{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T02:18:56Z","timestamp":1773800336107,"version":"3.50.1"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Math Sci"],"published-print":{"date-parts":[[2009,1]]},"DOI":"10.1007\/s10958-008-9274-1","type":"journal-article","created":{"date-parts":[[2009,1,5]],"date-time":"2009-01-05T17:26:12Z","timestamp":1231176372000},"page":"440-567","source":"Crossref","is-referenced-by-count":3,"title":["Generalized solutions for singular optimal control problems"],"prefix":"10.1007","volume":"156","author":[{"given":"M.","family":"Guerra","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2009,1,6]]},"reference":[{"key":"9274_CR1","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1070\/SM1979v035n06ABEH001623","volume":"35","author":"A. A. Agrachev","year":"1979","unstructured":"A. A. Agrachev and R. V. Gamkrelidze, \u201cExponential representation of flows and chronological calculus,\u201d Mat. Sb., 35, 727\u2013785 (1979).","journal-title":"Mat. Sb."},{"issue":"1","key":"9274_CR2","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1070\/SM1987v058n01ABEH003090","volume":"58","author":"A. A. Agrachev","year":"1987","unstructured":"A. A. Agrachev and A. V. Sarychev, \u201cOn reduction of a smooth system linear in the control,\u201d Mat. Sb., 58, No. 1, 15\u201330 (1987).","journal-title":"Mat. Sb."},{"key":"9274_CR3","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/BF01307214","volume":"14","author":"A. A. Agrachev","year":"1989","unstructured":"A. A. Agrachev, R. V. Gamkrelidze, and A. V. Sarychev, \u201cLocal invariants of smooth control systems,\u201d Acta Appl. Math., 14, 191\u2013237 (1989).","journal-title":"Acta Appl. Math."},{"issue":"6","key":"9274_CR4","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1016\/S0294-1449(16)30118-4","volume":"13","author":"A. A. Agrachev","year":"1996","unstructured":"A. A. Agrachev and A. V. Sarychev, \u201cAbnormal sub-Riemanian geodesics: Morse index and rigidity,\u201d Ann. Inst. Poincar\u00e9, Anal. Nonlin., 13, No. 6, 635\u2013690 (1996).","journal-title":"Ann. Inst. Poincar\u00e9, Anal. Nonlin."},{"key":"9274_CR5","doi-asserted-by":"crossref","unstructured":"A. A. Agrachev and Yu. L. Sachkov, Control Theory from the Geometric Viewpoint, Encycl. Math. Sci., 87, Springer-Verlag (2004).","DOI":"10.1007\/978-3-662-06404-7"},{"key":"9274_CR6","doi-asserted-by":"crossref","unstructured":"D. S. Bernstein and V. Zeidan, \u201cThe singular linear-quadratic regulator problem and the Goh\u2013Riccati equation,\u201d in: Proc. 29th Conf. Decision and Control, Honolulu, Hawaii (1990), pp. 334\u2013339.","DOI":"10.1109\/CDC.1990.203608"},{"key":"9274_CR7","first-page":"227","volume":"78","author":"A. Bressan","year":"1987","unstructured":"A. Bressan, \u201cOn differential systems with impulsive controls,\u201d Rend. Semin. Univ. Padova, 78, 227\u2013235 (1987).","journal-title":"Rend. Semin. Univ. Padova"},{"issue":"3","key":"9274_CR8","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1007\/BF02193094","volume":"81","author":"A. Bressan","year":"1994","unstructured":"A. Bressan and F. Rampazzo, \u201cImpulsive control systems without commutativity assumptions,\u201d J. Optim. Theory Appl., 81, No. 3, 435\u2013457 (1994).","journal-title":"J. Optim. Theory Appl."},{"key":"9274_CR9","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1137\/1022089","volume":"22","author":"J. Casti","year":"1980","unstructured":"J. Casti, \u201cThe linear-quadratic control problem: some recent results and outstanding problems,\u201d SIAM Rev., 22, 459\u2013485 (1980).","journal-title":"SIAM Rev."},{"key":"9274_CR10","unstructured":"L. Cesari, Optimization Theory and Applications. Problems with Differential Equations, Springer-Verlag (1983)."