Kostian N. Methods and tools for formation and numerical implementation of integral models for inverse tasks of system dynamics

The object of study: the processes of modeling of inverse tasks of system dynamics. Goal of study: to increase the effectiveness of the methods and means of mathematical modeling in solving inverse problems of dynamics based on the creation of methods of formation, numerical algorithms and software of the computer implementation of integral dynamic models. Methods of study: elements of the theory of integral equations; methods of equivalent and approximate transformations of the equations of dynamics; elements of matrix theory; numerical analysis methods; methods of organization of software based on typical modeling packages; methods of computational experiments. The novelty of the results: for the first time methods for identification of dynamic objects and systems based on integral models have been developed; further development received methods for solving Volterra equations of the type I providing improved accuracy and stability of the results by using the formulas of higher order and organization of multi-step calculations; a way of restoring the signal at the input of the linear dynamic object based on Hilbert transformation has been developed. The practical value of the results is that for the first time have been created a set of programs, based on the effective use of MATLAB environment, that allows to solve a wide class of inverse problems of the dynamics of the technical objects and systems with the ability to maintain necessary accuracy and performance. The results of studies have been implemented in the design- maintenance organization and in studying process.