Abstract:
It is proved that the linear combinations of shifts and contractions of the Gaussian function can be used for an arbitrarily accurate approximation in the space of continuous functions of one variable on any fixed intervals. On the example of the soft lunar landing problem, a method for the numerical solution of optimal control problems based on this approximation procedure of the control function is described. Within the framework of the same example, the sensitivity of constraint functionals to the specification error of optimal parameters is investigated using three approaches as follows: 1) Pontryagin’s maximum principle (both numerically and theoretically); 2) the control parametrization technique in combination with the method of sliding nodes; 3) the newly proposed method. A comparative analysis is performed that confirms the effectiveness of the third method.
Keywords:
control parametrization technique, lumped optimal control problem, approximation using Gaussian functions.
This work was supported by the Ministry of Education and Science of the Russian Federation within the State order for research in 2014–2016, project no. 1727.
Citation:
A. V. Chernov, “On application of Gaussian functions to numerical solution of optimal control problems”, Avtomat. i Telemekh., 2019, no. 6, 51–69; Autom. Remote Control, 80:6 (2019), 1026–1040
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\paper On application of Gaussian functions to numerical solution of optimal control problems
\jour Avtomat. i Telemekh.
\yr 2019
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\pages 51--69
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\crossref{https://doi.org/10.1134/S0005231019060035}
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\jour Autom. Remote Control
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\pages 1026--1040
\crossref{https://doi.org/10.1134/S0005117919060031}
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Linking options:
https://www.mathnet.ru/eng/at14869
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This publication is cited in the following 6 articles:
A. V. Chernov, “O monotonnoi approksimatsii kusochno nepreryvnykh monotonnykh funktsii s pomoschyu sdvigov i szhatii integrala Laplasa”, Izv. IMI UdGU, 61 (2023), 187–205
A. V. Arguchintsev, V. A. Srochko, “Protsedura regulyarizatsii bilineinykh zadach optimalnogo upravleniya na osnove konechnomernoi modeli”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 18:1 (2022), 179–187
A. V. Chernov, “O gibkosti sistemy ogranichenii pri approksimatsii zadach optimalnogo upravleniya”, Izv. IMI UdGU, 59 (2022), 114–130
A. V. Chernov, “On uniform monotone approximation of continuous monotone functions with the help of translations and dilations of the Laplace integral”, Comput. Math. Math. Phys., 62:4 (2022), 564–580
V. A. Srochko, E. V. Aksenyushkina, “On resolution of an extremum norm problem for the terminal state of a linear system”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 34 (2020), 3–17
V. A. Srochko, E. V. Aksenyushkina, “Parametrizatsiya nekotorykh zadach upravleniya lineinymi sistemami”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 30 (2019), 83–98
Citation in format AMSBIB
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