","volume":"56","author":"L Poggiolini","year":"2018","unstructured":"Poggiolini, L., Stefani, G.: Strong local optimality for a bang-bang-singular extremal: the fixed-free case. SIAM J. Control Optim. 56(3), 2274\u20132294 (2018). https:\/\/doi.org\/10.1137\/17M1140248","journal-title":"SIAM J. Control Optim."},{"key":"1700_CR2","doi-asserted-by":"crossref","unstructured":"Poggiolini, L., Stefani, G.: Constrained bang-bang-singular extremals. In: CDC 2019 Proceedings. IEEE (2019)","DOI":"10.1109\/CDC40024.2019.9029814"},{"key":"1700_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-06404-7","volume-title":"Control Theory from the Geometric Viewpoint","author":"AA Agrachev","year":"2004","unstructured":"Agrachev, A.A., Sachkov, Y.L.: Control Theory from the Geometric Viewpoint. Springer, Berlin (2004)"},{"issue":"4","key":"1700_CR4","doi-asserted-by":"publisher","first-page":"991","DOI":"10.1137\/S036301290138866X","volume":"41","author":"AA Agrachev","year":"2002","unstructured":"Agrachev, A.A., Stefani, G., Zezza, P.: Strong optimality for a bang\u2013bang trajectory. SIAM J. Control Optim. 41(4), 991\u20131014 (2002)","journal-title":"SIAM J. Control Optim."},{"key":"1700_CR5","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1016\/j.sysconle.2004.05.005","volume":"53","author":"L Poggiolini","year":"2004","unstructured":"Poggiolini, L., Stefani, G.: State-local optimality of a bang-bang trajectory: a Hamiltonian approach. Syst. Control Lett. 53, 269\u2013279 (2004)","journal-title":"Syst. Control Lett."},{"issue":"1","key":"1700_CR6","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1137\/090771405","volume":"49","author":"L Poggiolini","year":"2011","unstructured":"Poggiolini, L., Spadini, M.: Strong local optimality for a bang\u2013bang trajectory in a Mayer problem. SIAM J. Control Optim. 49(1), 140\u2013161 (2011). https:\/\/doi.org\/10.1137\/090771405","journal-title":"SIAM J. Control Optim."},{"key":"1700_CR7","doi-asserted-by":"publisher","unstructured":"Poggiolini, L., Spadini, M.: Bang\u2013bang trajectories with a double switching time in the minimum time problem. ESAIM: COCV (2015). https:\/\/doi.org\/10.1051\/cocv\/2015021","DOI":"10.1051\/cocv\/2015021"},{"key":"1700_CR8","doi-asserted-by":"crossref","unstructured":"Stefani, G.: Strong optimality of singular trajectories. In: Ancona, F., Bressan, A., Cannarsa, P., Clarke, F., Wolenski, P. R. (eds.) Geometric Control and Nonsmooth Analysis, Series on Advances in Mathematics for Applied Sciences, vol.\u00a076, pp. 300\u2013326. World\u00a0Scientific\u00a0Publishing\u00a0Co.\u00a0Pte.\u00a0Ltd., Hackensack (2008). Pp. 361 ISBN: 978-981-277-606-8","DOI":"10.1142\/9789812776075_0018"},{"key":"1700_CR9","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1007\/s10883-011-9127-y","volume":"17","author":"L Poggiolini","year":"2011","unstructured":"Poggiolini, L., Stefani, G.: Bang-singular-bang extremals: sufficient optimality conditions. J. Dyn. Control Syst. 17, 469\u2013514 (2011). https:\/\/doi.org\/10.1007\/s10883-011-9127-y","journal-title":"J. Dyn. Control Syst."},{"issue":"4","key":"1700_CR10","first-page":"1029","volume":"39","author":"FC Chittaro","year":"2010","unstructured":"Chittaro, F.C., Stefani, G.: Singular extremals in multi-input time-optimal problem: a sufficient condition. Control Cybernet. 39(4), 1029\u20131068 (2010)","journal-title":"Control Cybernet."},{"issue":"3","key":"1700_CR11","doi-asserted-by":"publisher","first-page":"786","DOI":"10.1051\/cocv\/2015026","volume":"22","author":"FC Chittaro","year":"2016","unstructured":"Chittaro, F.C., Stefani, G.: Minimum-time strong optimality of a singular arc: the multi-input non involutive case. ESAIM COCV 22(3), 786\u2013810 (2016). https:\/\/doi.org\/10.1051\/cocv\/2015026","journal-title":"ESAIM COCV"},{"issue":"1","key":"1700_CR12","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1137\/16M110304X","volume":"56","author":"AA Agrachev","year":"2018","unstructured":"Agrachev, A.A., Biolo, C.: Switching in time-optimal problem with control in a ball. SIAM J. Control Optim. 