On one method for solving the problem of identifying dynamic systems

To solve the problem of identifying dynamic systems, the theory and methods of optimal control are applied. The article deals with a new approach to solving the problem based on representing the conditions for improving control in the form of special problems on a fixed point of control operators. This representation makes it possible to apply and modify the theory and methods of fixed points for constructing relaxation control sequences in the optimization problems of the class under consideration. We have proposed an algorithm for the approximate solution of the identification problem based on iterative methods for finding fixed points. The considered algorithm is characterized by the properties of control non-local improvement and the fundamental possibility of strictly improving non-optimal controls that satisfy the known necessary optimality conditions, in contrast to gradient and other local methods. The effectiveness of the proposed optimization methods has been illustrated by calculating a model problem.