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

• Autorzy: Blizorukova M. , Maksimov V.

Identyfikatory

DOI

10.1515/amcs-2017-0031

• Języki publikacji: EN

Abstrakty

EN

In this paper, we consider the problem of tracking a solution of a reference parabolic equation by a solution of another equation. A stable algorithm based on the extremal shift method is proposed for this problem. The algorithm is designed to work on a sufficiently large time interval where both equations operate.

Słowa kluczowe

EN

parabolic equation; tracking problem; unknown disturbance

PL

równanie paraboliczne; śledzenie problemu; zakłócenie nieznane

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2017
• Tom: Vol. 27, no. 3
• Strony: 457--465
• Opis fizyczny: Bibliogr. 16 poz., wykr.

Twórcy

autor

Blizorukova M.

• Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, S. Kovalevskaya 16, Yekaterinburg 620990, Russia; Graduate School of Economics and Management, Ural Federal University, Yekaterinburg 620002, Russia

autor

Maksimov V.

• Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, S. Kovalevskaya 16, Yekaterinburg 620990, Russia; Graduate School of Economics and Management, Ural Federal University, Yekaterinburg 620002, Russia

Bibliografia

• [1] Banks, H.T. and Kappel, F. (1979). Spline approximation for functional–differential equations, Journal of Differential Equations 34(3): 406–522.
• [2] Bernier, C. and Manitius, A. (1978). On semigroups in Rn ×Lp corresponding to differential equations with delays, Canadian Journal of Mathematics 30(5): 897–914.
• [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 Science 11(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 Science 24(1): 75–85, DOI: 10.2478/amcs-2014-0006.
• [6] Krasovskii, N.N. and Subbotin, A.I. (1988). Game-Theoretical Control Problems, Springer Verlag, New York, NY/Berlin.
• [7] Kryazhimskiy, A.V. and Maksimov, V.I. (2011). Resource-saving tracking problem with infinite time horizon, Differential Equations 47(7): 1004–1013.
• [8] Maksimov, V.I. (2011). The tracking of the trajectory of a dynamical system, Journal of Applied Mathematics and Mechanics 75(6): 667–674.
• [9] Maksimov, V.I. (2002). Dynamic Inverse Problems of Distributed Systems, VSP, Utrecht/Boston, MA.
• [10] Maksimov, V.I. (2012). On tracking solutions of parabolic equations, Russian Mathematic 56(1): 35–42.
• [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.
• [12] Maksimov, V.I. (2014). Algorithm for shadowing the solution of a parabolic equation on an infinite time interval, Differential Equations 50(3): 362–371.
• [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 Science 23(1): 91–102, DOI: 10.2478/amcs-2013-0008.
• [16] Sontag, E.D. (1990). Mathematical Control Theory, Springer Verlag, Berlin.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).