Solution of a non-local problem of terminal control
Zapiski Nauchnykh Seminarov POMI, Investigations on applied mathematics and informatics. Part III, Tome 539 (2024), pp. 86-101 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper presents an algorithm of constructing a differentiable control function, that provides transition of a system from a given initial state to the origin in some finite time. The algorithm is applicable to a wide class of non-linear systems, described with ordinary differential equations. A constructive sufficient Kalman-type condition that guarantees the transition is obtained.
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A. N. Kvitko; A. S. Eremin. Solution of a non-local problem of terminal control. Zapiski Nauchnykh Seminarov POMI, Investigations on applied mathematics and informatics. Part III, Tome 539 (2024), pp. 86-101. http://geodesic.mathdoc.fr/item/ZNSL_2024_539_a4/

[1] V. I. Elkin, Reduktsiya nelineinykh upravlyaemykh sistem, Nauka, M., 1997

[2] M. I. Krastanov, “A necessary condition for small time local controllability”, J. Dynamic and Control Systems, 4 (1998), 425–456 | DOI | MR | Zbl

[3] M. Krastanov, M. Quincampoix, “Local small time controllability and attainability of a set for nonlinear control system”, ESAIM: Control, Optimisation and Calculus of Variations, 6 (2001), 499–516 | DOI | MR | Zbl

[4] M. I. Krastanov, “A sufficient condition for small-time local controllability”, SIAM J. Control and Optimization, 48:4 (2009), 2296–2322 | DOI | MR | Zbl

[5] C. O. Aguilar, A. D. Lewis, “Small-time local controllability for a class of homogeneous systems”, SIAM J. Control and Optimization, 50:3 (2012), 1502–1517 | DOI | MR | Zbl

[6] A. P. Krischenko, D. A. Fetisov, “Zadacha terminalnogo upravleniya dlya affinnykh sistem”, Diff. uravn., 49:11 (2013), 1410–1420

[7] S. Jafarpour, “On small-time local controllability”, SIAM J. Control and Optimization, 58:1 (2020), 425–446 | DOI | MR | Zbl

[8] M. I. Krastanov, M. N. Nikolova, “A necessary condition for small-time local controllability”, Automatica, 124 (2021), 109258 | DOI | MR | Zbl

[9] M. I. Krastanov, M. N. Nikolova, “On the small-time local controllability”, Systems and Control Letters, 177 (2023), 105535 | DOI | MR | Zbl

[10] H. Hermes, “Lie algebras of vector fields and local approximation of attainable sets”, SIAM J. Control and Optimization, 16:5 (1978), 715–727 | DOI | MR | Zbl

[11] K. A. Grasse, “On the relation between small-time local controllability and normal self-reachability”, Math. Control Signal Systems, 5 (1992), 41–66 | DOI | MR | Zbl

[12] A. P. Krischenko, D. A. Fetisov, “Terminalnaya zadacha dlya mnogomernykh affinnykh sistem”, Dokl. Akad. nauk, 452:2 (2013), 144–149 | DOI

[13] A. P. Krischenko, D. A. Fetisov, “Preobrazovanie affinnykh sistem i reshenie zadach terminalnogo upravleniya”, Vestnik MGTU im. N. E. Baumana. Estestvennye nauki, 2013, no. 2, 3–16

[14] D. A. Fetisov, “Reshenie terminalnykh zadach dlya affinnykh sistem kvazikanonicheskogo vida na osnove orbitalnoi linearizatsii”, Diff. uravneniya, 50:12 (2014), 1660–1668 | DOI | Zbl

[15] D. A. Fetisov, “Reshenie terminalnykh zadach dlya affinnykh sistem s vektornym upravleniem na osnove orbitalnoi linearizatsii”, Matematika i matematicheskoe modelirovanie, 2015, no. 6, 17–31

[16] D. A. Fetisov, “O postroenii reshenii terminalnykh zadach dlya mnogomernykh affinnykh sistem kvazikononicheskogo vida”, Dif. uravneniya, 52:12 (2016), 1709–1720 | DOI | Zbl

[17] A. N. Kvitko, “Ob odnom metode resheniya lokalnoi granichnoi zadachi dlya nelineinoi statsionarnoi upravlyaemoi sistemy v klasse differentsiruemykh upravlenii”, Zh. vychisl. matem. i matem. fiz., 61:4 (2021), 555–570 | DOI | Zbl