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Development of approach to the solving of problems of control motion for the technical systems modeled by differential inclusions

Keywords:

O.V. Druzhinina - Dr.Sc. (Phys.-Math.), Professor, General Research Scientist, Federal Research Center "Informatics and Management" RAS E-mail: ovdruzh@mail.ru O.N. Masina - Dr.Sc. (Phys.-Math.), Head of Department of Mathematical Modeling and Computer Technologies, Yelets state university n.a. I. A. Bunin E-mail: olga121@inbox.ru A.A. Petrov - Post-graduate Student, Yelets State University n.a. I. A. Bunin E-mail: xeal91@yandex.ru


The technical systems modeled by differential inclusions are considered. The approaches to optimal control search of the motion of specified systems are analyzed. The first approach is connected with construction of the dynamical model in two-dimensional space taking into account the multivalence and criteria of an optimality. The second approach is the development of the first approach and second approach is based on the construction of model in three-dimensional space taking into account the multivalence and variability. The third approach is the generalization of the first and second approaches in case when air resistance is taken into account. The generalized dynamic model is offered based on the third approach, stability analysis is carried out and the algorithm with using of artificial neural networks is developed that allows to find optimal parameters of the motion in case when the analytical research of model is difficult. The results of the work can find application in the problems of construction and research of the mathematical models of the motion for technical systems, in particular, in the control problems of aircrafts motion.
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