},{"key":"9274_CR11","doi-asserted-by":"crossref","unstructured":"D. J. Clements and B. D. O. Anderson, Singular Optimal Control: The Linear-Quadratic Problem, Lect. Notes Control Inform. Sci., Springer-Verlag (1978).","DOI":"10.1007\/BFb0004988"},{"key":"9274_CR12","unstructured":"P. A. M. Dirac, Lectures on Quantum Mechanics, Belfer Grad. School of Science (1964)."},{"key":"9274_CR13","doi-asserted-by":"crossref","unstructured":"R. V. Gamkrelidze, Principles of Optimal Control Theory, Plenum Press (1978).","DOI":"10.1007\/978-1-4684-7398-8"},{"issue":"3","key":"9274_CR14","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/s10450-006-0005-y","volume":"12","author":"J.-P. Gauthier","year":"2006","unstructured":"J.-P. Gauthier and V. Zakalyukin, \u201cOn the motion planning problem, complexity, entropy and nonholonomic interpolation,\u201d J. Dynam. Control Syst., 12, No. 3, 371\u2013404 (2006).","journal-title":"J. Dynam. Control Syst."},{"key":"9274_CR15","doi-asserted-by":"crossref","unstructured":"M. Guerra, \u201cGeneralized solutions for linear-quadratic optimal control problems,\u201d in: Equadiff\u201999: Int. Conf. on Differential Equations (B. Fiedler, K. Gr\u00f6ger, and J. Sprekels, eds.), Vol. 2, World Scientific (2000), pp. 856\u2013858.","DOI":"10.1142\/9789812792617_0168"},{"issue":"2","key":"9274_CR16","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1023\/A:1009534204516","volume":"6","author":"M. Guerra","year":"2000","unstructured":"M. Guerra, \u201cHighly singular L-Q problems: Solutions in distribution spaces,\u201d J. Dynam. Control Syst., 6, No. 2, 265\u2013309 (2000).","journal-title":"J. Dynam. Control Syst."},{"key":"9274_CR17","unstructured":"M. Guerra, \u201cSingular L-Q problems and the Dirac\u2013Bergmann theory of constraints,\u201d in: Nonlinear Control 2000 (A. Isidori, F. Lamnabhi-Lagarrigue, and W. Respondek, eds.), Springer-Verlag (2001), pp. 409\u2013422."},{"key":"9274_CR18","unstructured":"M. Guerra, Generalized Solutions for Singular L-Q Problems [in Portuguese], Ph.D. Thesis, Univ. of Aveiro (2001)."},{"issue":"1","key":"9274_CR19","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1023\/B:JOTH.0000013554.95339.07","volume":"120","author":"M. Guerra","year":"2004","unstructured":"M. Guerra, \u201cDistribution-like Hamiltonian flows and generalized optimal controls,\u201d J. Math. Sci., 120, No. 1, 895\u2013918 (2004).","journal-title":"J. Math. Sci."},{"key":"9274_CR20","doi-asserted-by":"crossref","unstructured":"M. Guerra, \u201cHamiltonian flows for impulsive control systems,\u201d in: Generalized Solutions in Control Problems (Yu. L. Sachkov, ed.), Proc. IFAC Workshop GSCP-04 and satellite events, Pereslavl-Zalessky, Russia, September 21\u201329, 2004, (2004), pp. 77\u201392.","DOI":"10.1016\/S1474-6670(17)30803-0"},{"issue":"4","key":"9274_CR21","first-page":"363","volume":"64","author":"M. Guerra","year":"2005","unstructured":"M. Guerra, \u201cDiscontinuous Hamiltonian flows for nonlinear control systems,\u201d Rend. Sem. Mat. Univ. Pol. Torino, 64, No. 4, 363\u2013382 (2005).","journal-title":"Rend. Sem. Mat. Univ. Pol. Torino"},{"key":"9274_CR22","unstructured":"M. Guerra, \u201cGeometrical synthesis for noncoercive nonconvex optimal control problems,\u201d in: Proc. CONTROLO\u20192006 (M. Ayala Botto, ed.), 7th Portuguese Conference on Automatic Control, IST September 11\u201313, 2006, (2006), WA2-1 (CD-ROM)."},{"key":"9274_CR23","unstructured":"M. Guerra and A. Sarychev, \u201cGeneralized optimal controls for the singular linear-quadratic problem,\u201d in: Proc. 3th Portuguese Conf. on Automatic Control, Controlo\u201998, APCA (1998), pp. 431\u2013436."