Renault, Vincent; Thieullen, Michèle; Trélat, Emmanuel Minimal time spiking in various ChR2-controlled neuron models. (English) Zbl 1383.49054 J. Math. Biol. 76, No. 3, 567-608 (2018). MSC: 49S05 49J15 49J30 93C15 92C20 PDF BibTeX XML Cite \textit{V. Renault} et al., J. Math. Biol. 76, No. 3, 567--608 (2018; Zbl 1383.49054) Full Text: DOI
Chittaro, Francesca; Stefani, Gianna Minimum-time strong optimality of a singular arc: the multi-input non involutive case. (English) Zbl 1344.49034 ESAIM, Control Optim. Calc. Var. 22, No. 3, 786-810 (2016). MSC: 49K15 49K30 49J15 49J30 PDF BibTeX XML Cite \textit{F. Chittaro} and \textit{G. Stefani}, ESAIM, Control Optim. Calc. Var. 22, No. 3, 786--810 (2016; Zbl 1344.49034) Full Text: DOI
Felgenhauer, Ursula Discretization of semilinear bang-singular-bang control problems. (English) Zbl 1338.49060 Comput. Optim. Appl. 64, No. 1, 295-326 (2016). MSC: 49M25 49M05 49J30 PDF BibTeX XML Cite \textit{U. Felgenhauer}, Comput. Optim. Appl. 64, No. 1, 295--326 (2016; Zbl 1338.49060) Full Text: DOI
Chyba, Monique; Coron, Jean-Michel; Gabriel, Pierre; Jacquemard, Alain; Patterson, Geoff; Picot, Gautier; Shang, Peipei Optimal geometric control applied to the protein misfolding cyclic amplification process. (English) Zbl 1309.93111 Acta Appl. Math. 135, No. 1, 145-173 (2015). MSC: 93C95 70Q05 70E60 PDF BibTeX XML Cite \textit{M. Chyba} et al., Acta Appl. Math. 135, No. 1, 145--173 (2015; Zbl 1309.93111) Full Text: DOI
Fall, Mouhamed Moustapha; Mahmoudi, Fethi Weighted Hardy inequality with higher dimensional singularity on the boundary. (English) Zbl 1296.35038 Calc. Var. Partial Differ. Equ. 50, No. 3-4, 779-798 (2014). Reviewer: Dumitru Motreanu (Perpignan) MSC: 35J20 35J57 35J75 35B33 35A01 PDF BibTeX XML Cite \textit{M. M. Fall} and \textit{F. Mahmoudi}, Calc. Var. Partial Differ. Equ. 50, No. 3--4, 779--798 (2014; Zbl 1296.35038) Full Text: DOI arXiv
Poggiolini, Laura; Stefani, Gianna A case study in strong optimality and structural stability of bang-singular extremals. (English) Zbl 1290.49007 Stefani, Gianna (ed.) et al., Geometric control theory and sub-Riemannian geometry. Proceedings of the meeting on geometric control theory and sub-Riemannian geometry, dedicated to Andrei A. Agrachev on the occasion of his 60th birthday, Cortona, Italy, May 21–25, 2012. Cham: Springer (ISBN 978-3-319-02131-7/hbk; 978-3-319-02132-4/ebook). Springer INdAM Series 5, 333-350 (2014). MSC: 49J30 49K30 49K40 49N60 PDF BibTeX XML Cite \textit{L. Poggiolini} and \textit{G. Stefani}, Springer INdAM Ser. 5, 333--350 (2014; Zbl 1290.49007) Full Text: DOI
Felgenhauer, Ursula Stability analysis of variational inequalities for bang-singular-bang controls. (English) Zbl 1318.49014 Control Cybern. 42, No. 3, 557-592 (2013). MSC: 49J40 49J30 PDF BibTeX XML Cite \textit{U. Felgenhauer}, Control Cybern. 42, No. 3, 557--592 (2013; Zbl 1318.49014)
