Asymptotic Method for Solution of Identification Problem of the Nonlinear Dynamic Systems

Abstract

The dynamic system, when the motion of the object is described by the system of nonlinear ordinary differential equations is considered. The right part of the system involves the phase coordinates as a unknown constant vector-parameter and a small number. The statistical data are taken from practice:  the initial and final values of the object coordinates. Using the method of quasilinearization the given equation is reduced to the system of linear differential equations, where the coefficients of the coordinate and unknown parameter, also of the perturbations depend on a small parameter linearly. Then, by using the least-squares method the unknown constant vector-parameter is searched in the form of power series on a small parameter and for the coefficients of zero and the first orders the analytical formulas are given.  The fundamental matrices both in a zero and in the first approach are constructed approximately, by means of the ordinary Euler method. On an example of determination of the coefficient of hydraulic resistance (CHR) in the lift in the oil extraction by gas lift method is illustrated, as the obtained results in the first approaching coincides with well-known results  on order of 10^-2.