The paper investigates stochastic polling systems using machine learning. M/M/1 and MAP/M/1-type polling systems with cyclic polling, as well as M/M/1-type polling systems with adaptive cyclic polling are considered. To train a machine model of a M/M/1-type polling system, we used the results of analytical calculations, and for other considered systems that do not allow exact analysis, we used the simulation results. Numerical examples are given, and it is shown that the results of machine learning are close enough to the results of analytical or simulation calculations.

The problems of artificial intelligence, control and decision-making with incomplete or unreliable information include a wide class of problems of abductive explanation of the observed, including cause–effect problems. The study is devoted to the substantiation of the method of logical formation of hypotheses explaining the observed. Means of knowledge representation and derivation of hypotheses are proposed. A language possessing the property of substitutability is introduced. The properties of language and the calculi introduced in it provide hypothesizing by combining deduction and abduction. In contrast to the well-known logical methods of abduction, the proposed techniques make it possible to derive hypotheses (minorants) that are necessary and sufficient for a formal explanation of the observed. Based on minorants in combination with the basic theory of the subject area, reliable causes of the observed or relevant circumstances leading to these causes are formed. In this case, in situations with the availability of empirical data, these causes and circumstances can also be formed in plausible versions. Examples from technology and medicine are considered.

The article is devoted to the development of information support mechanisms for the digital transformation of space industry enterprises. To ensure the operation of spacecraft in the conditions of uncertainty of external influences, the article proposes a model-oriented approach to the design and support of the development of space industry enterprises as socio-cyber-physical systems. The purpose of the socio-cyber-physical model is to build digital twins and models of enterprise products on a common methodological basis for the development and debugging of large-scale functional systems that obey heuristic norms and patterns of sustainable and safe existence, reflexive behavior in regular and non-standard situations. With the current requirements for increasing the operating time of the spacecraft in orbit, it is necessary to predict the behavior of the onboard equipment for a period longer than the standard one. The article shows that for a time interval less than the planned active lifetime, the reliability characteristic is underestimated. With the transition over the planned period, traditional methods give a significant overestimation of the reliability function. In order to improve the mechanisms for creating spacecraft, the onboard equipment we considered as a large system, which has characterizes by the interaction functions of its elements. This approach allows us to evaluate the functional reliability of on-board equipment. In this regard, for informational support, the article focuses on big data and its use for modeling multicomponent systems connected to the environment of new technologies. Based on the study of the dynamics of the technical condition of functional blocks, this technology supposes to find reserves.

We consider integrability structures of the generalized Hunter--Saxton equation. In particular, we obtain the Lax кepresentation with nonremovable spectral parameter, find local recursion operators for symmetries and cosymmetries, generate an infinite-dimensional Lie algebra of higher symmetries, and prove existence of infinite number of cosymmetries of higher order. Further, we give an example of employing the higher order symmetry to constructing exact globally defined solutions for the generalized Hunter--Saxton equation.

The problem of stabilizing a robot-wheel at a target point on a straight line subject to control and phase constraints is considered. The phase and control constraints are met by applying an advanced feedback law in the form of nested saturation functions. The selection of the feedback coefficients is discussed that optimizes the performance of the controller. An optimal controller is defined to be that that ensures the greatest convergence rate near the target point, while preserving a node-like phase portrait of the nonlinear system. The paper continues the work reported at the Optima 2020 conference [1], where an estimate of the greatest rate was obtained. The goal of this paper is to improve the results obtained in that work by considering a curvilinear asymptote and to get the exact value of the greatest rate.