@article{IIGUM_2019_30_a3,
author = {B. S. Mordukhovich},
title = {Optimal control of differential inclusions, {I:~Lipschitzian} case},
journal = {The Bulletin of Irkutsk State University. Series Mathematics},
pages = {45--58},
year = {2019},
volume = {30},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IIGUM_2019_30_a3/}
}
B. S. Mordukhovich. Optimal control of differential inclusions, I: Lipschitzian case. The Bulletin of Irkutsk State University. Series Mathematics, Tome 30 (2019), pp. 45-58. http://geodesic.mathdoc.fr/item/IIGUM_2019_30_a3/
[1] F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1983 | MR | Zbl
[2] T. Donchev, E. Farkhi, B. S. Mordukhovich, “Discrete approximations, relaxation, and optimization of one-sided Lipschitzian differential inclusions in Hilbert spaces”, J. Diff. Eqs., 243 (2007), 301–328 | DOI | MR | Zbl
[3] L. Euler, Methodus Inveniendi Curvas Lineas Maximi Minimive Proprietate Gaudentes Sive Solution Problematis Viso Isoperimetrici Latissimo Sensu Accepti, Lausanne, 1774 ; reprinted: Opera Omnia, Ser. 1, 24, 1952 | MR
[4] R. Gabasov, F. M. Kirillova, The Qualitative Theory of Optimal Processes, Marcel Dekker, New York, 1976 | MR | Zbl
[5] B. S. Mordukhovich, “Maximum principle in problems of time optimal control with nonsmooth constraints”, J. Appl. Math. Mech., 40 (1976), 960–969 | DOI | MR | Zbl
[6] B. S. Mordukhovich, Approximation Methods in Problems of Optimization and Control, Nauka, M., 1988 | MR | Zbl
[7] B. S. Mordukhovich, “Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions”, Trans. Amer. Math. Soc., 340 (1993), 1–35 | DOI | MR | Zbl
[8] B. S. Mordukhovich, “Discrete approximations and refined Euler-Lagrange conditions for differential inclusions”, SIAM J. Control Optim., 33 (1995), 882–915 | DOI | MR | Zbl
[9] B. S. Mordukhovich, Variational Analysis and Generalized Differentiation, v. I, Basic Theory, Springer, Berlin, 2006 | MR
[10] B. S. Mordukhovich, Variational Analysis and Generalized Differentiation, v. II, Applications, Springer, Berlin, 2006 | MR
[11] B. S. Mordukhovich, Variational Analysis and Applications, Springer, Switzerland, 2018 | Zbl
[12] B. S. Mordukhovich, “Optimal control of Lipschitzian and discontinuous differential inclusions with various applications”, Proc. Inst. Math. Mech., 45 (2019), 52–74 | MR | Zbl
[13] B. S. Mordukhovich, “Optimal control of differential inclusions, II: Sweeping”, The Bulletin of Irkutsk State University. Series Mathematics, 31 (2020)
[14] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Wiley, New York, 1962 | MR | Zbl
[15] R. T. Rockafellar, R. J.-B. Wets, Variational Analysis, Springer, Berlin, 1998 | MR | Zbl
[16] A. A. Tolstonogov, Differential Inclusions in a Banach Spaces, Kluwer, Dordrecht, the Netherlands, 2000 | MR
[17] O. V. Vasiliev, Optimization Methods, World Federation Publishers, Atlanta, GA, 1996 | MR | Zbl
[18] R. B. Vinter, Optimal Control, Birkhaüser, Boston, 2000 | MR | Zbl