The problem of identifying the input signal of dynamic systems modeled by Volterra polynomials

In this paper, we consider one class of Volterra equations of the first kind that appear in the problem of identifying the input signal of a dynamic system. We discuss an approach to the approximate solution of Volterra polynomial equations that model nonlinear dynamics by integro-power Volterra series. A method for constructing a numerical solution using the Newton–Kantorovich iterative process is proposed. Based on standard quadrature methods and the product integration method, we obtain calculation formulas.