Geodesic
Change of the attainability set after transition to a reduced system
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2020), pp. 58-60 
D. I. Bugrov; A. M. Formal'sky. Change of the attainability set after transition to a reduced system. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2020), pp. 58-60. http://geodesic.mathdoc.fr/item/VMUMM_2020_2_a11/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of changing the attainability region after the transition to a reduced system with decreasing order is considered, taking into account one linear completely controllable stationary system. The source system is a triple integrator. New system — a double integrator — with control in a set of piecewise continuous bounded functions is a result of the reduction of the problem. A comparison is made between the attainability region of the reduced system and the projection of the attainability region of the original system onto the coordinate plane of the reduced system.

[1] Zarodnyuk A., Cherkasov O., “Support reaction in the Brachistochrone Problem in a Resistant Medium”, Dynamical Systems in Applications, Springer Proc. Math. Stat., 249, Springer, Cham, 2018, 451–460 | DOI | MR

[2] Formalskii A. M., Upravlyaemost i ustoichivost sistem s ogranichennymi resursami, Nauka, M., 1974

[3] Bugrov D. I., Formalskii A. M., “Zavisimost ot vremeni oblastei dostizhimosti sistem tretego poryadka”, Prikl. matem. i mekhan., 81:2 (2017), 154–164 | MR | Zbl

[4] Aleksandrov V. V., Zueva I. O., Sidorenko G. Yu., “Robastnaya ustoichivost upravlyaemykh sistem tretego poryadka”, Vestn. Mosk. un-ta. Matem. Mekhan., 2014, no. 1, 39–45 | Zbl

[5] Sadovnichiy V. A., Alexandrov V. V., Lemak S. S., et al., “Robust Stability, Minimax Stabilization and Maximin Testing in Problems of Semi-Automatic Control”, Continuous and Distributed Systems II. Theory and Applications, Studies in Systems, Decision and Control, 30, Springer, Cham, 2015, 247–265 | DOI | MR | Zbl

[6] Polyak B. T., Scherbakov P. S., Robastnaya ustoichivost i upravlenie, Nauka, M., 2002

[7] Bugrov D. I., Formalskii A. M., “Osobennosti oblastei dostizhimosti pri ogranichennom impulse upravlyayuschego vozdeistviya”, Prikl. matem. i mekhan., 82:5 (2018), 631–643

[8] Chernousko F. L., Otsenivanie fazovogo sostoyaniya dinamicheskikh sistem. Metod ellipsoidov, Nauka, M., 1988 | MR