Have a personal or library account? Click to login
On an algorithm for the problem of tracking a trajectory of a parabolic equation Cover

On an algorithm for the problem of tracking a trajectory of a parabolic equation

Open Access
|Sep 2017

References

  1. Banks, H.T. and Kappel, F. (1979). Spline approximation for functional–differential equations, Journal of Differential Equations34(3): 406–522.10.1016/0022-0396(79)90033-0
  2. Bernier, C. and Manitius, A. (1978). On semigroups in ℝn ×Lpcorresponding to differential equations with delays, Canadian Journal of Mathematics30(5): 897–914.10.4153/CJM-1978-078-6
  3. Blizorukova, M., Kappel, F. and Maksimov, V. (2001). A problem of robust control of a system with time delay, International Journal of Applied Mathematics and Computer Science11(4): 821–834.
  4. Grimble, J.M., Johnson, M.A. (1988). Optimal Control and Stochastic Estimation: Theory and Applications, John Wiley & Sons, Chichester.
  5. Kapustyan, V. and Maksimov, V. (2014). On attaining the prescribed quality of a controlled fourth order system, International Journal of Applied Mathematics and Computer Science24(1): 75–85, DOI: 10.2478/amcs-2014-0006.10.2478/amcs-2014-0006
  6. Krasovskii, N.N. and Subbotin, A.I. (1988). Game-Theoretical Control Problems, Springer Verlag, New York, NY/Berlin.10.1007/978-1-4612-3716-7
  7. Kryazhimskiy, A.V. and Maksimov, V.I. (2011). Resource-saving tracking problem with infinite time horizon, Differential Equations47(7): 1004–1013.10.1134/S001226611107010X
  8. Maksimov, V.I. (2011). The tracking of the trajectory of a dynamical system, Journal of Applied Mathematics and Mechanics75(6): 667–674.10.1016/j.jappmathmech.2012.01.007
  9. Maksimov, V.I. (2002). Dynamic Inverse Problems of Distributed Systems, VSP, Utrecht/Boston, MA.10.1515/9783110944839
  10. Maksimov, V.I. (2012). On tracking solutions of parabolic equations, Russian Mathematic56(1): 35–42.10.3103/S1066369X12010057
  11. Maksimov, V.I. (2013). Regularized extremal shift in problems of stable control, in D. Hömberg and F. Tröltzsch (Eds.), IFIP Advances in Information and Communication Technology, Vol. 391, Springer, Berlin, pp. 112–121.10.1007/978-3-642-36062-6_12
  12. Maksimov, V.I. (2014). Algorithm for shadowing the solution of a parabolic equation on an infinite time interval, Differential Equations50(3): 362–371.10.1134/S0012266114030100
  13. Osipov, Yu.S. (2009). Selected Works, Moscow State University, Moscow.
  14. Pandolfi, L. and Priola, E. (2005). Tracking control of parabolic systems, Proceedings of the 21st IFIP TC7 Conference on System Modeling and Optimization, Sophia Antipolis, France, pp. 135–146.
  15. Prodan, I., Olaru, S., Stoica, C., and Niculescu, S.-I. (2013). Predictive control for trajectory tracking and decentralized navigation of multi-agent formations, International Journal of Applied Mathematics and Computer Science23(1): 91–102, DOI: 10.2478/amcs-2013-0008.10.2478/amcs-2013-0008
  16. Sontag, E.D. (1990). Mathematical Control Theory, Springer Verlag, Berlin.10.1007/978-1-4684-0374-9
DOI: https://doi.org/10.1515/amcs-2017-0031 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 457 - 465
Submitted on: Nov 30, 2016
Accepted on: May 4, 2017
Published on: Sep 23, 2017
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2017 Marina Blizorukova, Vyacheslav Maksimov, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.