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 variationalgradient 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.

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The features of application of the method of inverse problems of dynamics for the recovery control are considered. An expression for the controlling force is obtained as well as simulation for the stage of determining the controlling forces are carried out.

The paper represents the analysis of the main issues of system level self-diagnosis and explanation of its three basic problems. The main attention is paid to the problem of diagnosis which is expressed with the help of set theory. The influence of made assumptions concerning the allowable faulty sets on the diagnosis results is discussed with the help of simple example.

The article is devoted to the analysis of the possibility of applying the method of inverse problems of dynamics for the synthesis of a system of spatial stabilization of the motion of a dynamic object on an operatively programmable trajectory. The article proposes to apply the method of inverse problems of dynamics for the synthesis of a system for stabilizing the motion of a dynamic object on an operatively programmable trajectory. It is concluded that the procedure for applying the method of inverse problems of dynamics provides for the sequential execution of two procedures. The first procedure involves setting the desired trajectory of movement of a dynamic object and determining the vector of necessary control forces for the implementation of this trajectory of movement. The second procedure involves determining the control function (control deviations) to create such forces. In the development of the concepts of the algorithmic approach (inverse problems of dynamics), an analytical expression for the governing force is obtained. The proposed block diagram of the control algorithm can be used to synthesize control systems for complex dynamic objects, for example, remotely piloted aircraft. P (t) is n-dimensional vector of perturbations; X 0 is initial state; T = t T − t 0 is time of movement of the object.There are restrictions on the management and state of the object X(t) ∈ Q X ; U (t) ∈ Q U .