Minimax optimal control problem with state constraints

V. Alexandrov, M. Budninskiy, On kinematic control extremals, in: European Control Conference (ECC), Zurich, Switzerland, 2013, pp. 210–214. Arutyunov, 1991, Perturbations of extremal problems with constraints and necessary optimality conditions, J. Sov. Math., 54, 1342, 10.1007/BF01373649 Arutyunov, 2012, Properties of the Lagrange multipliers in the Pontryagin maximum principle for optimal control problems with state constraints, Differ. Equ., 48, 1586, 10.1134/S0012266112120051 Arutyunov, 2015, On some continuity properties of the measure Lagrange multiplier from the maximum principle for state constrained problems, SIAM J. Control Optim., 53, 2514, 10.1137/140981368 Arutyunov, 2005, A nondegenerate maximum principle for the impulse control problem with state constraints, SIAM J. Control Optim., 43, 1812, 10.1137/S0363012903430068 Arutyunov, 2011, R.V. Gamkrelidze׳s maximum principle for optimal control problems with bounded phase coordinates and its relation to other optimality conditions, Dokl. Math., 83, 131, 10.1134/S1064562411010285 Arutyunov, 2015, State constraints in impulsive control problems, J. Optim. Theory Appl., 166, 440, 10.1007/s10957-014-0690-8 Arutyunov, 1992, Maximum principle and second-order conditions for minimax problems of optimal control, J. Optim. Theory Appl., 75, 521, 10.1007/BF00940490 Arutyunov, 1984, The maximum principle in a problem with phase constraints, Sov. J. Comput. Syst. Sci., 23, 28 Arutyunov, 2000 Arutyunov, 1997, Investigation of the degeneracy phenomenon of the maximum principle for optimal control problems with state constraints, SIAM J. Control Optim., 35, 930, 10.1137/S036301299426996X Arutyunov, 2016, Non-degenerate necessary optimality conditions for the optimal control problem with equality-type state constraints, J. Global Optim., 64, 623, 10.1007/s10898-015-0272-9 Arutyunov, 2011, The maximum principle for optimal control problems with state constraints by R.V. Gamkrelidze, J. Optim. Theory Appl., 149, 474, 10.1007/s10957-011-9807-5 Arutyunov, 2016, Conditions for the absence of jumps of the solution to the adjoint system of the maximum principle for optimal control problems with state constraints, Proc. Steklov Inst. Math., 292, 27, 10.1134/S0081543816020036 Clarke, 1983 Davydova, 2015, On some properties of the shortest curve in a compound domain, Differ. Equ., 51, 1626, 10.1134/S0012266115120101 Dubovitskij, 1985, Necessary conditions for a strong minimum in optimal control problems with degeneration of final and phase constraints, Uspekhi Mat. Nauk., 40, 175 Dubovitskij, 1963, Extremum problems with constraints, Sov. Math. Dokl., 4, 452 Ekeland, 1974, On the variational principle, J. Math. Anal. Appl., 47, 324, 10.1016/0022-247X(74)90025-0 Ferreira, 1999, Nondegenerate necessary conditions for nonconvex optimal control problems with state constraints, J. Math. Anal. Appl., 233, 116, 10.1006/jmaa.1999.6270 Ferreira, 1994, When is the maximum principle for state constrained problems nondegenerate?, J. Math. Anal. Appl., 187, 438, 10.1006/jmaa.1994.1366 Gamkrelidze, 1960, Optimal control processes for bounded phase coordinates, Izv. Akad. Nauk. SSSR Ser. Mat., 24, 315 Karamzin, 2007, Necessary conditions for an extremum in a control problem with phase constraints, Zh. Vychisl. Mat. Mat. Fiz, 47, 1123 Kolmogorov, 1975 Kurzhanski, 2006, Optimization techniques for state-constrained control and obstacle problems, J. Optim. Theory Appl., 128, 499, 10.1007/s10957-006-9029-4 Mordukhovich, 1976, Maximum principle in the problem of time optimal response with nonsmooth constraints, J. Appl. Math. Mech., 40, 960, 10.1016/0021-8928(76)90136-2 B.S. Mordukhovich, Variational Analysis and Generalized Differentiation I. Basic Theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 330, Springer-Verlag, Berlin, 2006. Neustadt, 1966, An abstract variational theory with applications to a broad class of optimization problems. ii. Applications, SIAM J. Control Optim., 4, 505, 10.1137/0304040 L. Pontryagin, V. Boltyanskij, R. Gamkrelidze, E. Mishchenko, Selected works. Vol. 4. The Mathematical Theory of Optimal Processes. Ed. and with a preface by R.V. Gamkrelidze. Transl. from the Russian by K.N. Trirogoff. Transl. ed. by L.W. Neustadt. With a preface by L.W. Neustadt and K.N. Trirogoff. Reprint of the 1962 Engl. translation, Classics of Soviet Mathematics, xxiv, Gordon and Breach Science Publishers, New York, NY, 1986, 360 p. Russak, 1970, On general problems with bounded state variables, J. Optim. Theory Appl., 6, 424, 10.1007/BF00932720 Russak, 1975, Second-order necessary conditions for general problems with state inequality constraints, J. Optim. Theory Appl., 17, 43, 10.1007/BF00933916 Vinter, 2000 Vinter, 2005, Minimax optimal control, SIAM J. Control Optim., 44, 939, 10.1137/S0363012902415244 Vinter, 1982, A maximum principle for nonsmooth optimal-control problems with state constraints, J. Math. Anal. Appl., 89, 212, 10.1016/0022-247X(82)90099-3 Warga, 1972 Zakharov, 2015, On the study of conditions for the continuity of the lagrange multiplier measure in problems with state constraints, Differ. Equ., 51, 399, 10.1134/S0012266115030106 Zelikin, 1965, Determined differential games, Uspekhi Mat. Nauk, 20, 151