Geodesic
Calculation of the derivative of an inaccurately defined function by means of feedback laws
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control, Tome 291 (2015), pp. 231-243.

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The problem of calculating the derivative of an inaccurately defined function is considered. This problem is one of the “classical” problems in mathematical analysis. Various algorithms for solving this problem have been proposed by many authors. In the present study, constructions of positional control theory are invoked to solve this problem. Due to the presence of error in the measurement of the values of a function, the exact calculation of the derivative seems to be impossible. In view of this feature, a problem solving algorithm is presented that is based on an appropriate modification of the method of models controlled by feedback laws and is robust with respect to informational noise and measurement errors. 
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V. I. Maksimov. Calculation of the derivative of an inaccurately defined function by means of feedback laws. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control, Tome 291 (2015), pp. 231-243. http://geodesic.mathdoc.fr/item/TM_2015_291_a16/

[1] Stechkin S.B., “Nailuchshee priblizhenie lineinykh operatorov”, Mat. zametki, 1:2 (1967), 137–148 | Zbl

[2] Vasin V.V., “Ob ustoichivom vychislenii proizvodnoi v prostranstve $C(-\infty ,\infty )$”, ZhVMiMF, 13:6 (1973), 1383–1389 | MR

[3] Stechkin S.B., Subbotin Yu.N., Splainy v vychislitelnoi matematike, Nauka, M., 1976 | MR

[4] Ivanov V.K., Vasin V.V., Tanana V.P., Teoriya lineinykh nekorrektnykh zadach i ee prilozheniya, Nauka, M., 1978 | MR

[5] Arestov V.V., “O ravnomernoi regulyarizatsii zadachi vychisleniya znachenii operatora”, Mat. zametki, 22:2 (1977), 231–244 | MR | Zbl

[6] Tikhonov A.N., Arsenin V.Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1974 | MR

[7] Osipov Yu.S., Kryazhimskii A.V., Inverse problems for ordinary differential equations: Dynamical solutions, Gordon and Breach, Amsterdam, 1995 | MR | Zbl

[8] Osipov Yu.S., Kryazhimskii A.V., Maksimov V.I., Metody dinamicheskogo vosstanovleniya vkhodov upravlyaemykh sistem, UrO RAN, Ekaterinburg, 2011

[9] Blizorukova M.S., Maksimov V.I., Pandolfi L., “Dinamicheskaya rekonstruktsiya vkhoda v nelineinoi sisteme s zapazdyvaniem”, Avtomatika i telemekhanika, 2002, no. 2, 3–13 | MR | Zbl

[10] Maksimov V.I., “Metod upravlyaemykh modelei v zadache rekonstruktsii granichnogo vkhoda”, Tr. MIAN, 262 (2008), 178–186 | MR | Zbl

[11] Kryazhimskiy A.V., Maksimov V.I., “On rough inversion of a dynamical system with a disturbance”, J. Inverse Ill-Posed Probl., 16:6 (2008), 587–600 | DOI | MR | Zbl

[12] Maksimov V.I., Fedina N.A., “Metod upravlyaemykh modelei v zadache rekonstruktsii nelineinoi sistemy s zapazdyvaniem”, Dif. uravneniya, 43:1 (2007), 36–40 | MR | Zbl

[13] Lavrentev M.M., Maksimov V.I., “O vosstanovlenii pravoi chasti parabolicheskogo uravneniya”, ZhVMiMF, 48:4 (2008), 674–680 | MR | Zbl

[14] Kryazhimskii A.V., Osipov Yu.S., “O nailuchshem priblizhenii operatora differentsirovaniya v klasse neuprezhdayuschikh operatorov”, Mat. zametki, 37:2 (1985), 192–199 | MR

[15] Maksimov V.I., Pandolfi L., “O rekonstruktsii neogranichennykh upravlenii v nelineinykh dinamicheskikh sistemakh”, PMM, 65:3 (2001), 385–391 | MR | Zbl

[16] Krasovskii N.N., Subbotin A.I., Pozitsionnye differentsialnye igry, Nauka, M., 1974 | MR