Deterministic identification methods for nonlinear dynamical systems based on the Volterra Model

Abstract

The paper solves an important scientific and practical problem, which is to improve the accuracy and computational
stability of the methods of deterministic identification of nonlinear dynamic systems in the form of Volterra model based on
experimental data of observations ”input-output” taking. On the base of theoretical and experimental studies created effective
instrumental algorithmic and software tools for estimating Volterra kernels in the time domain Into account measurement errors.
Results of the further development of methods of deterministic identification of nonlinear dynamic systems based on Volterra models
using irregular pulse sequences show. The methods are based on the use of the Tikhonov regularization procedure. The amplitude of
test impulses is used as a regularization parameter. In the identification, procedure applies wavelet filtering for smooth the estimates
of the Volterra kernels apply. This gives increase the accuracy and noise immunity of identification methods. The approximation
method of identification of the nonlinear dynamic systems based on Volterra models is improved. Method is consists in the choice of
amplitudes of test signals and of coefficients scaling of the partial components of responses a nonlinear system in procedure of
processing of signals-responses. The improvement is reduced to minimizing the methodological error in the allocation of partial
components from the response of the identification object and allows obtaining more accurate estimates of Volterra nuclei. To
improve the computational stability of the developed identification algorithms and for noise reduction in the obtained estimates of
multidimensional Volterra kernels the wavelet filtration is used. This allows obtaining smoothed solutions and decreases error of the
identification by 1,5-2,5 times. A new robust method of deterministic identification of nonlinear dynamic systems based on Volterra
models in the time domain is developed. In contrast to the interpolation method, where finite difference formulas with a
predetermined number of experimental studies of the object of identification are used for numerical differentiation. It is proposed to
solve the corresponding Volterra integral equations of the first kind, for the numerical implementation of which an unlimited number
of experiments can be used. This makes it possible to increase the accuracy of the calculation of derivatives, and consequently, the
accuracy of identification. Software tools on the system Matlab platform have been developed to implement the developed
computational algorithms for deterministic identification of nonlinear dynamic systems in the form of Volterra kernels.