The problem of synthesizing an observer of a vector of state variables for a class of linear nonstationary systems with an arbitrary relative degree r under conditions of external multi-harmonic disturbances is considered. The input signal is assumed to be unknown. At the first stage of solving the problem, an observer of the vector of state variables is synthesized from the measurements of the output variable. To implement it, it is necessary to measure the r-th derivative of the output signal. To overcome this limitation, an auxiliary observer is introduced, which provides an estimate of the initial observation error using the method of dynamic expansion of the regressor with a finite convergence time. Based on the obtained estimate, the reconstruction of the signals required to construct an output observer in the form of an autoregressive model is carried out. The proposed algorithm provides an estimate of the state vector of an object based on output in a finite time. A rigorous mathematical proof of the obtained solution is given. The results of computer simulation in the MatLab Simulink software environment are presented, demonstrating the effectiveness and efficiency of the proposed approach. The developed algorithm can be used in various technical systems to create virtual sensors and solve diagnostic problems.

The dynamics of a non-smooth mapping with a large number of switching manifolds, which describes the behavior of a unipolar pulse-width control system for the energy supply of a heating installation (furnace) for growing sapphire single crystals, is studied. Such a mapping is shown to demonstrate a special type of multistability, when several nested attractive closed invariant curves corresponding to stable two-frequency oscillations coexist in the phase space of the dynamic system. Results of the research are important for creating new methods of predicting, detecting, and suppressing irregular oscillations and catastrophic phenomena that arise when parameters vary and are exposed to interference, as well as for designing pulsed automatic control systems with specified dynamic properties and predictable dynamics.

The problem of parametric synthesis of control laws for continuous automatic control systems with distributed parameters is considered. As a mathematical apparatus for solving the problem, the method of separation of variables (Fourier) is used to implement the transition from partial differential equations to ordinary differential equations, in order to extend the generalized Galerkin method to a new class of systems with distributed parameters.

A solution to the problem of estimating the parameters of a dynamic model of the diving depth of an uninhabited underwater vehicle is presented. To solve the problem, a new identification law is proposed, based on the procedure of dynamic expansion and mixing of the regressor and an algorithm for averaging estimates of unknown parameters. The resulting model with identified parameters approximates the dynamics of the immersion depth of a real apparatus with sufficient accuracy and is suitable for further calculation of robust standard controllers based on it.

Based on the descriptive open set model, varieties of classification problems are formulated and implemented in the new version of the software system for selection and ranking „SVIR-M“. In this system, the list of object classification problems is expanded, where the problems, according to the principle of solution, are divided into two groups: according to the given conditions of belonging to classes and according to deviations from the class accepted as the norm. The first group consists of problems of choosing a class based on a logical expression and membership functions, and the second group consists of problems of choosing an action to deviate from the norm or comparing objects according to the degree of deviation from the norm. The selection of a class by membership function is carried out on the basis of both ordered classes on indicator scales (fuzzy choice) and unordered classes (entity recognition by many indicators). The lack of connection with the subject language and the generality of mathematical models makes it possible to solve the stated problems in various subject areas. Ease of operation in the „SVIR“ system is ensured by a context-sensitive interface for formulating tasks and automation of the creation of a domain model and evaluation functions of indicators based on source data specified in the Excel package.

A generalized analysis of an innovative group of diffraction interferometry methods and instruments is presented in comparison with traditional interferometers. New possibilities are considered for reducing the error and increasing the sensitivity of measurements, obtaining reliable results of metrologically high quality. Reliability is achieved through diffraction and a stable reference wavefront that is not sensitive to vibration, thermal and gravitational influences. The devices considered use a reference wavefront formed on an unpolished optical surface. The front is formed with negligible errors as a result of diffraction of a laser beam focused on a pinhole in a metal screen. The feasibility of developing diffraction interferometry methods based on new schematic solutions and modern element base using assessment of the image quality of optical systems with computer decoding of the interferogram and the mathematical apparatus of interferometric information processing is noted. The proposed approach can be applied in real optical production, medical practice, and scientific research.

The features of the functioning of an experimental setup based on application of two-frequency laser radiation using the method of two exposures of holographic interferometry are studied. The installation is intended to determine the amount of movement of an object along the OX axis in the plane of its installation. The holographic interferometry method ensures long-term storage of information on photo carriers, allows for maximum contrast of the interference pattern and high-quality reconstruction of wave fronts. The appearance, optical design and technical characteristics of the experimental setup are presented. Expressions are obtained to determine an object displacement magnitude and measurement

A fully functional prototype of the first domestic automated device ensuring the maintenance of safe pressure in the cuffs of endotracheal and tracheostomy tubes is presented. The operating algorithms of the device are described. To formulate the distinctive features of the prototype being developed and determine its functional composition, a comparative analysis of existing solutions is performed and patent research is carried out. The developed pneumatic circuit and control board make it possible to implement the operating modes necessary to provide medical care. Tests of the device carried out in laboratory conditions demonstrate the high reliability and energy efficiency of the prototype; the device is suitable for all mechanical ventilation devices and anesthesia-respiratory devices, and therefore, can be used in anesthesiology and intensive care departments in medical institutions.

The permeability of nanoporous glasses with the pore radius of 5–200 nm is studied. Such porous glasses are used as thin filters, optical materials with adjustable refractive index, solid adsorbents, selective membranes, and as the basis for composite materials in laser technology and optical instrument making. Models of the structure and methods for calculating the molecular permeability of such materials are proposed. Results of calculation using the proposed models are compared with experimental data.

A new algorithm for finite control of an unmanned aerial vehicle in roll and pitch is proposed. The control algorithm allows to save the output signal of the object under consideration within pre-known boundaries for a certain time interval regardless of incoming external perturbations. An analysis of the dynamic system is performed; the control goal is determined with the main requirement to the output signal of finding in a given set. Effectiveness of the proposed control algorithm is tested in simulations carried out in the MatLab environment using various restrictions and generated signals for external disturbances.