Using a tensor model to handle uncertainty in complex dynamical systems

Abstract. The article is devoted to research related to the processing of uncertainty by means of tensor algebra in complex dynamical systems. The “smart electronic hitch” system is considered as an example of a complex dynamic system. The use of such a system is especially important when organizing traffic in difficult conditions. The solution of this problem occurs under conditions of uncertainty that may appear at different levels of the traffic management process. To identify and study in detail the properties of uncertainty, the author suggests using a tensor model. The tensor model makes it possible to identify additional properties of uncertainty, the study of which is not available when using traditional formalisms to represent uncertainty. Using the tensor model allows us to study the spatial model of uncertainty, real and imaginary values of uncertainty, as well as uncertainty invariants with respect to various transformations of the coordinate system. The article proposes a classification of uncertainty in a complex system. Using the example of the organization of interaction of “smart” controllers in an electronic coupling, the author shows the results of applying tensor analysis methods of networks to obtain a computational base of an electronic coupling. Tensor equations provide efficient processing of big data, obtaining information in real time, the stability of the dynamic system to changes in the topology of the connection of controllers and changes in the soft and hard components of the connection. The results obtained in the article show that the tensor uncertainty model can be successfully implemented in a dynamic system of any complexity level.