Extremal solutions of a control system. (English) Zbl 0135.32802

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[1] Blackwell, D., The range of certain vector integrals, (Proc. Am. Math. Soc., 2 (1951)), 390-395 · Zbl 0044.27702
[2] Dunford, N.; Schwartz, J. T., Linear Operators, Part I (1958), Interscience: Interscience New York · Zbl 0084.10402
[3] Filippov, A. F., Differential equations with multi-valued discontinuous righthand side, Dokl. Akad. Nauk SSSR, 151, 65-68 (1963), (in Russian) · Zbl 0141.27704
[4] Halkin, H.J. Soc. Ind. Appl. Math.; Halkin, H.J. Soc. Ind. Appl. Math.
[5] Halmos, P. R., Measure Theory (1954), Van Nostrand: Van Nostrand Princeton, New Jersey · Zbl 0117.10502
[6] Kurzweil, J., On the linear theory of optimal control systems, C̆asopis Pěst. Mat., 89, 90-101 (1964), (in Russian) · Zbl 0137.12003
[7] La Salle, J. P., The time optimal control problem, (Contributions to the Theory of Non linear Oscillations, Vol. 5 (1960), Princeton Univ. Press: Princeton Univ. Press Princeton, New Jersey), 1-24 · Zbl 0095.29503
[8] Liapunov, A. A., Sur les fonctions-vecteurs completement additives, Izv. Akad. Nauk SSSR, Ser. Mat., 8, 465-478 (1940) · Zbl 0024.38504
[9] Neustadt, L. W., The existence of optimal controls in the absence of convexity conditions, J. Math. Anal. Appl., 7, 110-117 (1963) · Zbl 0115.13304
[10] Olech, C.; Olech, C.
[11] Olech, C., A note concerning extremal points of a convex set, Bull. Acad. Polon. Sci., Ser. Sci. Math. Astron. Phys., 13, 347-351 (1965) · Zbl 0136.18805
[12] Olech, C., A note concerning set-valued measurable functions, Bull. Acad. Polon. Sci., Ser. Sci. Math. Astron. Phys., 13, 317-321 (1965) · Zbl 0145.28302
[13] Pliś, A., Remark on measurable set-valued functions, Bull. Acad. Polon. Sci., Ser. Sci. Math. Astron. Phys., 9, 857-859 (1961) · Zbl 0101.04303
[14] Pontryagin, L. S.; Boltyanski, V. G.; Gamkrelidze, R. V.; Mishchenko, E. F., The Mathematical Theory of Optimal Control (1961), (in Russian). English translation: Interscience, New York, 1962 · Zbl 0102.31901
[15] Roxin, E., Pontryagin’s maximum principle, (LaSalle, J. P.; Lefschetz, S., Proc. Intern. Symp. on Nonlinear Differential Eqs. and Nonlinear Mech. (1963), Academic Press: Academic Press New York), 303-324 · Zbl 0139.04808
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