Dmitruk, Andrei; Samylovskiy, Ivan A simple trolley-like model in the presence of a nonlinear friction and a bounded fuel expenditure. (English) Zbl 1297.49030 Discuss. Math., Differ. Incl. Control Optim. 33, No. 2, 135-147 (2013). MSC: 49K15 49N90 70Q05 PDF BibTeX XML Cite \textit{A. Dmitruk} and \textit{I. Samylovskiy}, Discuss. Math., Differ. Incl. Control Optim. 33, No. 2, 135--147 (2013; Zbl 1297.49030) Full Text: DOI
Poggiolini, Laura; Stefani, Gianna Structural stability for bang-singular-bang extremals in the minimum time problem. (English) Zbl 1280.49011 SIAM J. Control Optim. 51, No. 5, 3511-3531 (2013). MSC: 49J30 49K30 49J15 49K15 49K40 93C10 PDF BibTeX XML Cite \textit{L. Poggiolini} and \textit{G. Stefani}, SIAM J. Control Optim. 51, No. 5, 3511--3531 (2013; Zbl 1280.49011) Full Text: DOI arXiv
Fall, Mouhamed Moustapha On the Hardy-Poincaré inequality with boundary singularities. (English) Zbl 1259.35077 Commun. Contemp. Math. 14, No. 3, 1250019, 13 p. (2012). MSC: 35J20 35J57 35J75 35B33 35A01 PDF BibTeX XML Cite \textit{M. M. Fall}, Commun. Contemp. Math. 14, No. 3, 1250019, 13 p. (2012; Zbl 1259.35077) Full Text: DOI arXiv
Sánchez Licea, Gerardo Sufficiency in optimal control without the strengthened condition of Legendre. (English) Zbl 1244.49036 J. Appl. Math. Bioinform. 1, No. 1, 1-20 (2011). MSC: 49K15 PDF BibTeX XML Cite \textit{G. Sánchez Licea}, J. Appl. Math. Bioinform. 1, No. 1, 1--20 (2011; Zbl 1244.49036)
Rosenblueth, Javier F.; Licea, Gerardo Sánchez Sufficient variational conditions for isoperimetric control problems. (English) Zbl 1245.49033 Int. Math. Forum 6, No. 5-8, 303-324 (2011). MSC: 49K15 PDF BibTeX XML Cite \textit{J. F. Rosenblueth} and \textit{G. S. Licea}, Int. Math. Forum 6, No. 5--8, 303--324 (2011; Zbl 1245.49033) Full Text: Link
Smol’yakov, E. R. Using singular extremals to obtain new equations of motion and unknown constants. (English. Russian original) Zbl 1182.49006 Cybern. Syst. Anal. 45, No. 4, 605-612 (2009); translation from Kibern. Sist. Anal. 2009, No. 4, 115-124 (2009). MSC: 49J30 93B17 PDF BibTeX XML Cite \textit{E. R. Smol'yakov}, Cybern. Syst. Anal. 45, No. 4, 605--612 (2009; Zbl 1182.49006); translation from Kibern. Sist. Anal. 2009, No. 4, 115--124 (2009) Full Text: DOI
Licea, Gerardo Sánchez Sufficiency by a direct method in the variable state problem of calculus of variations: singular extremals. (English) Zbl 1173.49019 IMA J. Math. Control Inf. 26, No. 3, 257-279 (2009). MSC: 49K15 PDF BibTeX XML Cite \textit{G. S. Licea}, IMA J. Math. Control Inf. 26, No. 3, 257--279 (2009; Zbl 1173.49019) Full Text: DOI
Borisov, V. F. Kelley condition and structure of Lagrange manifold in a neighborhood of a first-order singular extremal. (English. Russian original) Zbl 1219.49037 J. Math. Sci., New York 151, No. 6, 3431-3472 (2008); translation from Sovrem. Mat., Fundam. Napravl. 19, 5-44 (2006). MSC: 49Q20 49N10 37J05 49K15 PDF BibTeX XML Cite \textit{V. F. Borisov}, J. Math. Sci., New York 151, No. 6, 3431--3472 (2008; Zbl 1219.49037); translation from Sovrem. Mat., Fundam. Napravl. 19, 5--44 (2006) Full Text: DOI
