Email this article On dynamic reconstruction of a disturbances in distributed parameter systems
- Authors: Blizorukova M.S.1, Maksimov V.I.1
-
Affiliations:
- N. N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences
- Issue: Vol 30, No 150 (2025)
- Pages: 97-109
- Section: Original articles
- URL: https://journal-vniispk.ru/2686-9667/article/view/298046
- ID: 298046
Cite item
Full Text
Abstract
The problem of dynamic reconstruction of disturbances acting on a nonlinear system composed of two coupled parabolic-type equations is under consideration. Assuming that a solution of the system is measured (with errors) at discrete times, an algorithm for solving the problem is proposed. The algorithm, based on the principles of feedback control theory, is shown to be robust with respect to informational noises and computational inaccuracies. An estimate of the convergence rate of the algorithm is provided.
About the authors
Marina S. Blizorukova
N. N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences
Author for correspondence.
Email: msb@imm.uran.ru
ORCID iD: 0000-0002-1728-1270
Candidate of Physical and Mathematical Sciences, Senior Researcher
Russian Federation, 16 S. Kovalevskaya St., Yekaterinburg 620077, Russian FederationVyacheslav I. Maksimov
N. N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences
Email: maksimov@imm.uran.ru
ORCID iD: 0000-0001-5643-7998
Doctor of Physical and Mathematical Sciences, Head of Department
Russian Federation, 16 S. Kovalevskaya St., Yekaterinburg 620077, Russian FederationReferences
- J.-L. Lions, Contrôle des Systèmes Distribués Singuliers, Gauthier Villars, Paris, 1983.
- R. Griesse, “Parametric sensitivity analysis in optimal control of a reaction diffusion system. I. Solution differentiability”, Numerical Functional Analysis and Optimization, 25:1–2 (2004), 93-117.
- N. Krasovskii, A. Subbotin, Game-Theoretical Control Problems, Springer, Berlin, 1988.
- A.V. Kryazhimskiy, Yu.S. Osipov, “Modelling of a control in a dynamic system”, Engrg. Cybernetics, 21:2 (1983), 38–47.
- Yu.S. Osipov, A.V. Kryazhimskii, Inverse Problems for Ordinary Differential Equations: Dynamical Solutions, Gordon and Breach, London, 1995.
- Yu.S. Osipov, A.V. Kryazhimsky, V.I. Maksimov, Methods of Dynamic Restoration of Inputs of Controlled Systems, Publishing house of the Ural Branch of the Russian Academy of Sciences, Ekaterinburg, 2011 (In Russian).
- V.I. Maksimov, “The methods of dynamical reconstruction of an input in a system of ordinary differential equations”, Journal of Inverse and Ill-Posed Problems, 29:1 (2021), 125–156.
- Yu.S. Osipov, V.I. Maksimov, “On dynamical input reconstruction in a distributed second order equation”, Journal of Inverse and Ill-Posed Problems, 29:5 (2021), 707–719.
- M.S. Blizorukova, “On the dynamic reconstruction of the input of a control system”, Differential Equations, 50:7 (2014), 847–853.
- V.I. Maksimov, “On a stable solution of the dynamical reconstruction and tracking control problems for coupled ordinary differential equation-heat equation”, Mathematical Control and Related Fields, 14:1 (2024), 322–345.
- V.I. Maksimov, Yu.S. Osipov, “Extremal shift in the problem of tracking a disturbance in a parabolic inclusion describing the two-phase Stefan problem”, Proceedings of the Steklov Institute of Mathematics, 327, Suppl. 1 (2024), S182–S197.
- F. Tröltzsch, Optimal Control of Partial Differential Equations. Theory, Methods and Applications, AMS, Providence, Rhode Island, 2010.
Supplementary files
