Abstract
A parameter-dependent control system is considered in Euclidean space \({{\mathbb{R}}^{n}}\). The dependence, on the parameter, of the reachable sets and integral funnels of the differential inclusion corresponding to the system is investigated. Estimates are obtained that characterize this dependence.
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REFERENCES
A. B. Kurzhanski and I. Valyi, Ellipsoidal Calculus for Estimation and Control (Birkhäuser, Basel, 1997).
Selected Works by A.B. Kurzhanskii, Ed. by A. N. Dar’in, I. A. Digailova, and I. V. Rublev (Mosk. Univ., Moscow, 2009) [in Russian].
F. L. Chernousko, State Estimation for Dynamic Systems (Nauka, Moscow, 1988; CRC, Boca Raton, 1994).
F. L. Chernousko and A. A. Melikyan, Game-Theoretic Problems of Control and Search (Nauka, Moscow, 1978) [in Russian].
N. N. Krasovskii and A. I. Subbotin, Game-Theoretical Control Problems (Nauka, Moscow, 1974; Springer-Verlag, New York, 1988).
F. Lempio and V. M. Veliov, Bayr. Math. Schriften 54, 149–232 (1998).
M. S. Nikol’skii, Vest. Mosk. Gos. Univ. Ser. 15: Vychisl. Mat. Kibern., No. 4, 31–34 (1987).
S. A. Vdovin, A. M. Taras’ev, and V. N. Ushakov, J. Appl. Math. Mech. 68 (5), 631–646 (2004). https://doi.org/10.1016/j.jappmathmech.2004.09.001
I. M. Anan’evskii, Differ. Equations 39 (1), 1–10 (2003). https://doi.org/10.1023/A:1025170521270
M. I. Gusev, Proc. Steklov Inst. Math. 269, suppl. 1, 134–146 (2010). https://doi.org/10.1134/S008154381006012X
T. F. Filippova, Proc. Steklov Inst. Math. 269, suppl. 1, 95–102 (2010). https://doi.org/10.1134/S008154381006009X
V. N. Ushakov, A. R. Matviichuk, and A. V. Ushakov, Vestn. Udmurt. Univ. Mat. Mekh. Komp’yut. Nauki, No. 4, 23–39 (2011).
A. A. Ershov and V. N. Ushakov, Sb. Math. 208 (9), 1312–1352 (2017). https://doi.org/10.1070/SM8761
A. V. Beznos, A. A. Grishin, A. V. Lenskii, D. E. Okhotsimskii, and A. M. Formal’skii, “Flywheel control of a pendulum,” Ed. by V. V. Aleksandrov (Mosk. Univ., Moscow, 2009), pp. 170–195 [in Russian].
B. T. Polyak, M. V. Khlebnikov, and P. S. Shcherbakov, Control of Linear Systems under External Disturbances: Technique of Linear Matrix Inequalities (LENAND, Moscow, 2014) [in Russia].
Funding
This work was performed within the research conducted at the Ural Mathematical Center and was supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-02-2021-1383).
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Translated by I. Ruzanova
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Ushakov, V.N., Ershov, A.A. Reachable Sets and Integral Funnels of Differential Inclusions Depending on a Parameter. Dokl. Math. 104, 200–204 (2021). https://doi.org/10.1134/S1064562421040153
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DOI: https://doi.org/10.1134/S1064562421040153