Chyba, M.; Haberkorn, T. Autonomous underwater vehicles: singular extremals and chattering. (English) Zbl 1214.49005 Ceragioli, F. (ed.) et al., Systems, control, modeling and optimization. Proceedings of the 22nd IFIP TC7 conference, July 18–22, 2005, Turin, Italy. New York, NY: Springer (ISBN 0-387-33881-0/hbk). IFIP, International Federation for Information Processing 202, 103-113 (2006). MSC: 49J30 49K15 93C85 93B10 49N90 PDF BibTeX XML Cite \textit{M. Chyba} and \textit{T. Haberkorn}, IFIP, Int. Fed. Inf. Process. 202, 103--113 (2006; Zbl 1214.49005) Full Text: DOI
Rosenblueth, Javier F. Three improved notions of conjugate points in optimal control. (English) Zbl 1115.49028 IMA J. Math. Control Inf. 22, No. 4, 489-515 (2005). MSC: 49N60 49K15 PDF BibTeX XML Cite \textit{J. F. Rosenblueth}, IMA J. Math. Control Inf. 22, No. 4, 489--515 (2005; Zbl 1115.49028) Full Text: DOI
Berlanga, Ricardo; Rosenblueth, Javier F. Extended conjugate points in the calculus of variations. (English) Zbl 1049.49020 IMA J. Math. Control Inf. 21, No. 2, 159-173 (2004). MSC: 49K05 PDF BibTeX XML Cite \textit{R. Berlanga} and \textit{J. F. Rosenblueth}, IMA J. Math. Control Inf. 21, No. 2, 159--173 (2004; Zbl 1049.49020) Full Text: DOI
Rosenblueth, Javier F.; Sánchez Licea, Gerardo Strengthening Weierstrass’ condition. (English) Zbl 1076.49011 IMA J. Math. Control Inf. 21, No. 3, 275-294 (2004). MSC: 49K10 PDF BibTeX XML Cite \textit{J. F. Rosenblueth} and \textit{G. Sánchez Licea}, IMA J. Math. Control Inf. 21, No. 3, 275--294 (2004; Zbl 1076.49011) Full Text: DOI
Chyba, M.; Leonard, N. E.; Sontag, E. D. Singular trajectories in multi-input time-optimal problems: Application to controlled mechanical systems. (English) Zbl 1019.49002 J. Dyn. Control Syst. 9, No. 1, 103-129 (2003). MSC: 49J15 70Q05 93C15 49K15 34H05 49N90 PDF BibTeX XML Cite \textit{M. Chyba} et al., J. Dyn. Control Syst. 9, No. 1, 103--129 (2003; Zbl 1019.49002) Full Text: DOI arXiv
Popescu, M. Singular normal extremals and conjugate points for Bolza functionals. (English) Zbl 1028.49020 J. Optimization Theory Appl. 115, No. 2, 267-282 (2002). Reviewer: Jong Yeoul Park (Pusan) MSC: 49K15 PDF BibTeX XML Cite \textit{M. Popescu}, J. Optim. Theory Appl. 115, No. 2, 267--282 (2002; Zbl 1028.49020) Full Text: DOI
Popescu, Mihai Sufficient optimality conditions for singular control. (English) Zbl 1106.49034 Proc. Rom. Acad., Ser. A, Math. Phys. Tech. Sci. Inf. Sci. 2, No. 3, 71-73 (2001). MSC: 49K15 PDF BibTeX XML Cite \textit{M. Popescu}, Proc. Rom. Acad., Ser. A, Math. Phys. Tech. Sci. Inf. Sci. 2, No. 3, 71--73 (2001; Zbl 1106.49034)
Fattorini, H. O. Existence of singular extremals and singular functionals in reachable spaces. (English) Zbl 0997.93050 J. Evol. Equ. 1, No. 3, 325-347 (2001). Reviewer: Stanislaw Walczak (Łódź) MSC: 93C25 49J27 PDF BibTeX XML Cite \textit{H. O. Fattorini}, J. Evol. Equ. 1, No. 3, 325--347 (2001; Zbl 0997.93050) Full Text: DOI
