Hakavuori, Eero ODE trajectories as abnormal curves in Carnot groups. (English) Zbl 1481.53044 J. Differ. Equations 300, 458-486 (2021). Reviewer: Peibiao Zhao (Nanjing) MSC: 53C17 37N35 22E25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sachkov, Yu. L.; Sachkova, E. F. The structure of abnormal extremals in a sub-Riemannian problem with growth vector \((2, 3, 5, 8)\). (English. Russian original) Zbl 1467.53035 Sb. Math. 211, No. 10, 1460-1485 (2020); translation from Mat. Sb. 211, No. 10, 112-138 (2020). Reviewer: Peibiao Zhao (Nanjing) MSC: 53C17 22E25 49K15 × Cite Format Result Cite Review PDF Full Text: DOI
Barilari, Davide; Chitour, Yacine; Jean, Frederic; Prandi, Dario; Sigalotti, Mario On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures. (English) Zbl 1434.53033 J. Math. Pures Appl. (9) 133, 118-138 (2020). Reviewer: Peibiao Zhao (Nanjing) MSC: 53C17 49J15 53C22 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sachkov, Yuriĭ L.; Sachkova, Elena F. Symmetries and parameterization of abnormal extremals in the sub-Riemannian problem with the growth vector (2, 3, 5, 8). (English) Zbl 1447.53033 Russ. J. Nonlinear Dyn. 15, No. 4, 577-585 (2019). MSC: 53C17 × Cite Format Result Cite Review PDF Full Text: DOI MNR
Le Donne, Enrico; Leonardi, Gian Paolo; Monti, Roberto; Vittone, Davide Extremal polynomials in stratified groups. (English) Zbl 1397.53046 Commun. Anal. Geom. 26, No. 4, 723-757 (2018). MSC: 53C17 17B30 58A35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Ayala, Victor; Jouan, Philippe Almost-Riemannian geometry on Lie groups. (English) Zbl 1359.53012 SIAM J. Control Optim. 54, No. 5, 2919-2947 (2016). Reviewer: Hubert Gollek (Berlin) MSC: 53B20 53C17 34H05 93B27 22E70 53C30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Doubrov, Boris; Zelenko, Igor Geometry of rank 2 distributions with nonzero Wilczynski invariants. (English) Zbl 1420.58002 J. Nonlinear Math. Phys. 21, No. 2, 166-187 (2014). MSC: 58A30 53A55 34C14 × Cite Format Result Cite Review PDF Full Text: DOI
Monti, Roberto A family of nonminimizing abnormal curves. (English) Zbl 1304.53025 Ann. Mat. Pura Appl. (4) 193, No. 6, 1577-1593 (2014). MSC: 53C17 49K30 × Cite Format Result Cite Review PDF Full Text: DOI Link
Barbero-Liñán, María; Muñoz-Lecanda, Miguel C. Constraint algorithm for extremals in optimal control problems. (English) Zbl 1181.49021 Int. J. Geom. Methods Mod. Phys. 6, No. 7, 1221-1233 (2009). MSC: 49K15 70G45 70H05 70H45 49M05 34H05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Barbero-Liñán, M.; Martín de Diego, D.; Muñoz-Lecanda, M. C. Lie algebroids and optimal control: abnormality. (English) Zbl 1178.49057 Etayo, Fernando (ed.) et al., Geometry and physics. XVII international fall workshop on geometry and physics, Castro Urdiales, Spain, 3–6 September 2008. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0666-7/pbk). AIP Conference Proceedings 1130, 113-119 (2009). MSC: 49S05 70H25 × Cite Format Result Cite Review PDF
Barbero-Liñán, M.; Muñoz-Lecanda, M. C. Optimal control problems for affine connection control system: characterization of extremals. (English) Zbl 1357.49088 Fernandes, Rui Loja (ed.) et al., Geometry and physics. XVI international fall workshop, Lisbon, Portugal, September 5–8, 2007. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0546-2/hbk). AIP Conference Proceedings 1023, 127-131 (2008). MSC: 49K20 × Cite Format Result Cite Review PDF
