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ЖУРНАЛЫ // Ural Mathematical Journal

Ural Math. J., 2023, том 9, выпуск 2, страницы 141–156 (Mi umj211)

Convexity of reachable sets of quasilinear systems
Ivan O. Osipov

References

1. Al'brekht E. H., “The optimal control of the motion of quasilinear systems”, Differ. Uravn., 5:3 (1969), 430–442 (in Russian)  mathnet  zmath
2. Al'brekht E. H., “The coming together of quasilinear objects in the regular case”, Differ. Uravn., 7:7 (1971), 1171–1178 (in Russian)  mathnet  zmath
3. Albrecht E. G., Metod Lyapunova-Puankare v zadachah optimalnogo upravleniya, Diss. dokt. fiz.-mat. nauk, Sverdlovsk, 1986, 280 pp. (in Russian)
4. Calvet J.-P., Arkun Y., “Design of P and PI stabilizing controllers for quasi-linear system.”, Comput. Chem. Eng., 14:4–5 (1990), 415–426  crossref
5. Ching Sh., Eun Yo., Gokcek C., Kabamba P. T., Meerkov S. M., Quasilinear Control: Performance Analysis and Design of Feedback Systems with Nonlinear Sensors and Actuators, Cambridge University Press, Cambridge, 2010, 282 pp.  crossref
6. Dauer J. P., “Nonlinear perturbations of quasi-linear control systems”, J. Math. Anal. Appl., 54:3 (1976), 717–725  crossref  mathscinet  zmath
7. Filippov A. F., Differential Equations with Discontinuous Righthand Sides, Springer, Dordrecht, 1988, 304 pp.  crossref
8. Filippov A. F., Vvedenie v teoriju differencial'nyh uravnenij [Introduction to the theory of differential equations], Comkniga, Moscow, 2007, 240 pp. (in Russian)
9. Gabasov R. F., Kalinin A. I., Kirillova F. M., Lavrinovich L. I., “On asymptotic optimization methods for quasilinear control systems”, Trudy Inst. Mat. Mekh. UrO RAN, 25:3 (2019), 62–72  mathnet  crossref
10. Guo Y., Kabamba P. T., Meerkov S. M., Ossareh H. R., Tang C. Y., “Quasilinear control of wind farm power output”, IEEE Trans. Control Syst. Technol., 23:4 (2015), 1555–1562  crossref
11. Gusev M. I., Zykov I. V., “On Extremal properties of the boundary points of reachable sets for control systems with integral constraints”, Proc. Steklov Inst. Math., 300:Suppl. 1 (2018), 114–125  mathnet  crossref  mathscinet
12. Gusev M. I., “The limits of applicability of the linearization method in calculating small-time reachable sets”, Ural Math. J., 6:1 (2020), 71–83  mathnet  crossref  mathscinet  zmath
13. Gusev M. I., Osipov I. O., “Asymptotic behavior of reachable sets on small time intervals”, Proc. Steklov Inst. Math., 309:Suppl. 1 (2020), S52–S64  mathnet  crossref
14. Gusev M. I., Osipov I. O., “On a local synthesis problem for nonlinear systems with integral constraints”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 32:2 (2022), 171–186  mathnet  crossref  zmath
15. Kalinin A. I., Lavrinovich L. I., “Asymptotic minimization method of the integral quadratic functional on the trajectories of a quasilinear dynamical system”, Dokl. NAN Belarusi, 62:5 (2018), 519–524 (in Russian)  crossref  zmath
16. Kiselev Yu. N., “An asymptotic solution of the problem of time-optimal control systems which are close to linear ones”, Soviet Math. Dokl., 9:5 (1968), 1093–1097  zmath
17. Krasovskii N. N., Teoriya upravleniya dvizheniem [Theory of Control of Motion], Nauka, Moscow, 1968, 476 pp. (in Russian)
18. Kremlev A. G., “Control of a quasilinear system under indeterminate initial conditions”, Differ. Uravn., 16:11 (1980), 1967—1979 (in Russian)  mathnet  zmath
19. Osipov I. O., “On the convexity of the reachable set with respect to a part of coordinates at small time intervals”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 31:2 (2021), 210–225  mathnet  crossref  zmath
20. Polyak B. T., “Gradient methods for solving equations and inequalities”, USSR Comput. Math. Math. Phys., 4:6 (1964), 17–32  mathnet  crossref
21. Polyak B. T., “Convexity of nonlinear image of a small ball with applications to optimization”, Set-Valued Analysis, 9 (2001), 159–168  crossref  mathscinet  zmath
22. Polyak B. T., “Convexity of the reachable set of nonlinear systems under $L_2$ bounded controls”, Dynam. Contin. Discrete Impuls. Systems Ser. A Math. Anal., 11:Suppl. 2–3 (2004), 255–267  zmath
23. Subbotin A. I., “Control of motion of a quasilinear system”, Differ. Uravn., 3:7 (1967), 1113–1118 (in Russian)  mathnet  zmath
24. Zykov I. V., Osipov I. O., A program for constructing the reachable sets of nonlinear systems with integral control constraints by the Monte Carlo method, Certificates of State Registration of a Computer Program or a Database, No. 2020661557, 2020
25. Zykov I. V., “An algorithm for constructing reachable sets for systems with multiple integral constraints.”, Mathematical Analysis with Applications: Int. Conf. CONCORD-90 (Ekaterinburg, July 2018), Springer Proc. Math. Stat., no. 318, eds. Pinelas S., Kim A., Vlasov V., Springer, Cham, 2020, 51–60  crossref  mathscinet  zmath
26. Zykov I. V., “External estimates of reachable sets for control systems with integral constraints”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 190 (2021), 107–114  mathnet  crossref


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