Improvement of variational-gradient method in dynamical systems of automated control for integro-differential models

The dynamical systems given by integro-differentiation models with K-symmetric K-positive-definite operator are considered.  The variational-gradient method was applied to those models.  The analysis showed that the implementation of this method does not require knowledge of the operator spectrum, in addition, it has a better convergence rate and is more resistant to disturbances than gradient methods.  The theorem is proved in this paper, which allows us to draw conclusions about the effectiveness of the application of the variational-gradient method for the research of control problems.  Investigation of an integro-differential model with a K-positive-definite K-symmetric operator using the variational-gradient method will increase the efficiency of information processing in the processes of control and research of dynamic systems.  Application of the variational-gradient method to the control tasks will allow expanding the range of tasks under consideration.  It is noted that the development of modern technologies entails an increase in the complexity of control objects, an increase in the quality requirements and the accuracy of control due to the increase in the cost of control error.  This makes to be essential further development and improvement of methods that solve the problems of optimal control, for example, unmanned aerial vehicles.  As the model example, the application of the variational-gradient method to the models of automated control systems for unmanned aerial vehicles is considered.