Zelenko, I. Fundamental form and the Cartan tensor of \((2,5)\)-distributions coincide. (English) Zbl 1118.58004 J. Dyn. Control Syst. 12, No. 2, 247-276 (2006). Reviewer: Marian Ioan Munteanu (Iaşi) MSC: 58A30 53A55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zelenko, Igor On variational approach to differential invariants of rank two distributions. (English) Zbl 1091.58002 Differ. Geom. Appl. 24, No. 3, 235-259 (2006). MSC: 58A30 53A55 58A17 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zimmerman, Jason A. Optimal control of the sphere \(S^n\) rolling on \(E^n\). (English) Zbl 1064.49021 Math. Control Signals Syst. 17, No. 1, 14-37 (2005). MSC: 49K15 70F25 70E18 70Q05 37J60 93C85 × Cite Format Result Cite Review PDF Full Text: DOI
Boscain, Ugo; Charlot, Grégoire Resonance of minimizers for \(n\)-level quantum systems with an arbitrary cost. (English) Zbl 1072.49002 ESAIM, Control Optim. Calc. Var. 10, 593-614 (2004). MSC: 49J15 49N60 81V80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Numdam EuDML
Bruni, C.; Iacoviello, D. A study on abnormality in variational and optimal control problems. (English) Zbl 1056.49023 J. Optimization Theory Appl. 121, No. 1, 41-64 (2004). MSC: 49K15 × Cite Format Result Cite Review PDF Full Text: DOI
Langerock, B. Geometric aspects of the maximum principle and lifts over a bundle map. (English) Zbl 1054.49023 Acta Appl. Math. 77, No. 1, 71-104 (2003). MSC: 49K15 53C17 58E25 93C15 93B29 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF Full Text: DOI
Boscain, Ugo; Piccoli, Benedetto On automaton recognizability of abnormal extremals. (English) Zbl 1024.49020 SIAM J. Control Optimization 40, No. 5, 1333-1357 (2002). Reviewer: Rosa Maria Bianchini (Firenze) MSC: 49K15 49N35 49J15 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF Full Text: DOI
Ledzewicz, Urszula; Schättler, Heinz High-order approximations for abnormal bang-bang extremals. (English) Zbl 0938.49015 Polis, Michael P. (ed.) et al., Systems modelling and optimization. Proceedings of the 18th IFIP TC7 conference, Detroit, MI, USA, July 22-25, 1997. Boca Raton, FL: Chapman & Hall/ CRC. Chapman Hall/CRC Res. Notes Math. 396, 126-134 (1999). Reviewer: R.De Arcangelis (Napoli) MSC: 49K15 49K30 × Cite Format Result Cite Review PDF
Chitour, Yacine; Sussmann, Héctor J. Line-integral estimates and motion planning using the continuation method. (English) Zbl 0946.70003 Baillieul, John (ed.) et al., Essays on mathematical robots. Proceedings of a workshop, Minneapolis, MN, USA, January 25-29, 1993. New York, NY: Springer. IMA Vol. Math. Appl. 104, 91-125 (1998). Reviewer: Bojidar Cheshankov (Sofia) MSC: 70B15 70B10 70Q05 × Cite Format Result Cite Review PDF
Ledzewicz, Urszula; Schättler, Heinz An extended maximum principle. (English) Zbl 0879.49019 Nonlinear Anal., Theory Methods Appl. 29, No. 2, 159-183 (1997). Reviewer: Zs.Páles (Debrecen) MSC: 49K15 × Cite Format Result Cite Review PDF Full Text: DOI
Liu, Wensheng; Sussman, Héctor J. Shortest paths for sub-Riemannian metrics on rank-two distributions. (English) Zbl 0843.53038 Mem. Am. Math. Soc. 564, 104 p. (1995). Reviewer: U.Hamenstädt (Bonn) MSC: 53C22 49K15 58A30 53-02 × Cite Format Result Cite Review PDF Full Text: DOI Link
Agrachev, A. A.; Sarychev, A. V. On abnormal extremals for Lagrange variational problems. (English) Zbl 0826.49012 J. Math. Syst. Estim. Control 5, No. 1, 127-130 (1995). MSC: 49K15 90C30 93B05 93B29 × Cite Format Result Cite Review PDF
Montgomery, Richard Abnormal minimizers. (English) Zbl 0816.49019 SIAM J. Control Optimization 32, No. 6, 1605-1620 (1994). Reviewer: N.Papaghiuc (Iaşi) MSC: 49K40 49J15 49Q20 58E10 × Cite Format Result Cite Review PDF Full Text: DOI
Warga, J. Controllability, extremality, and abnormality in nonsmooth optimal control. (English) Zbl 0497.49033 J. Optimization Theory Appl. 41, 239-260 (1983). MSC: 93B03 49K15 49K99 93B05 × Cite Format Result Cite Review PDF Full Text: DOI