An input identification problem in a hybrid system of differential equations is considered from the viewpoint of the approach of the theory of dynamic inversion. The first equation of the system is a quasi-linear stochastic Ito equation, whereas the second one is a linear ordinary equation containing an unknown disturbance. The identification should be performed from the discrete information on a number of realizations of the stochastic process that solves the first equation. The problem is reduced to an inverse problem for a new system of differential equations, which includes, instead of the stochastic equation, an ordinary equation describing the dynamics of the mathematical expectation of the original process. A finite-step software-oriented solution algorithm based on the method of auxiliary feedback controlled models is designed, and its convergence is proved. An example illustrating the operation of a procedure for calibrating the algorithm parameters is presented.
Keywords: hybrid type system, dynamic input identification, controlled model
Received April 12, 2024
Revised April 30, 2024
Accepted May 6, 2024
Funding Agency: The work was performed as part of research conducted in the Ural Mathematical Center with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Agreement number 075-02-2024-1377).
Valeriy Lvovich Rozenberg, Cand. Sci. (Phys.-Math.), Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia, e-mail: rozen@imm.uran.ru
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Cite this article as: V.L. Rozenberg. Dynamic identification of an unknown input in a hybrid type system. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2024, vol. 30, no. 2, pp. 164–172.
