On Integral Funnel of Control Systems, Changed at Several Small Time Interval

V. N. Ushakov; Ушаков В. Н.; A. A. Ershov; Ершов А. А.; A. V. Ushakov; Ушаков А. В.

doi:10.31857/S0032823523050156

On Integral Funnel of Control Systems, Changed at Several Small Time Interval

作者: Ushakov V.¹, Ershov A.¹, Ushakov A.¹
隶属关系:
1. N.N. Krasovskii Institute of Mathematics and Mechanics UB RAS
期: 卷 87, 编号 5 (2023)
页面: 829-861
栏目: Articles
URL: https://journals.rcsi.science/0032-8235/article/view/232516
DOI: https://doi.org/10.31857/S0032823523050156
EDN: https://elibrary.ru/UZKZIZ
ID: 232516

如何引用文章

全文:

开放存取

##reader.subscriptionAccessGranted##
受限制的访问

订阅存取

详细
作者简介
参考
补充文件
统计

详细

A nonlinear control system in a finite-dimensional Euclidean space and on a finite time interval is considered, the dynamics of which changes significantly over several small sections from a given time interval. We study the degree of change in the reachable sets and integral funnels of the system under consideration when it varies in these sections. The corresponding changes are estimated in the Hausdorff metric.

关键词

control system, differential inclusion, reachable set, integral funnel, variable structure, system variation, Hausdorff distance

作者简介

V. Ushakov

N.N. Krasovskii Institute of Mathematics and Mechanics UB RAS

编辑信件的主要联系方式.
Email: ushak@imm.uran.ru
Russia, Yekaterinburg

A. Ershov

N.N. Krasovskii Institute of Mathematics and Mechanics UB RAS

编辑信件的主要联系方式.
Email: ale10919@yandex.ru
Russia, Yekaterinburg

A. Ushakov

N.N. Krasovskii Institute of Mathematics and Mechanics UB RAS

编辑信件的主要联系方式.
Email: aushakov.pk@gmail.com
Russia, Yekaterinburg

参考

Krasovskii N.N. Dynamical System Control. Moscow: Nauka, 1985. 520 p. (in Russian)
Kurjanskii A.B. Selected Works. Moscow: MSU Publ., 2009. 756 p. (in Russian)
Shmatkov A.M. Control of systems with inteference of bounded magnitude // J. Comput.&Syst. Sci. Int., 1995, vol. 33, no. 5, pp. 57–63. https://elibrary.ru/item.asp?id=31080527
Krasovskii N.N., Subbotin A.I. Positional Differential Games. Moscow: Fizmatlit, 1974. 456 p. (in Russian)
Ushakov V.N., Matviichuk A.R., Parshikov G.V. A method for constructing a resolving control in an approach problem based on attraction to the feasibility set // Proc. Steklov Inst. Math., 2014, vol. 284, suppl. 1, pp. S135–S144.
Matviychuk A.R., Ukhobotov V.I., Ushakov A.V., Ushakov V.N. The approach problem of a nonlinear controlled system in a finite time interval // JAMM, 2017, vol. 81, no. 2, pp. 114–128.
Ershov A.A., Ushakov V.N. An approach problem for a control system with an unknown parameter // Sb.: Math., 2017, vol. 208, no. 9, pp. 1312–1352.
Chernous’ko F.L. State Estimation for Dynamic Systems. Boca Raton, Florida: CRC Press, 1994. 320 p.
Chernous’ko F.L. Optimal guaranteed estimates of indeterminacies with the aid of ellipsoids. I // Eng. Cybern., 1980, vol. 18, no. 3, pp. 1–9.
Chernous’ko F.L. Optimal guaranteed estimates of indeterminacy with the aid of ellipsoids. II // Eng. Cybern., 1980, vol. 18, no. 4, pp. 1–9.
Chernous’ko F.L. Optimal guaranteed estimates of indeterminacy with the aid of ellipsoids. III // Eng. Cybern., 1980, vol. 18, no. 5, pp. 3–9.
Kurjanskii A., Valyi I. Ellipsoidal Calculus for Estimation and Control. Systems & Control: Foundations & Applications. Basel: Birkhӓuser Basel and IIASA, 1997. 321 p.
Schweppe F.C. Recursive state estimation: unknown but bounded errors and system inputs // IEEE Trans. Automat. Control, 1968, vol. AC_13, no. 1, pp. 22–28.
Bertsekas D.P., Rhodes J.B. Recursive state estimation for a set-membership description of uncertainty // IEEE Trans. Automat. Control, 1971, vol. AC-16, no. 2, pp. 117–128.
Gusev V.I. Estimates of reachable sets of multidimensional control systems with nonlinear interconnections // Proc. Steklov Inst. Math., 2010, vol. 269, suppl. 1, pp. S134–S146.
Filippova T.F. Differential equations for ellipsoidal estimates for reachable sets of a nonlinear dynamical control system // Proc. Steklov Inst. Math., 2010, vol. 271, suppl. 1, pp. S75–S84.
Chernousko F.L. Estimation of the attainability sets of linear systems with an indeterminate matrix // Dokl. Math., 1996, vol. 54, no. 1, pp. 634–636.
Rokityanskii D.Y. Perturbed linear mapping of sets // J. Comput.&Syst. Sci. Int., 1996, vol. 35, no. 6, pp. 948–954.
Kostousova E.K. On the boundedness and unboundedness of external polyhedral estimates for reachable sets of linear differential systems // Proc. Steklov Inst. Math., 2010, vol. 269, suppl. 1, pp. S162–S173.
Guseinov K.G., Moiseyev A.A., Ushakov V.N. The approximation of reachable domains of control systems // JAMM, 1998, vol. 62, no. 2, pp. 169–175.
Nikol’skii M.S. On the approximation of the reachable set of a differential inclusion // Moscow Univ. Bull. Ser. 15. Comput. Math.&Cybern., 1987, no. 4, pp. 31–34. (in Russian)
Lempio F., Veliov V.M. Discrete approximation of differential inclusions // Bayr. Math. Schriften, 1998, vol. 54, pp. 149–232.
Anan’evskii I.M. Control of a nonlinear vibratory system of the fourth order with unknown parameters // Automat.&Remote Control, 2001, vol. 62, pp. 343–355.
Anan’evskii I.M. Control synthesis for linear systems by methods of stability theory of motion // Differ. Eqns., 2003, vol. 39, pp. 1–10.
Polyak B.T., Khlebnikov M.V., Shcherbakov P.S. Control of Linear Systems under External Disturbances: Technique of Linear Matrix Inequalities. Moscow: Lenand, 2014. 560 p.
Beznos A.V., Grishin A.A., Lenskiy A.V. et al. Control of the Pendulum Using a Flywheel. Special workshop on theoretical and applied mechanics / Ed. by V.V. Alexandrov. Moscow: MSU Publ., 2009. pp. 170–195. (in Russian)
Gornov A.Yu., Tyatyushkin A.I., Finkelstein E.A. Numerical methods for solving terminal optimal control problems // Comput. Math. Math. Phys., 2016, vol. 56, no. 2, pp. 221–234.