ON ROBUST ON-LINE PARAMETER IDENTIFICATION TECHNIQUES IN ENVIRONMENTAL MODELING

Abstract

In our paper we would like to discuss about one method of auxiliary controlled models and the application of this method to solving some problems of identification for differential equations. Problems of determining some parameters through the information on equation's solutions are often called reconstruction (identification) problems. Therewith it is assumed that the input information (results of measurements of current phase states of a dynamical system) forthcomes in the process. As to unknown parameters, they should be reconstructed in the process too. One of the methods of solving similar problems was suggested in (Kryazhimskii and Osipov, 1983; Kryazhimskii and Osipov, 1984; Osipov and Kryazhimskii, 1995; Maksimov, 1995; Maksimov, 2002a; Maksimov, 2002b). This method based on the ideas of the theory of ill-posed problems actually reduces an identification problem to a control problem for an auxiliary dynamical system—the model (Krasovskii and Subbotin, 1988). Regularization of the problem under consideration is locally realized during the process of choosing a positional control in the system-model. The method mentioned above was applied to a number of problems described by some classes of ordinary differential equations as well as by equations with distributed parameters. Different system's characteristics varying in time were under reconstruction, for example, unknown discontinuous inputs, initial and boundary data, distributed disturbances, coefficients of an elliptic operator and so on. In the present paper, we illustrate this method with a model example.