Abstract
In this paper, we solve the problem of estimating the parameters of a system of ordinary differential equations from observations on a short interval of argument values. By analogy with linear regression analysis, a sufficiently large number of observations are selected on this segment and the values of the functions on the right side of the system and the values of the derivatives are estimated. According to the obtained estimates, unknown parameters are determined, using the differential equations system. The consistency of the estimates obtained in this way is proved with an increase in the number of observations over a short period of argument values. Here, an algorithm for estimating parameters acts as a system. The error of the obtained estimate is an indicator of its quality. A sequence of inaccurate measurements is a random process. The method of linear regression analysis applied to an almost linear regression function is used as an optimization procedure.
Highlights
The problem of estimating the parameters of a system of nonlinear ordinary differential equations, based on inaccurate deterministic observations, using known optimization algorithms, is solved in the papers [1,2,3]
In this paper, we solve the problem of estimating the parameters of a system of ordinary differential equations from observations on a short interval of argument values
The advantage of the first approach is the possibility of using known optimization algorithms, and the disadvantage of it is the lack of analytical estimates of the convergence rate to the estimated parameters
Summary
The problem of estimating the parameters of a system of nonlinear ordinary differential equations, based on inaccurate deterministic observations, using known optimization algorithms, is solved in the papers [1,2,3]. The problem of estimating parameters over a small observation interval is interesting, which is closely related to discrete optimization methods of experiment planning (see, for example, [6,7]) In this paper, this problem is solved for a system of non-linear ordinary differential equations. The method of linear regression analysis is used in relation to a regression function that slightly deviates from the original function in a small neighbourhood of some time moment [8,9,10,11,12,13] This method is based on minimizing the standard deviation of a sequence of observations from a linear regression function. Estimating the Coefficients of a System of Ordinary Differential Equations by Inaccurate Observations
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