Pelletier, Michèle Singular systems in dimension 3: Cuspidal case and tangent elliptic flat case. (English) Zbl 0967.93023 Isidori, Alberto (ed.) et al., Nonlinear control in the year 2000. Vol. 2. London: Springer. Lect. Notes Control Inf. Sci. 259, 193-203 (2001). Reviewer: Manuel Guerra (Lisboa) MSC: 93B29 53C17 49J15 PDF BibTeX XML Cite \textit{M. Pelletier}, Lect. Notes Control Inf. Sci. 259, 193--203 (2001; Zbl 0967.93023) Full Text: DOI
Osmolovskii, N. P. Second-order conditions for broken extremal. (English) Zbl 0971.49010 Ioffe, Alexander (ed.) et al., Calculus of variations and optimal control. Technion 1998. Selected papers of the international conference on the calculus of variations and related topics held at Technion - Israel Institute of Technology, Haifa, Israel, March 25-31, 1998. Vol. II. Boca Raton, FL: Chapman & Hall. Chapman Hall/CRC Res. Notes Math. 411, 198-216 (2000). Reviewer: Władysław Hejmo (Kraków) MSC: 49K15 49J15 93C15 PDF BibTeX XML Cite \textit{N. P. Osmolovskii}, Chapman Hall/CRC Res. Notes Math. 411, 198--216 (2000; Zbl 0971.49010)
Dmitruk, A. V. Quadratic order conditions of a local minimum for singular extremals in a general optimal control problem. (English) Zbl 0921.49012 Ferreyra, G. (ed.) et al., Differential geometry and control. Proceedings of the Summer Research Institute, Boulder, CO, USA, June 29–July 19, 1997. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 64, 163-198 (1999). Reviewer: Gianna Stefani (Firenze) MSC: 49K15 49K27 PDF BibTeX XML Cite \textit{A. V. Dmitruk}, Proc. Symp. Pure Math. 64, 163--198 (1999; Zbl 0921.49012)
Borisov, V. F. Singular extremals of order 3 and chattering. (English) Zbl 0943.49004 Ferreyra, G. (ed.) et al., Differential geometry and control. Proceedings of the Summer Research Institute, Boulder, CO, USA, June 29-July 19, 1997. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 64, 135-147 (1999). Reviewer: E.G.Al’brekht (Ekaterinburg) MSC: 49J15 34C05 93C15 PDF BibTeX XML Cite \textit{V. F. Borisov}, Proc. Symp. Pure Math. 64, 135--147 (1999; Zbl 0943.49004)
Agrachev, A. A. Feedback-invariant optimal control theory and differential geometry. II. Jacobi curves for singular extremals. (English) Zbl 0972.49014 J. Dyn. Control Syst. 4, No. 4, 583-604 (1998). Reviewer: Constantin Udrişte (Bucureşti) MSC: 49K15 53C22 93B52 53B05 53B15 PDF BibTeX XML Cite \textit{A. A. Agrachev}, J. Dyn. Control Syst. 4, No. 4, 583--604 (1998; Zbl 0972.49014) Full Text: DOI
Krupková, Olga The geometry of ordinary variational equations. (English) Zbl 0936.70001 Lecture Notes in Mathematics. 1678. Berlin: Springer. x, 251 p. (1997). Reviewer: A.Akutowicz (Berlin) MSC: 70-02 70H50 49K15 58E30 70H03 70H20 70H33 PDF BibTeX XML Cite \textit{O. Krupková}, The geometry of ordinary variational equations. Berlin: Springer (1997; Zbl 0936.70001) Full Text: DOI
