Abstract <p> We consider the method of internal interval estimation of the information set in theparametric identification problem for dynamical systems, where the experimental data arespecified in the form of intervals. The state of the dynamical systems under consideration at eachtime is a parametric set. The objective function is constructed in the space of interval estimates ofparameters, characterizing the degree of inclusion of parametric sets of states in the specifiedexperimental interval estimates of the state variables. An expression for the gradient of theobjective function is obtained. The proposed approach consists of two stages. At the first stage,the objective function is minimized by first-order optimization methods, and at the second stage,the resulting estimate of the information set is successively expanded with control of the objectivefunction value. To solve a variety of direct problems when constructing the desired estimate, theadaptive interpolation algorithm previously developed by the authors is used. The efficiency andperformance of the approach under consideration is demonstrated on a representative series ofproblems.</p>