doi: 10.18698/2309-3684-2017-2-94106
We conducted a numerical experiment in applying the shooting method to solve problems of optimal control with switching. We used the problem of lunar soft-landing to test an algorithm that ensures convergence of Newton's method in problems of this type. We analysed the accuracy of our computations.
[1] Pontryagin L.S., Boltyanskiy V.G., Gamkrelidze R.V., Mishchenko E.F. Matematicheskaya teoriya optimalnykh protsessov [Mathematical theory of optimal processes]. Moscow, Nauka Publ., 1983, 393 p.
[2] Athans M., Falb P.L. Optimal Control. An Introduction to the Theory and Its Applications. McGraw-Hill, Inc., New York, 1963, 894 p. [In Russ.: Athans M., Falb P.L. Optimalnoe upravlenie. Moscow, Mashinostroenie Publ., 1968, 764 p.].
[3] Leitmann G., ed. Optimization techniques, with applications to aerospace systems. Academic Press, New York, 1962. [In Russ.: Leitmann G., ed. Metody optimizatsii s prilozheniyami k mekhanike kosmicheskogo poleta. Moscow, Nauka Publ., 1965, 538 p.].
[4] Fedorenko R.P. Priblizhennoe reshenie zadach optimalnogo upravleniya [Approximate solutions to optimal control problems]. Moscow, Nauka Publ., 1978, 486 p.
[5] Grigorev I.S. Metodicheskoe posobie po chislennym metodam dlya resheniya kraevykh zadach printsipa maksimuma v zadachakh optimalnogo upravleniya [Methodological manual on numerical methods for solving boundary problems on the maximum principle in optimal control problems]. Moscow, Centre for Applied Research of the Faculty of Mechanics and Mathematics of Lomonosov
Moscow State University Publ., 2005, 160 p.
[6] Meditch J. IEEE Transactions on Automatic Control, 1964, no. 9 (4), pp. 477–484.
[7] Huang Y. Trudy MAI — Trudy MAI journal (Proc. of the Moscow Aviation Institute), 2016, no. 90. Available at: http://trudymai.ru/published.php?ID=74747 (accessed September 21, 2017).
[8] Blackmore L. The Bridge, Winter 2016, vol. 46, no. 4. Available at: http://web.mit.edu/larsb/www/nae_bridge_2016.pdf (accessed September 21, 2017).
[9] Dimitrienko Yu.I., Dimitrienko I.D., Koryakov M.N. Inzhenernyy zhurnal: nauka i innovatsii — Engineering Journal: Science and Innovation, 2013, no. 9. Available at: http://engjournal.ru/catalog/mathmodel/technic/1120.html (accessed September 21, 2017).
[10] Zhukov B.I., Likhachev V.N., Sikharulidze Yu.G., Trifonov O.V., Fedotov V.P., Yaroshevskiy V.S. Kombinirovannyy algoritm upravleniya posadkoy kosmicheskogo apparata “Luna-Glob” [Combined control algorithm for Luna-Glob spacecraft landing]. Sb. mat. Vseros. sezda po fundamentalnym problemam teoreticheskoy i prikladnoy mekhaniki. Kazan, 20–24 avgusta 2015 [Proc. of the 11-th
All-Russian congress on basic problems of theoretical and applied mechanics. Kazan, August 20–24, 2015], pp. 1395–1398.
[11] Zhukov B.I., Likhachev V.N., Sazonov V.V., Sikharulidze Yu.G., Tuchin D.A., Fedotov V.P., Yaroshevskiy V.S. Kosmicheskie issledovaniya — Cosmic Research, 2015, no. 6, p. 480.
[12] Afanasev V.A., Degtyarev G.L., Meshchanov A.S., Sirazetdinov T.K. Vestnik Kazanskogo gosudarstvennogo tekhnicheskogo universiteta im. A.N. Tupoleva — “Vestnik KGTU im. A.N. Tupoleva” Scientific Technical Journal (Bulletin of the Kazan State Technical University named after A.N. Tupolev), 2007, no. 3, pp. 56–59.
[13] Gubareva E.A., Mozzhorina T.Yu. Inzhenernyy zhurnal: nauka i innovatsii — Engineering Journal: Science and Innovation, 2015, no. 8. Available at: http://engjournal.ru/catalog/arse/adb/1415.html (accessed September 21, 2017).
[14] Mozzhorina T.Yu., Gubareva E.A. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2014, no. 3 (3), pp. 74–88.
Mozzhorina T. Yu. Numerical solution to problems of optimal control with switching by means of the shooting method. Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 94-106
Количество скачиваний: 880