Interval Approach to Solving Parametric Identification Problems for Dynamical Systems
A. Yu. Morozov, Dmitry Leonidovich Reviznikov · Differential Equations · 2022
Abstract We present an approach to solving parametric identification problems for dynamical systems. The approach is aimed at finding an interval estimate of the model parameters in which the solution of the corresponding modeling problem would contain the initial (experimental) data or minimize the deviation from them. The approach is based on an earlier-developed, tested, and justified adaptive interpolation algorithm for modeling dynamical systems with interval parameters. The problem of minimizing the distance between the solution of the interval problem and the experimental values of the phase variables in the space of bounds of the interval estimates of the model parameters is formulated. An expression for the gradient of the objective function to be minimized is obtained for further application of first-order optimization methods. The proposed approach is tested on a representative set of problems.