Melnychuk S. Solving the frequency-domain identification problem and guaranteed estimation under uncertainty.

An object of research is stationary linear dynamic system. The subject of research is the development of a new method of system identification in the frequency domain, that determinates a dimension of a model and its parameters, as well as a method for solving overdetermined linear systems under uncertainty. The purpose of research is to develop the method of structural-parametric identification of continuous-time stable linear time-invariant models for complex dynamic systems in frequency domain, as well as to develop a method for solving overdetermined linear systems with noisy right-hand side. Research methods: numerical methods, mathematical modeling, optimization, regularization, guaranteed estimation, interval arithmetic, mathematical analysis, linear algebra. Scientific novelty of work includes the following: 1. The new method for the identification of linear dynamical systems in the frequency domain is developed. It does not require the use of a priori assumptions about the noise and the structure of the model. 2. The influence of uncertainty in data was investigated, and the need of problem regularization is shown. A special algorithm that constructs multiple estimates and recognizes the ill-posed problems is created. A method for determining the maximum allowable dimension of the model is developed. 3. A method for solving overdetermined linear systems is proposed. When the error vector of the right side are limited by predetermined values, the method allows to find guaranteed interval estimations. The practical significance of the results includes a creation of the effective identification method for linear time-invariant systems, the complexity of which is consistent with the original data. The method of structural-parametric identification in the frequency domain can be applied to high-dimensional complex systems, such as a construction of aircraft. The proposed combinatorial method for solving overdetermined linear systems is universal and can be applied to problems associated with indirect measurement and estimation. The work of method is demonstrated by the spacecraft attitude determination problem. The results are obtained in the form of set estimation, which allows to compare different configurations of the sensor arrangement to improve the accuracy of the solution. The results are also valid for other methods. Thus they can be used in further development of identification theory, as well as used in training programs. The results obtained are used in fundamental and practical works in Dynamic systems management department of Space Research Institute of NASU, NVP "Hartron-UCOM" and learning process in NTUU KPI.