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- Title
On stable solutions of the dynamical reconstruction and tracking control problems for a coupled ordinary differential equation–heat equation.
- Authors
Maksimov, Vyacheslav
- Abstract
A dynamical reconstruction problem for a system described by a coupled ordinary differential equation—heat equation is considered. The problem consists in reconstructing an unknown varying in time right-hand part of this system on the basis of inaccurate measurements of its solution. A dynamical algorithm for solving this problem is designed. An estimate for convergence rate is presented. The algorithm is stable with respect to informational noises and computational errors. It is based on the combination of the feedback control method and the method of smoothing functional well-known in the theory of ill-posed problems. The algorithm suggested in the paper is applied to solve tracking control problems. Results of a numerical experiment are discussed.
- Subjects
ORDINARY differential equations; TRACKING algorithms; DIFFERENTIAL-difference equations; HEAT equation; PROBLEM solving; INVERSE problems
- Publication
Mathematical Control & Related Fields, 2024, Vol 14, Issue 1, p1
- ISSN
2156-8472
- Publication type
Article
- DOI
10.3934/mcrf.2023005