Bonnard, B.; Kupka, I. Generic properties of singular trajectories. (English) Zbl 0907.93020 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 14, No. 2, 167-186 (1997). Reviewer: Gianna Stefani (Firenze) MSC: 93B29 49N60 PDF BibTeX XML Cite \textit{B. Bonnard} and \textit{I. Kupka}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 14, No. 2, 167--186 (1997; Zbl 0907.93020) Full Text: DOI Numdam EuDML
Dmitruk, A. V. Second order optimality conditions for singular extremals. (English) Zbl 0826.49019 Bulirsch, R. (ed.) et al., Computational optimal control. Proceedings of the 9th IFAC workshop on control applications of optimization held at the Fachhochschule München in September 1992. Basel: Birkhäuser. ISNM, Int. Ser. Numer. Math. 115, 71-81 (1994). Reviewer: E.O.Roxin (Kingston/Rhode Island) MSC: 49K15 PDF BibTeX XML Cite \textit{A. V. Dmitruk}, ISNM, Int. Ser. Numer. Math. 115, 71--81 (1994; Zbl 0826.49019)
Zelikin, M. I.; Borisov, V. F. Optimal synthesis containing chattering arcs and singular arcs of the second order. (English) Zbl 0745.49021 Nonlinear synthesis, Proc. IIASA Workshop, Sopron/Hung. 1989, Prog. Syst. Control Theory 9, 283-296 (1991). Reviewer: M.I.Zelikin MSC: 49K20 93B50 PDF BibTeX XML
Jurdjevic, V. Singular optimal problems. (English) Zbl 0717.49015 Perspectives in control theory, Proc. Conf., Sielpia/Pol. 1988, Prog. Syst. Control Theory 2, 75-88 (1990). Reviewer: R.M.Bianchini MSC: 49K15 49N10 PDF BibTeX XML
Zelikin, M. I.; Borisov, V. F. Fields of optimal trajectories containing singular second order extremals and extremals with frequent switchings. (English. Russian original) Zbl 0698.49014 Sov. Math., Dokl. 39, No. 1, 188-191 (1989); translation from Dokl. Akad. Nauk SSSR 304, No. 5, 1050-1053 (1989). Reviewer: M.Zelikin MSC: 49K15 37J99 34C30 49J52 93B50 93C15 PDF BibTeX XML Cite \textit{M. I. Zelikin} and \textit{V. F. Borisov}, Sov. Math., Dokl. 39, No. 1, 188--191 (1989; Zbl 0698.49014); translation from Dokl. Akad. Nauk SSSR 304, No. 5, 1050--1053 (1989)
Ashchepkov, L. T.; Vasil’ev, O. V. Methods of nonlinear programming in the theory of singular controls. (Russian) Zbl 0597.49022 Questions of stability and optimization of dynamical systems, Collect. Artic., Irkutsk 1983, 5-23 (1983). Reviewer: V.Chernyatin MSC: 49K30 49K15 90C30 93C10 93C15 PDF BibTeX XML
Brunovsky, P. Regular synthesis and singular extremals. (English) Zbl 0445.49021 Optimization techniques, Proc. 9th IFIP Conf., Warsaw 1979, Part 1, Lect. Notes Control Inf. Sci. 22, 280-284 (1980). MSC: 49K15 PDF BibTeX XML
Dunn, J. C. Rates of convergence for conditional gradient algorithms near singular and nonsingular extremals. (English) Zbl 0403.49028 SIAM J. Control Optimization 17, 187-211 (1979). MSC: 49M05 93B05 65K10 PDF BibTeX XML Cite \textit{J. C. Dunn}, SIAM J. Control Optim. 17, 187--211 (1979; Zbl 0403.49028) Full Text: DOI