The paper considers the problem of analytical design of optimal controllers (ADOC) in the Letov-Kalman formulation for stable single-channel high-order objects whose motion is described by a system of differential equations with continuous nonlinearities from the phase coordinates of the object with a linear entry of the control signal. The studied class of control objects is relatively wide for applications, for example, it includes most electromechanical devices. The proposed method for synthesizing optimal controllers for objects of the specified class is based on the use of a known optimal control algorithm for a first-order nonlinear object. For this purpose, the initial description of a high-order object is transformed to a conditionally equivalent model of a first-order object using the so-called aggregated variable (macrovariable) of the object (the terminology of A. A. Kolesnikov is used), which is a certain function of the state vector of the original object. For the adequacy of the object models, this function must satisfy the corresponding linear partial differential equation, the solution of which can be found by known methods. The admissible set of such functions determines a whole set of simply calculated, analytical control algorithms for the original object. Methods for determining the macrovariable are proposed, ensuring the stability of the closed control system and its optimality according to the corresponding quality functional. For linear subobjects of the class under consideration, it is established that the solution of the partial differential equation describing the conditional adequacy of object models is equivalent to solving the well-known problem of determining the eigenvalues and eigenvectors of the transposed matrix of the object model with its state vector. The conditionally adequate first-order model obtained by these standard matrix calculations ensures the optimality of a high-order control system according to the corresponding quadratic quality functional.

The paper solves the problem of constructing and estimating the limit reachable sets and null-controllable sets for linear discrete-time systems with geometric constraints on control. Where the reachable set consists of those terminal states to which the system can be transferred from the origin in any finite number of steps, and the null-controllable set consists of those initial states from which the system can be transferred to the origin in any finite number of steps. For the class of periodic systems, it is possible to construct these sets explicitly. If the considered linear system is almost periodic, i.e. its matrix has only complex non-multiple eigenvalues, it is possible to obtain external estimates of the limit reachable and null-controllable sets of an arbitrary order of accuracy in the sense of Hausdorff distance. A feature of these estimates is that the rate of their convergence does not depend on the spectral radius of the system matrix, but is determined only by the accuracy of approximation of the almost periodic equations of dynamics by some periodic ones. The efficiency of the developed theoretical methods is demonstrated by the example of a damping system of a high-rise structure located in a seismic activity zone. A sequence of material points connected by elastic and damping links is considered as a physical model. The control is assumed to be piecewise constant and limited in power, which allows discretization of the initially continuous-time system. An external estimate of the limit reachable set is constructed for the discrete-time system obtained in this way. The calculation results are presented numerically and graphically.

   This study addresses the automation of predicting emergency situations in control systems through artificial-intelligence methods. As a case example, well-operation control is examined: the prediction of emergencies is carried out by processing large volumes of data comprising sensor readings from the hoisting-unit telemetry system and routine event logs from the well. To handle these data sets, a recurrent neural network is proposed. A mathematical model is constructed, on the basis of which a structural model of the prototype prediction program integrating data and knowledge is developed.
   A conceptual architectural scheme of the neural-network-based program for automating emergency prediction in control systems is presented, together with an information model and a description of the program’s operating principles. The program is implemented in Python using the Pandas and PyTorch libraries. The paper reports the resulting performance metrics, which also enable related tasks such as linking emergency situations to specific crews and repair types. Neuralnetwork varieties suited to particular subtasks are discussed: recurrent neural networks (RNN), convolutional neural networks (CNN), and long short-term memory networks (LSTM). Developing a neural-network program for automated emergency prediction represents an important tool for improving safety, reducing risks, and optimizing production processes in the oiland gas industry.

   The article considers a solution to one of the complex problems associated with the organization of collective behavior of autonomous intelligent robots, when in order to perform a complex subtask on a given section of the problem environment, obtained by dividing the general task into autonomous subtasks, it is necessary to involve several robots for joint purposeful activity. Various in capabilities, purpose and structure elements of knowledge representation of intelligent robots have been developed, regardless of a specific subject area, providing the ability to organize the search for solutions to subtasks of varying complexity under uncertainty. In particular, planning the joint purposeful activity of several robots based on frame micro programs of behavior that determine the solution of elementary typical subtasks allows to significantly reducing the search space by defining a number of effective actions for various intelligent agents at each step of the search for a solution to complex subtasks. In turn, planning of joint purposeful activity of intelligent robots based on frames of relations and actions, as well as micro programs of behavior associated with the transfer of certain objects from the current to a given state when it is necessary to eliminate individual differences between the initial and target situation of the problem environment, ensures flexibility in finding solutions to subtasks of varying complexity. This is achieved due to the fact that the proposed decision-making tools allow groups of robots, differing in number, to effectively plan joint purposeful activity associated with solving the subtasks assigned to them by rationally combining elements of the knowledge representation model with different purposes. The main operations performed in the process of decision-making are the operations of determining fuzzy nested equality and fuzzy equality between different semantic networks.
   In general, the developed model of knowledge representation and processing allows creating problem solvers that allow organizing joint purposeful activity of intelligent robots in the process of solving problems and subtasks of varying complexity in a priori undescribed problem environments.

Nowadays, additive manufacturing or 3D printing technologies are very popular. The kinematic scheme of a 3D printer determines how the movement of motors will affect the movement of the working carriage relative to the product. This paper presents an analysis of different kinematic schemes of 3D printers. A comparative analysis of kinematic schemes was carried out, the results of the analysis of various sources are integrated, the conclusions obtained in the course of the work are substantiated. Abstraction and harmonization of descriptions and visual representations of kinematic schemes from classical solutions to new ones that remain within the prototype were made. On the basis of the obtained results a generalization has been carried out, allowing to draw conclusions about the tendencies of development of the scientific direction. Recommendations for the development of a generalized mathematical model of the mechanism of movement of the working tool are given. The practical significance of the work consists in improving the characteristics of devices and printing quality, as well as reducing production costs due to the optimization of design processes; in addition, the description of the mathematical model will accelerate the creation of digital twins, and the adaptation of devices to new technologies; also the results of the study can find application for training and development of personnel.