Abstract
We consider a terminal game control problem for a linear system with discontinuous control coefficients subject to impulse constraints. We construct a generalized game control problem in the class of finitely additive measures with the property of the weak absolute continuity with respect to the restriction of the Lebesgue measure to some “sufficient” measurable structure.
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References
N. N. Krasovskii and A. I. Subbotin, Positional Differential Games (Nauka, Moscow, 1974).
N. N. Krasovskii, Theory of Motion Control (Nauka, Moscow, 1968).
J. Warga, Optimal Control of Differential and Functional Equations (Acad. Press, 1972; Nauka, Moscow, 1977).
R. V. Gamkrelidze, Foundations of Optimal Control (Tbilissk. Gos. Univ., Tbilisi, 1977).
A. D. Ioffe and V. M. Tikhomirov, Theory of Extremal Problems (Nauka, Moscow, 1974).
A. G. Chentsov, “The Universal Asymptotic Realization of Integral Constraints and Constructions of Extension in the Class of Finitely Additive Measures,” Trudy Inst.Matem. iMekh.UrO RAN, Ekaterinburg, 5(2), 328–356 (1998).
A. G. Chentsov, Asymptotic Attainability (Kluwer Publishers, Dordrecht-Boston-London, 1997).
A. G. Chentsov, Finitely Additive Measures and Relaxations of Extremal Problems (Plenum Publishing Corporation, New York, London, and Moscow, 1996).
K. Kuratowski and A. Mostowski, Set Theory (North-Holland Publ. Comp. 1967; Mir, Moscow, 1970).
R. Engelking, General Topology (PWN, Warsaw, 1977; Mir, Moscow, 1986).
N. Bourbaki, General Topology. Main Structures, (Hermann, Paris, 1940; Nauka, Moscow, 1968).
J. L. Kelley, General Topology, (D. Van Nostrand Company Inc., Toronto-New York-London, 1955; Nauka, Moscow, 1981).
J. Neveu, Mathematical Foundations of the Calculus of Probability, (Holden Day, London, 1965; Mir, Moscow, 1969).
K. P. S. B. Rao and M. B. Rao, Theory of Charges. A Study of Finitely Additive Measures (Academic Press, London, 1983).
N. Dunford and J. T. Schwartz, Linear Operators. General Theory (Interscience Publishers, New York, 1958; In. Lit., Moscow, 1962).
J. P. R. Christensen, “Finitely Additive Measure Defined on Sigma-Field is Automatically Countably Additive,” Atti Sem. Fis. Univ.Modena, 509–511 (2001).
A. G. Chentsov, “On Compactification of a Bundle of Trajectories of One Abstract Controllable System,” Izv. Vyssh. Uchebn. Zaved.Mat., No. 5, 55–66 (2006) [RussianMathematics (Iz. VUZ) 50 (5), 50–61 (2006)].
A. G. Chentsov and S. I. Morina, Extensions and Relaxation (Kluwer Academic Publishers, Dordrecht-Boston-London, 2002).
A. G. Chentsov and D. V. Khlopin, “Some Constructions of Extension of Game Problems with Information Discrimination,” Probl. Upr. i Inform., No. 5, 5–17 (2000).
D. S. Zavalishchin and A. N. Sesekin, Impulse Processes. Models and Applications (Nauka, Moscow, 1991).
V. A. Dykhta and O. N. Samsonyuk, Optimal Impulse Control with Applications (Fizmatlit, Moscow, 2000).
A. Halanay and D. Wexler, Qualitative Theory of Impulse Systems (Academiei Republici Socialiste Romania, Bucuresti, 1968; Mir, Moscow, 1971).
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Original Russian Text © A.G. Chentsov and Yu.V. Shapar’, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 7, pp. 86–102.
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Chentsov, A.G., Shapar’, Y.V. On a generalization of one game control problem in the class of finitely additive measures. Russ Math. 54, 75–90 (2010). https://doi.org/10.3103/S1066369X1007008X
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DOI: https://doi.org/10.3103/S1066369X1007008X