56(1), 183\u2013200 (2018). https:\/\/doi.org\/10.1137\/16M110304X","journal-title":"SIAM J. Control Optim."},{"issue":"2","key":"1700_CR13","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/s10883-018-9416-9","volume":"25","author":"AA Agrachev","year":"2019","unstructured":"Agrachev, A.A., Biolo, C.: Optimality of broken extremals. J. Dyn. Control Syst. 25(2), 289\u2013307 (2019). https:\/\/doi.org\/10.1007\/s10883-018-9416-9","journal-title":"J. Dyn. Control Syst."},{"key":"1700_CR14","doi-asserted-by":"crossref","unstructured":"Caillau, J.B., Orieux, M.: Sufficient conditions for time optimality of systems with control on the disk. In: CDC 2019 Proceedings. IEEE (2019)","DOI":"10.1109\/CDC40024.2019.9029896"},{"key":"1700_CR15","unstructured":"Caillau, J.-B., Fejoz, J., Orieux, M., Roussarie, R.: Singularities of min time affine control systems. (2018). https:\/\/hal.inria.fr\/hal-01718345"},{"key":"1700_CR16","doi-asserted-by":"crossref","unstructured":"Maurer, H., Osmolovskii, N.: Second-order conditions for optimal control problems with mixed control-state constraints and control appearing linearly. In: 2013 IEEE 52nd Annual Conference on Decision and Control (CDC), IEEE Conference on Decision and Control, pp. 514\u2013519 (2013)","DOI":"10.1109\/CDC.2013.6759933"},{"issue":"3","key":"1700_CR17","doi-asserted-by":"publisher","first-page":"511","DOI":"10.3934\/naco.2012.2.511","volume":"2","author":"MS Aronna","year":"2012","unstructured":"Aronna, M.S., Bonnans, J.F., Dmitruk, A.V., Lotito, P.A.: Quadratic order conditions for bang\u2013singular extremals. Numer. Algebra Control Optim. 2(3), 511\u2013546 (2012). https:\/\/doi.org\/10.3934\/naco.2012.2.511","journal-title":"Numer. Algebra Control Optim."},{"issue":"2","key":"1700_CR18","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1051\/cocv:2007012","volume":"13","author":"B Bonnard","year":"2007","unstructured":"Bonnard, B., Caillau, J.B., Tr\u00e9lat, E.: Second order optimality conditions in the smooth case and applications in optimal control. ESAIM COCV 13(2), 207\u2013236 (2007). https:\/\/doi.org\/10.1051\/cocv:2007012","journal-title":"ESAIM COCV"},{"issue":"4","key":"1700_CR19","doi-asserted-by":"publisher","first-page":"1705","DOI":"10.1051\/cocv\/2017070","volume":"24","author":"RS Hilscher","year":"2018","unstructured":"Hilscher, R.S., Zeidan, V.: Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity. ESAIM COCV 24(4), 1705\u20131734 (2018). https:\/\/doi.org\/10.1051\/cocv\/2017070","journal-title":"ESAIM COCV"},{"issue":"2","key":"1700_CR20","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/s10957-009-9594-4","volume":"144","author":"G Vossen","year":"2010","unstructured":"Vossen, G.: Switching time optimization for bang\u2013bang and singular controls. J. Optim. Theory Appl. 144(2), 409\u2013429 (2010). https:\/\/doi.org\/10.1007\/s10957-009-9594-4","journal-title":"J. Optim. Theory Appl."},{"key":"1700_CR21","volume-title":"Contemporary Trends in Non-linear Geometric Control Theory and Its Applications","author":"AA Agrachev","year":"2002","unstructured":"Agrachev, A.A., Stefani, G., Zezza, P.: Symplectic methods for strong local optimality in the bang-bang case. In: Anzaldo-Meneses, J.G.A., Bonnard, B., Monroy-Perez, F. (eds.) Contemporary Trends in Non-linear Geometric Control Theory and Its Applications. World Scientific, London (2002)"},{"key":"1700_CR22","doi-asserted-by":"crossref","unstructured":"Stefani, G., Zezza, P.: Variational Methods in Imaging and Geometric Control, chap. A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I. De Gruyter, Berlin (2016)","DOI":"10.1515\/9783110430394-017"},{"issue":"5","key":"1700_CR23","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1080\/002071798221533","volume":"71","author":"AA Agrachev","year":"1998","unstructured":"Agrachev, A.A., Stefani, G., Zezza, P.: An invariant second variation in optimal control. Int. J. Control 71(5), 689\u2013715 (1998)","journal-title":"Int. J. Control"},{"issue":"3","key":"1700_CR24","doi-asserted-by":"publisher","first-page":"876","DOI":"10.1137\/S0363012995286848","volume":"35","author":"G Stefani","year":"1997","unstructured":"Stefani, G., Zezza, P.: Constrained regular LQ-control problems. SIAM J. Control Optim. 