This is a preview of subscription content, log in via an institution to check access.
Literature cited
A. T. Fuller, “Relay control systems optimized for various performance criteries,” in: Proc. 1st IFAC Congress, Moscow,2, 584–605, Butterworths, London (1961).
C. Marchal, “Chattering arcs and chattering controls,” J. Optimization Theory Applic.,11, No. 5, 441–468 (1973).
C. M. Dorling and E. P. Ryan, “Minimization of nonquadratic cost functional for third-order saturating system,” Internat. J. Control,34, No. 2, 231–258 (1981).
V. R. Telesnin, “On optimization of transition distortions,” Trudy MIAN,166, No. 1, 261–271.
M. Z. Borshchevskii and I. V. Yoslovich, “On the problem of optimal speed in braking the rotation of an axis-symmetric rigid body around its center of gravity,” Prikl. Mat. Mekh.,49, No. 1, 35–42 (1985).
P. Brunovsky and L. Mallet-Paret, “Switchings of optimal controls and the equationy (4) + ya sgny=0, 0<α<1,” Casopis Pest. Mat.,110, No. 3, 302–313 (1985).
Ya. M. Bershchevskii, “Adjoining singular and nonsingular segments of optimal control,” Avtom. Telemekh., No. 3, 5–12 (1979).
M. I. Zelikin and V. F. Borisov, “Modes of operation with participating switchings in the problem of robot control,” Prikl. Mat. Mekh.,52, No. 6, 939–946 (1988).
I. Kupka, “Geometric theory of extremals. Fuller phenomenon,” in: Proc. 24th Conference on Decision and Control, Ft. Lauderdale, Florida,2, 711–713 (1985).
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Wiley, N.Y.
A. F. Filippov, Differential Equations with Discontinuous Right-Hand Side [in Russian], Nauka, Moscow (1985).
H. J. Kelley, R. E. Kopp, and A. G. Moyer, Singular Extremals, Optimization Theory and Applications (G. Leitmann, ed.), Academic Press, N.Y. (1967), pp. 63–103.
P. Hartman, Ordinary Differential Equations, Wiley, N.Y. (1964).
A. N. Shoshitaishvili, “On bifurcation of a topological type of vector fields dependent on a parameter,” in: Trudy Smeinara im. I. G. Petrovskogo (Transactions of I. G. Petrovskii Seminar),1, 279–309 (1975).
V. M. Alekseyev, V. M. Tikhomirov, and S. V. Fomin, Optimal Control [in Russian], Nauka, Moscow (1979).
C. Marchal, “Second-order tests in optimization theories,” J. Optimization Theory Applic.,15, No. 6, 633–666 (1975).
J. V. Breakwell and J. F. Dixon, “Minimum-fuel rocket trajectories involving intermediate-thrust arcs,” J. Optimization Theory Applic.,17, No. 5/6, 465–479 (1975).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskii Zametki, Vol. 47, No. 1, pp. 62–73, January, 1990.
Rights and permissions
About this article
Cite this article
Zelikin, M.I., Borisov, V.F. Synthesis in problems of optimal control containing trajectories with participating switchings and singular trajectories of the second order. Mathematical Notes of the Academy of Sciences of the USSR 47, 41–49 (1990). https://doi.org/10.1007/BF01157282
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01157282