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Estimates for the attainable set for differential inclusions

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Literature cited

  1. A. B. Kurzhanskii, Control and Observation in Uncertain Conditions [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  2. F. L. Chernous'ko, “Optimal guaranteed estimates of uncertainties using ellipsoids. I, II, and III,” Izv. Akad. Nauk SSSR, Ser. Tekh. Kibern., No. 3, 3–11; No. 4, 3–11; No. 5, 5–11 (1980).

  3. F. C. Schweppe, Uncertain Dynamic Systems, Prentice-Hall (1973).

  4. F. L. Chernous'ko, A. I. Ovseevich, B. P. Klepfish, and V. L. Trushchenkov, “Ellipsoidal estimation of the state of controlled dynamic systems,” Preprint Inst. Probl. Mekh. Akad. Nauk SSSR, No. 224, Moscow (1983).

  5. S. N. Abramenko, E. A. Balin, and Yu. B. Seisov, “Estimates for the attainable sets of controlled systems,” Izv. Akad. Nauk TSSR, Ser. Fiz.-Tekh. Khim. Geol. Nauk, No. 4, 3–7 (1980).

    Google Scholar 

  6. V. A. Komarov, “Estimates for the attainable set and the construction of admissible controls for linear systems,” Dokl. Akad. Nauk SSSR,268, No. 3, 537–541 (1983).

    Google Scholar 

  7. V. A. Komarov, “The synthesis of bounded controls for linear nonautonomic systems,” Avtom. Telemekh., No. 10, 44–50 (1984).

    Google Scholar 

  8. R. Vinter, “A characterization of the reachable set for nonlinear control systems,” SIAM J. Control Optimization,18, No. 6, 599–610 (1980).

    Google Scholar 

  9. V. I. Gurman and G. N. Konstantinov, “Estimates for the attainable sets of control systems,” Lecture theses from the All-Union Conference “Dynamic Control,” Sverdlovsk (1979), pp. 72–73.

  10. A. I. Ovseevich and F. L. Chernous'ko, “Two-sided estimates for the attainable region of control systems,” Prikl. Mat. Mekh.,46, No. 5, 727–744 (1982).

    Google Scholar 

  11. V. A. Komarov, “Estimates for the attainable sets for linear nonautonomic systems,” Izv. Akad. Nauk SSSR, Ser. Mat., No. 4, 865–879 (1984).

    Google Scholar 

  12. F. L. Chernous'ko, “Ellipsoidal estimates for the region of attainment of a control system,” Prikl. Mat. Mekh.,45, No. 1, 11–19 (1981).

    Google Scholar 

  13. A. I. Ovseevich, “Extremal properties of ellipsoids approximating the attainable region,” Prob. Upr. Teor. Inf. (VNR),12, No. 1, 43–54 (1983).

    Google Scholar 

  14. V. I. Blagodatskikh, The Theory of Differential Inclusions [in Russian], Vol. I, Moscow State Univ. (1979).

  15. J. L. Davy, “Properties of the solution set of a generalized differential equation,” Bull. Austral. Math. Soc.,6, No. 3, 379–398 (1972).

    Google Scholar 

  16. A. Kh. Gelig, G. A. Leonov, and V. A. Yakubovich, The Stability of Nonlinear Systems with Nonunique Equilibrium State [in Russian], Nauka, Moscow (1978).

    Google Scholar 

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Authors and Affiliations

  1. Department of Theoretical Problems, Academy of Sciences of the USSR, USSR

    V. A. Komarov

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  1. V. A. Komarov
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Translated from Matematicheskie Zametki, Vol. 37, No. 6, pp. 916–925, June, 1985.

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Komarov, V.A. Estimates for the attainable set for differential inclusions. Mathematical Notes of the Academy of Sciences of the USSR 37, 501–506 (1985). https://doi.org/10.1007/BF01157690

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