35(3), 876\u2013900 (1997)","journal-title":"SIAM J. Control Optim."},{"key":"1700_CR25","doi-asserted-by":"publisher","first-page":"525","DOI":"10.2140\/pjm.1951.1.525","volume":"1","author":"MR Hestenes","year":"1951","unstructured":"Hestenes, M.R.: Applications of the theory of quadratic forms in Hilbert space to calculus of variations. Pacific J. Math. 1, 525\u2013581 (1951)","journal-title":"Pacific J. Math."},{"key":"1700_CR26","unstructured":"Maurer, H.: Theory and applications of bang\u2013bang and singular control problems. In: Conference Slides (2007). 23rd IFIP TC 7 Conference on System Modelling and Optimization Krak\u00f3w, Poland, July 23\u201327, 2007"},{"issue":"4B","key":"1700_CR27","first-page":"1305","volume":"38","author":"U Felgenhauer","year":"2009","unstructured":"Felgenhauer, U., Poggiolini, L., Stefani, G.: Optimality and stability result for bang-bang optimal controls with simple and double switch behaviour. Control Cybernet. 38(4B), 1305\u20131325 (2009)","journal-title":"Control Cybernet."},{"issue":"5","key":"1700_CR28","doi-asserted-by":"publisher","first-page":"3511","DOI":"10.1137\/120895421","volume":"51","author":"L Poggiolini","year":"2013","unstructured":"Poggiolini, L., Stefani, G.: Structural stability for bang-singular-bang extremals in the minimum time problem. SIAM J. Control Optim. 51(5), 3511\u20133531 (2013). https:\/\/doi.org\/10.1137\/120895421","journal-title":"SIAM J. Control Optim."},{"key":"1700_CR29","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/978-3-319-02132-4_19","volume-title":"Geometric Control Theory and Sub-Riemannian Geometry, Springer INdAM Series","author":"L Poggiolini","year":"2014","unstructured":"Poggiolini, L., Stefani, G.: A case study in strong optimality and structural stability of bang-singular extremals. In: Stefani, G., Boscain, U., Gauthier, J.P., Sarychev, A., Sigalotti, M. (eds.) Geometric Control Theory and Sub-Riemannian Geometry, Springer INdAM Series, vol. 5, pp. 333\u2013350. Springer, Berlin (2014). https:\/\/doi.org\/10.1007\/978-3-319-02132-4_19"},{"issue":"6","key":"1700_CR30","doi-asserted-by":"publisher","first-page":"3779","DOI":"10.1137\/16M1083761","volume":"55","author":"L Poggiolini","year":"2017","unstructured":"Poggiolini, L.: Structural stability of bang-bang trajectories with a double switching time in the minimum time problem. SIAM J. Control Optim. 55(6), 3779\u20133798 (2017). https:\/\/doi.org\/10.1137\/16M1083761","journal-title":"SIAM J. Control Optim."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-020-01700-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-020-01700-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-020-01700-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,19]],"date-time":"2021-06-19T23:24:39Z","timestamp":1624145079000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-020-01700-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,20]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,7]]}},"alternative-id":["1700"],"URL":"https:\/\/doi.org\/10.1007\/s10957-020-01700-2","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"type":"print","value":"0022-3239"},{"type":"electronic","value":"1573-2878"}],"subject":[],"published":{"date-parts":[[2020,6,20]]},"assertion":[{"value":"23 January 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 June 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 June 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}