The parametric identification of controlled systems based on the extended model of observations (Q1386985)

Different modifications of the Gauss-Markov scheme are often used for a wide range of identification problems. The considered approach permits one to design a smoothing curve in the form of an approximating polynomial. This curve is, in a sense, the best approximation to a real motion of a control object within a given interval. However, for a wide class of problems, it is characteristic to have measuring information not only about phase coordinates of a control object, but also about their derivatives of different orders (the extended model of observations). In this paper, the author obtains finite analytic relations for the identification of current parameters of a motion model within the framework of the regularization theory for the case of the extended model of observations. The obtained relations permit one to design algorithms stable to observation errors and inaccuracies of input data specification. Characteristics of the obtained solutions are also analyzed.