Identification of nonlinear systems with periodic external actions (Part I)

Abstract

The problem of identifying nonlinear systems with periodic external actions is considered in the article. The number of such actions in the system is not limited, and these actions can be either additive or multiplicative. We use a time series of observed system variables to calculate unknown equation coefficients. The proven theorem allows us to separate the unknown coefficients of the system into variables and constants. The proposed computational procedure allows us to avoid possible errors caused by the discrete nature of observable time series. Identification of zero coefficients is carried out in two ways, eliminating erroneous zeroing of the terms of the equations. The method is illustrated with a numerical example of identifying a chaotic system with periodic external actions.

Keywords

• identification
• ordinary differential equation
• external action
• periodic coefficient
• constant coefficient