Geodesic
Number of limit cycles of the quotient system of the $n$-dimensional Fuller problem
Sbornik. Mathematics, Tome 187 (1996) no. 12, pp. 1737-1753 Cet article a éte moissonné depuis la source Math-Net.Ru

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The number of limit cycles of the quotient system of the $n$-dimensional Fuller problem (that is, the number of one-parameter families of self-similar solutions of the equation $y^{(2n)}=(-1)^{n+1}\operatorname {sgn}y$) is proved to be equal to $[n/2]$. 
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     author = {V. F. Borisov},
     title = {Number of limit cycles of the~quotient system of the $n$-dimensional {Fuller} problem},
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     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_12_a0/}
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V. F. Borisov. Number of limit cycles of the quotient system of the $n$-dimensional Fuller problem. Sbornik. Mathematics, Tome 187 (1996) no. 12, pp. 1737-1753. http://geodesic.mathdoc.fr/item/SM_1996_187_12_a0/

[1] Kelley H. J., Kopp R. E., Moyer H. G., “Singular extremals”, Topics in Optimization, ed. G. Leitmann, Acad. Press, New York, 1967, 63–103 | MR

[2] Kupka I., “The ubiquity of Fuller's phenomenon”, Nonlinear controllability and optimal control, Monograph textbooks, Pure Appl. Math., no. 133, ed. H. Sussman, Dekker, New York, 1990, 313–350 | MR | Zbl

[3] Berschanskii Ya. M., “Povedenie optimalnykh traektorii vblizi terminalnogo uchastka”, Issledovaniya po teorii mnogosvyaznykh sistem, VNIISI, M., 1982, 76–88

[4] Zelikin M. I., Borisov V. F., Theory of Chattering Control with Applications to Astronautics, Robotics, Economics, and Engineering, Birkhäuser, Boston, 1994 | MR | Zbl

[5] Dorling C. M., Ryan R. E., “Minimization of nonquadratic cost functionals for third order saturating system”, Internat. J. Control, 34:2 (1981), 231–258 | DOI | MR | Zbl

[6] Fuller A. T., Grensted P. E., “Minimization of integral square error for nonlinear control system of third and higher order”, Internat. J. Control, 2:1 (1965), 33–73 | DOI | MR

[7] Fuller A. T., “Minimization of nonquadratic performance indices for a system with bounded control”, Internat. J. Control, 41:1 (1985), 1–37 | DOI | MR | Zbl

[8] Marchal C., “Chattering arcs and chattering controls”, J. Optim. Theory Appl., 11:5 (1973), 441–446 | DOI | MR

[9] Brunovsky P., Mallet-Paret J., “Switchings of optimal controls and the equation $y^{(4)}+y^\alpha\operatorname{sgn}y=0$, $0\alpha1$”, Časopis Pěst. Mat., 110:3 (1985), 302–313 | MR | Zbl

[10] Magaril-Ilyaev G. G., “O neravenstvakh Kolmogorova na polupryamoi”, Vestn. MGU. Ser. 1, matem., mekh., 1976, no. 5, 33–41 | Zbl

[11] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1976 | Zbl

[12] Filippov A. F., Differentsialnye uravneniya s razryvnoi pravoi chastyu, Nauka, M., 1985 | MR