},{"key":"9274_CR24","unstructured":"M. Guerra and A. Sarychev, \u201cRegularizations of optimal control problems for control-affine systems,\u201d in: Proc. 17th Int. Symp. on Mathematical Theory of Networks and Systems (MTNS 2006) (Y. Yamamoto, ed.), Kyoto, Japan, July 24-28, 2006, (2006), pp. 490\u2013500."},{"key":"9274_CR25","unstructured":"M. Guerra and A. Sarychev, \u201cApproximation of generalized minimizers and regularization of optimal control problems,\u201d in: Proc. IFAC 3rd Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (LHMNLC\u201906) (F. Bullo and K. Fujimoto, eds.), Nagoya, Japan, July 19\u201321, 2006, (2006), pp. 233\u2013238."},{"key":"9274_CR26","doi-asserted-by":"crossref","unstructured":"M. Guerra and A. Sarychev, \u201cExistence and Lipschitzian regularity for relaxed minimizers,\u201d submitted to Proc. Workshop on Mathematical Control Theory and Finance, Lisbon, Portugal, April 2007.","DOI":"10.1007\/978-3-540-69532-5_13"},{"key":"9274_CR27","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1051\/cocv:2003024","volume":"9","author":"F. Jean","year":"2003","unstructured":"F. Jean, \u201cEntropy and complexity of a path in sub-Riemannian geometry,\u201d ESAIM Control Optim. Calc. Var., 9, 485\u2013508 (2003).","journal-title":"ESAIM Control Optim. Calc. Var."},{"key":"9274_CR28","doi-asserted-by":"crossref","unstructured":"V. Jurdjevic, \u201cThe Lie saturate and its applications to singular control problems,\u201d in: New Trends in Nonlinear Control Theory. Proc. Int. Conf. Nonlinear Syst., Nantes, France, 1988, Lect. Notes Control Inf. Sci., 122 (1989), pp. 222\u2013230.","DOI":"10.1007\/BFb0043031"},{"key":"9274_CR29","doi-asserted-by":"crossref","unstructured":"V. Jurdjevic, Geometric Control Theory, Cambridge Univ. Press (1997).","DOI":"10.1017\/CBO9780511530036"},{"key":"9274_CR30","unstructured":"V. Judjevic and I. A. K. Kupka, Linear systems with singular quadratic cost, Preprint (1992)."},{"key":"9274_CR31","first-page":"102","volume":"5","author":"R. E. Kalman","year":"1960","unstructured":"R. E. Kalman, \u201cContributions to the theory of optimal control,\u201d Bol. Soc. Mat. Mexicana, II. Ser., 5, 102\u2013119 (1960).","journal-title":"Bol. Soc. Mat. Mexicana, II. Ser."},{"key":"9274_CR32","first-page":"92","volume":"27","author":"M. A. Krasnosel\u2019skii","year":"1972","unstructured":"M. A. Krasnosel\u2019skii and A. V. Pokrovskii, \u201cVibrostable differential equations with discontinuous right-hand sides,\u201d Tr. Mosk. Math. Obshch., 27, 92\u2013112 (1972).","journal-title":"Tr. Mosk. Math. Obshch."},{"key":"9274_CR33","doi-asserted-by":"crossref","unstructured":"I. A. K. Kupka, \u201cDegenerate linear systems with quadratic cost under finiteness assumptions,\u201d in: New Trends in Nonlinear Control Theory. Proc. Int. Conf. Nonlinear Syst., Nantes, France, 1988, Lect. Notes Control Inf. Sci., 122, (1989), pp. 231\u2013239.","DOI":"10.1007\/BFb0043032"},{"key":"9274_CR34","unstructured":"E. B. Lee and L. Markus, Foundations of Optimal Control Theory, Wiley (1967)."},{"key":"9274_CR35","doi-asserted-by":"crossref","unstructured":"B. M. Miller and E. Ya. Rubinovich, Impulsive Control in Continuous and Discrete-Continuous Systems, Springer-Verlag (2003).","DOI":"10.1007\/978-1-4615-0095-7"},{"key":"9274_CR36","first-page":"160","volume":"48","author":"Yu. Orlov","year":"1987","unstructured":"Yu. Orlov, \u201cVariational analysis of optimal systems with generalized controls of measure type, I,\u201d Autom. Remote Control, 48, 160\u2013165 (1987).","journal-title":"Autom. Remote Control"},{"key":"9274_CR37","first-page":"306","volume":"48","author":"Yu. Orlov","year":"1987","unstructured":"Yu. Orlov, \u201cVariational analysis of optimal systems with generalized controls of measure type, II\u201d, Autom. Remote Control, 48, 306\u2013316 (1987).","journal-title":"Autom. Remote Control"},{"key":"9274_CR38","volume-title":"Theory of Optimal Systems with Generalized Controls [in Russian]","author":"Yu. Orlov","year":"1988","unstructured":"Yu. Orlov, Theory of Optimal Systems with Generalized Controls [in Russian], Nauka, Moscow (1988)."