AIMS Mathematics, 2020, 5(5): 4108-4120. doi: 10.3934/math.2020263

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On a problem of dynamical input reconstruction for a system of special type under conditions of uncertainty

1 Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, S. Kovalevskoi str. 16, Yekaterinburg, 620990 Russia
2 Ural Federal University, Mira str. 19, Yekaterinburg, 620002 Russia

From the viewpoint of the approach of the theory of dynamic inversion, an input reconstruction problem in a differential system of special type is under investigation. The first equation of the system is a linear stochastic Ito equation, whereas the second is a linear ordinary equation containing an unknown disturbance. The statement when the reconstruction is performed from the discrete information on several realizations of the stochastic process being a solution of the first equation is considered. The problem is reduced to an inverse problem for the system of ordinary differential equations, which includes, instead of the stochastic equation, the equation describing the dynamics of the mathematical expectation of the desired process. A finite-step software-oriented solving algorithm based on the method of auxiliary feedback controlled models is designed; an estimate for its convergence rate with respect to the number of measurable realizations is obtained. An illustrating example is given, for which the calibration of algorithm’s parameters is discussed.
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