Internal Estimation of the Information Set of the Problem of Parametric Identification of Dynamic Systems Based on Interval Data

The paper considers the method of internal interval estimation of the information set of the problem of parametric identification of dynamic systems, when the experimental data are specified in the form of intervals. The state of the dynamic systems under consideration at each moment of time is a parametric set. The objective function is constructed in the space of interval estimates of parameters, characterizing the degree of inclusion of parametric sets of states in the specified experimental interval estimates of phase variables. An expression for the gradient of the objective 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 obtained estimate of the information set is successively expanded with control of the value of the objective function. To solve a variety of direct problems in the process of constructing the desired estimate, the adaptive interpolation algorithm previously developed by the authors is used. The efficiency and performance of the approach under consideration is demonstrated on a representative series of problems.