Identification of Integral Models of Nonlinear Multi-input Dynamic Systems Using the Product Integration Method

Abstract

AbstractThis paper discusses a method for constructing Volterra polynomials in the case of a vector input signal. The key idea behind the new approach to constructing integral polynomials is based on the identification of integrals from Volterra kernels. We describe in detail the numerical modeling of a multi-input dynamic system using the cubic Volterra polynomial. This approach is based on solving a specific system of linear algebraic equations (SLAE) obtained by approximating multidimensional convolutions by the product integration method (pi-method). The pi-approximation makes it possible to avoid essential difficulties arising in the solution of multidimensional Volterra equations of the first kind. The numerical efficiency is tested for the problem of modeling the nonlinear dynamics of a heat exchanger element. The results of the computational experiment showed that in most cases the new approach increases the accuracy of modeling.