Asymptotic method for solution of identification problem of the nonlinear dynamic systems
2018
A 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 the 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.
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