On reconstructing unknown characteristics of a nonlinear system of differential equations

• Autorzy: Kuklin A. , Maksimov V. , Nikulina N.

Identyfikatory

DOI

10.1515/acsc-2015-0010

• Języki publikacji: EN

Abstrakty

EN

Problems of dynamical reconstruction of unknown characteristics for nonlinear equations described the process of diffusion of innovations through results of observations of phase states are considered. Solving algorithms, which are stable with respect to informational noises and computational errors, are designed. The algorithms are based on the principle of auxiliary models with adaptive controls.

Słowa kluczowe

EN

nonlinear differential equations; dynamical reconstruction

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2015
• Tom: Vol. 25, no. 2
• Strony: 163--176
• Opis fizyczny: Bibliogr. 12 poz., wzory

Twórcy

autor

Kuklin A.

• Institute of Economics of UD RAS, Ekaterinburg, 620014, Russia

autor

Maksimov V.

• Ural Federal University and Institute of Mathematics and Mechanics of UD RAS, Ekaterinburg, 620990, Russia

autor

Nikulina N.

• Institute of Economics of UD RAS, Ekaterinburg, 620014, Russia

Bibliografia

• [1] V. Capasso, A. Di Liddo and L. Maddalena: Asymptotic behavior of a nonlinear model for the geographical diffusion of innovations. Dynamic Systems and Applications, 3 (1994), 207-220.
• [2] C.S. Bertuglia, S. Lombado and P. Nijkamp: Innovation Behavior in Space and Time. Springer, Berlin, 1997.
• [3] M. Blizorukowa and V. Maksimov: On some dynamical reconstruction problems for a nonlinear system of the second-order. Opuscula Mathematica, 30(4), (2010), 399-410.
• [4] M. Blizorukova, A. Kuklin and V. Maksimov: On reconstructing an unknown coordinate of a nonlinear system of differential equations. Opuscula Mathematica, 34(2), (2014), 257-270.
• [5] Yu.S. Osipov and A. V. Kryazhimskii: Inverse Problems of Ordinary Differential Equations: Dynamical Solutions. Gordon and Breach, London, 1995.
• [6] V. I. Maksimov: Dynamical Inverse Problems of Distributed Systems. VSP, Boston, 2002.
• [7] V. Maksimov: On one algorithm of input action reconstruction for linear systems. J. of Computer and Systems Sciences International, 48(5), (2009), 681-690.
• [8] V. Maksimov: On the reconstruction of unknown characteristics of a distributed system using a regularized extremal shift. Proc. of the Steklov Mathematical Institute, 268 Suppl. 1, (2010), 188-213.
• [9] M. Blizorukova and V. Maksimov: An algorithm for dynamic reconstruction of input disturbancrs from observations of some of the coordinates. Computational Mathematics and Mathematical Physics, 51(6), (2011), 942-951.
• [10] V. Maksimov: An algorithm for reconstructing controls in a uniform metric. J. of Applied Mathematics and Mechanics, 77(2), (2013), 212-219.
• [11] V. Maksimov: On one algorithm for solving the problem of source function reconstruction. Int. J. of Applied Mathematics and Computer Science, 20(2), (2010), 239-247.
• [12] V. Maksimov and L. Pandolfi: Robust identification of parasitic feedback disturbances for linear lumped parameter system. Int. J. of Applied Mathematics and Computer Science. Special Issue. Edited by R. Triggiani and V. Maksimov, 11(4), (2001), 835-858.

Uwagi

EN

The work was supported by RFBR (project 13-01-12446-ofi-M2), by the Russian Fund for Humanities (project 14-02-00331a), and by the Program of UD RAS (project 15-7-1-22).