},{"key":"9274_CR39","unstructured":"F. Rampazzo, \u201cLie brackets and impulsive controls: An unavoidable connection,\u201d in: Differential Geometry and Control (G. Ferreyra et al., eds.), Proc. Summer Research Inst., Boulder, USA, 1997, Amer. Math. Soc., Proc. Symp. Pure Math., 64, (1999), pp. 279\u2013296."},{"key":"9274_CR40","unstructured":"F. Riesz and B. Sz.-Nagy, Functional Analysis, Dover Publ. (1990)."},{"key":"9274_CR41","unstructured":"W. Rudin, Real and Complex Analysis, McGraw-Hill (1987)."},{"issue":"9","key":"9274_CR42","first-page":"1551","volume":"24","author":"A. Sarychev","year":"1988","unstructured":"A. Sarychev, \u201cIntegral representation of trajectories of control systems with generalized right sides,\u201d Differ. Uravn., 24, No. 9, 1551\u20131564 (1988).","journal-title":"Differ. Uravn."},{"key":"9274_CR43","doi-asserted-by":"crossref","unstructured":"A. Sarychev, \u201cNonlinear systems with impulsive and generalized function controls,\u201d in: Nonlinear Synthesis (C. I. Byrnes and A. Kurzhansky, eds.), Proc. IIASA Workshop, Sopron, Hungary, June 1989, Birk\u00e4user (1991), pp. 244\u2013257.","DOI":"10.1007\/978-1-4757-2135-5_19"},{"key":"9274_CR44","unstructured":"E. D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems, Texts Appl. Math., 6, Springer-Verlag (1990)."},{"issue":"3","key":"9274_CR45","doi-asserted-by":"crossref","first-page":"876","DOI":"10.1137\/S0363012995286848","volume":"35","author":"G. Stefani","year":"1997","unstructured":"G. Stefani and P. Zezza, \u201cConstrained regular LQ-control problems,\u201d SIAM J. Control Optim., 35, No. 3, 876\u2013900 (1997).","journal-title":"SIAM J. Control Optim."},{"key":"9274_CR46","doi-asserted-by":"crossref","unstructured":"K. Volckaert and D. Aeyels, \u201cThe Gotay\u2013Nester algorithm in singular optimal control,\u201d in: Proc. 38th Conf. Decision and Control, Phoenix, Arizona, USA (1999), pp. 873\u2013874.","DOI":"10.1109\/CDC.1999.832901"},{"issue":"2","key":"9274_CR47","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1137\/0324018","volume":"24","author":"J. C. Willems","year":"1986","unstructured":"J. C. Willems, A. Kitap\u00e7i, and L. M. Silverman, \u201cSingular optimal control: A geometric approach,\u201d SIAM J. Control Optim., 24, No. 2, 323\u2013337 (1986).","journal-title":"SIAM J. Control Optim."},{"key":"9274_CR48","doi-asserted-by":"crossref","unstructured":"S. T. Zavalischin and A. N. Sesekin, Dynamic Impulse Systems. Theory and Applications. Mathematics and Its Applications, 394, Kluwer (1997).","DOI":"10.1007\/978-94-015-8893-5"}],"container-title":["Journal of Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10958-008-9274-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10958-008-9274-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10958-008-9274-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T06:09:24Z","timestamp":1559455764000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10958-008-9274-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":48,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["9274"],"URL":"https:\/\/doi.org\/10.1007\/s10958-008-9274-1","relation":{},"ISSN":["1072-3374","1573-8795"],"issn-type":[{"value":"1072-3374","type":"print"},{"value":"1573-8795","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}