On the Guaranteed Accuracy of a Dynamical Recovery Procedure for Controls with Bounded Variation in Systems Depending Linearly on the Control

We obtain an upper bound for the accuracy of a modification of the finite-step dynamical reconstruction algorithm proposed by Yu. S. Osipov and A. V. Kryazhimskii for the unknown control in the dynamical system from inaccurate data on its trajectory We establish that, for the case in which the control is a function of bounded variation and the subspace of the image of the matrix of its coefficients has constant dimension, the asymptotic order in the metric of the space $L_1[a,b]$ of its accuracy with respect to the input error is $1/2$.