250
Views
0
CrossRef citations to date
0
Altmetric
Articles

Solution of the local boundary value problem for a nonlinear non-stationary system in the class of synthesising controls with account of perturbations

ORCID Icon
Pages 1931-1941 | Received 12 Feb 2018, Accepted 13 Oct 2018, Published online: 31 Oct 2018

References

  • Afanas'ev, V. N., Kolmanovskii, V. B., & Nosov, V. R (1996). Mathematical theory of control systems design. Translated and revised from the 1989 Russian original. Mathematics and its Applications, 341, xxiv+668.
  • Aisagaliev, S. A (1991). On the theory of the controllability of linear systems. Automation and Remote Control, 52(1), 163–171, 2.
  • Balachandran, K (1985). Global and local controllability of nonlinear systems. IEE Proceedings D Control Theory and Applications, 132(1), 14–17. doi: 10.1049/ip-d.1985.0003
  • Balachandran, K (1988). Controllability of class of perturbed nonlinear systems. Kybernetica, 24(1), 61–64.
  • Balachandran, K., & Govindaraj, V (2014). Numerical controllability of fractional dynamical systems. Optimization, 63(8), 1267–1279. doi: 10.1080/02331934.2014.906416
  • Barbashin, E. A (1970). Introduction to stability theory. Groningen: Wolters-Noordhoff.
  • Benzaid, Z (1987). Global null controllability of perturbed linear periodic systems. IEEE Transactions on Automatic Control, 32(7), 623–625. doi: 10.1109/TAC.1987.1104670
  • Berdyshev, Y. I (2006). On the construction of the attainability domain in a nonlinear problem. Izvestiya Rossiiskoi Akademii Nauk. Teoriya i Sistemy Upravleniya, 4, 22–26. (in Russian).
  • Chernous'ko, F. L (1987). Approximation of the attainability sets of controllable systems. Differential Equations and Applications, I(II), 469–474. (in Russian).
  • Coron, J. M (2007). Control and nonlinearity. Providence, RI: American Mathematical Society.
  • Dirk, A (1984). Controllability for polynomial systems. Lecture Notes in Control and Information Sciences, 63, 542–545. doi: 10.1007/BFb0006310
  • Emel'yanov, S. V., Krishchenko, A. P., & Fetisov, D. A (2013). Investigation of the controllability of affine systems. Doklady Mathematics, 87(2), 245–248. doi: 10.1134/S1064562413020026
  • Furi, M., Nistri, P., Pera, M. P., & Zezza, P. L. (1985). Topological methods for the global controllability of nonlinear systems. Journal of Optimization Theory and Applications, 45(2), 231–256. doi: 10.1007/BF00939979
  • Gabasov, R., & Kirillova, F. (1971). The qualitative theory of optimal processes. Monographs in Theoretical Foundations of Technical Cybernetics. Moscow: Nauka. (in Russian).
  • Huashu, O (1985). On the controllability of nonlinear control system. Computers & Mathematics with Applications, 10(6), 441–451.
  • Kalman, R. E., Falb, P. L., & Arbib, M. A (1969). Topics in mathematical system theory. New York, NY: McGraw-Hill Book Company.
  • Komarov, V. A (1984). Design of constrained control signals for nonlinear non-autonomous systems. Automation and Remote Control, 45(10), 1280–1286.
  • Komarov, V. A (1985). Estimates of reachable sets for linear systems. Mathematics of the USSR-Izvestiya, 25(1), 193–206. doi: 10.1070/IM1985v025n01ABEH001276
  • Kondrat'yev, D. L., & Lotov, A. V (1990). External estimates and construction of attainability sets for controlled systems. USSR Computational Mathematics and Mathematical Physics, 30(2), 93–97. doi: 10.1016/0041-5553(90)90083-5
  • Korobov, V. I (2007). Geometric criterion for controllability under arbitrary constraints on the control. Journal of Optimization Theory and Applications, 134(2), 161–176. doi: 10.1007/s10957-007-9212-2
  • Krasovskii, N. N (1968). Theory of control of motion. Moscow: Nauka.
  • Krishchenko, A. P (1984). Controllability and attainability sets of nonlinear control systems. Automation and Remote Control, 45(6), 707–713.
  • Kvitko, A. N (2004). On a control problem. Differential Equations, 40(6), 789–796. doi: 10.1023/B:DIEQ.0000046857.76463.21
  • Kvitko, A., & Yakusheva, D. (2017). On one boundary problem for nonlinear stationary controlled system. International Journal of Control, 1(12). doi:10.1080/00207179.2017.1370727
  • Lepe, N. L (1984). A geometrical approach to studying the controllability of second-order bilinear systems. Automation and Remote Control, 45(11), 1401–1406.
  • Levakov, A. A (1987). On the controllability of linear nonstationary systems. Differentsial'nye Uravneniya, 23(5), 798–806. (in Russian).
  • Lotov, A. V (1987). Approximation and stability of generalized attainability sets (Russian). Cybernetics and Computer Technology, 3, 197–208.
  • Panteleev, V. P (1985). Controllability of time-dependent linear systems. Differentsial'nye Uravneniya, 21(4), 623–628. (in Russian).
  • Popova, S. N (2003). Local attainability for linear control systems. Differential Equations, 39(1), 51–58. doi: 10.1023/A:1025115923996
  • Radhakrishnan, B., Balachandran, K., & Anukokila, P (2014). Controllability results for fractional integrodifferential systems in Banach spaces. International Journal of Computing Science and Mathematics, 5(2), 184–197. doi: 10.1504/IJCSM.2014.064067
  • Smirnov, E. Y (2000). Stabilization of programmed motion. Amsterdam: Gordon and Breach Science.
  • Sontag, E. D. (1998). Mathematical control theory. Deterministic finite dimensional systems. New York: Springer Science + Business Media.
  • Walczak, S (1984). A Note on the controllability of nonlinear systems. Mathematical Systems Theory, 17(4), 351–356. doi: 10.1007/BF01744449
  • Zubov, V. I (1975). Lectures on control theory. Moscow: Nauka. (in Russian)

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.