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Existence of optimal solutions in general discrete systems. (English) Zbl 0318.49007


MSC:

49J27 Existence theories for problems in abstract spaces
93C55 Discrete-time control/observation systems
93C25 Control/observation systems in abstract spaces
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References:

[1] R. E. Bellman: Dynamic Programming. Princeton Univ. Press, Princeton, New Jersey, 1957. · Zbl 0995.90618
[2] C. Berge: Topological Spaces: Multivalued Functions. 2nd edition, Dunod, Paris 1966
[3] V. I. Blagodatskich: Sufficient Optimality Conditions for Differential Inclusions. Izvestia AN USSR, Ser. Math. 38 (1974), 615-624
[4] V. I. Blagodatskich: Time Optimal Control Problem for Differential Inclusions. Preprints of the IFIP Conference on Optimalization Techniques, Novosibirsk 1974
[5] V. G. Boltjanskij: Optimal Control of Discrete Systems. Nauka, Moscow 1973
[6] M. D. Canon C. D. Cullum E. Polak: Theory of Optimal Control and Mathematical Programming. McGraw-Hill, New York 1970. · Zbl 0264.49001
[7] J. L. Davy: Properties of the Solution Set of a Generalized Differential Equation. Bull. Austr. Math. Soc., 6 (1972), 379-398. · Zbl 0239.49022
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[9] N. Dunford J. T. Schwartz: Linear Operators. Part I: General Theory. Interscience, New York 1958. · Zbl 0084.10402
[10] Y. D., Joffe V. M. Tichomirov: Extremum Problems Theory. Nauka, Moscow 1974
[11] A. N. Kolmogorov S. V. Fomin: Elements of Functions Theory and Functional Analysis. Nauka, Moscow 1972 · Zbl 0235.46001
[12] C. Olech: Existence Theorems for Optimal Problem with Vector-Valued Cost Function. Trans. American Math. Soc. 136 (1969), 159-180. · Zbl 0179.14002
[13] A. I. Propoj: Discrete Control Problems with State Constraints. Žurnal vyč. mat. i mat. fiziki 12 (1965), 1128-1144
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