Advanced Laser-Photoionization Scheme of Separation of Heavy Isotopes in the Gases Separator Devices

An effective approach to determining the parameters of the optimal schemes of the method of laser selective photoionization of atoms (elements and isotopes) with finite ionization due to collisions, ionization by a pulsed electric field, ionization through high (Rydberg) states and narrow autoionization resonances for the separation of heavy isotopes has been proposed. in gas separator devices. On the basis of the theory of optimal control and previously developed quantum models for calculating the characteristics of elementary atomic processes, optimization models of isotope separation are numerically implemented in the scheme of selective laser photoionization with ionization due to collisions in gas mixtures, ionization by a pulsed electric field, autoionization, etc. etc. The data obtained quantitatively confirm the promise of the method of laser photoionization with finite ionization due to collisions, ionization by a pulsed electric field, ionization through high-lying (Rydberg) states and narrow autoionization resonances and give a set of parameters for the desired optimal schemes, in particular, the laser pulse optimal shape for rubidium and uranium isotopes.

The Interconnection and Damping Assignment Passivity-Based Control Synthesis via the Optimal Control Method for Electric Vehicle Subsystems

The interconnection between optimal control theory and the theory of energy-shaping control is described in our paper. For linear and nonlinear systems, the application of the theory of optimal control for the synthesis of parameters of energy-shaping control matrices is demonstrated in detail. The use of a Riccati equation allows us to form an optimality criterion and to synthesize the energy-shaping control system that provides the desired transient processes. The proposed approach was applied to the synthesis of control influences for electric vehicle subsystems, such as a two-mass system and a permanent magnets synchronous motor. The results of computer simulation studies, as well as those conducted on real experimental installations, are given in this paper.

FORMATION AND USE OF FINANCIAL POTENTIAL OF INVESTMENT ACTIVITY OF SMALL ENTERPRISES

The purpose of the paper is to study the processes of formation and use of financial potential of investment activity of small enterprises. The subject of research is the patterns of formation of financial potential of investment activity of small enterprises. Methodology included structural and systems analysis, as well as the theory of optimal control. In addition, methods of economic and statistical analysis were used. The main results of the study include the definition of the essence and selection of types of the financial potential of investment activity of enterprises. It is found that the financial potential of investment activity of the enterprise is its ability to attract financial resources to ensure this activity. The available, aggregate, and long-term financial potentials of investment activity are defined and characterized. The possibility of distinguishing the general, effective and optimal varieties of this potential are also noted. It is shown that the aggregate financial potential of investment activity of the enterprise, in addition to the available potential, also includes the available reserve for the growth of the financial potential of investment activity due to the implementation of measures that do not require investment. It is proven that the financial potential of investment activity of small enterprises is at the intersection of two other types of their economic opportunities: investment potential and the potential of the flow of the financial resources to finance investment activity of enterprises. The generalized model of the course of processes of formation and use of the financial potential of investment activity of small enterprises is constructed and analyzed. A number of indicators for assessing the level of use of the financial potential of investment activity of small enterprises are proposed. In particular, these indicators include the share of the actual volume of realization of the available financial potential of investment activity of enterprises in the amount of the potential, the share of the available financial potential of investment activity of enterprises in the value of their investment potential, the share of the actual volume of realization of the available financial potential of investment activity of enterprises in the value of their investment potential. The third indicator is the product of the previous two. The level of investment activity and use of the available financial potential of investment activity of fifty Ukrainian small enterprises is studied. It is established that the largest share includes enterprises with a low and satisfactory level of investment activity. At the same time, the average level of realization of the available financial potential of investment activity of enterprises increases with the growth of investment activity. The practical significance of the results in the work of small enterprises will allow to identify and implement untapped opportunities for growth in the financial potential of investment activity of these enterprises. Also, these results make it possible to establish the level of actual realization of this potential and identify areas for increasing this level, which is especially relevant in the context of the COVID-19 pandemic.

THE MAIN HAMILTON FUNCTION AND THE NECESSARY CONDITIONS FOR THE EXISTENCE OF A SITUATION IN THE FORM OF THE HAMILTON-JACOBI EQUATIONS

Interdisciplinary application of learning outcomes is essential to the field of mathematics, attainable at intersection of math with other subjects – which includes applied tasks When studying a number of technical disciplines, as well as solving applied problems, it is possible to use certain aspects of the theory of optimal control - which is an example of interdisciplinary link. Analytical mechanics, among other disciplines, enables leverage of certain aspects of the theory of differential games, namely, equilibrium conditions in non-coalitional differential games of several players. This article provides studies of the necessary and sufficient conditions for the existence of equilibrium situations, using some concepts of analytical mechanics. In line with Hamilton’s definition, necessary conditions were obtained in the form of Hamilton-Jacobi equations. This form of necessary conditions in differential games of N persons is of interest to students of natural and technical fields. The main goal of the article is to demonstrate interdisciplinary link, an important component of the process of training future engineers for various sectors of the economy. It is necessary for the holistic understanding of the material, so that students of technical specialties of various fields can use it. Proposed work can aid in study of this area of analytical mechanics by university students and young scientists alike.

Control of an Asynchronous Electric Drive Based on Forecasting Its State

Variants of constructing control systems with a lagging argument for the positioning problem of an asyn-chronous electric motor (IM) and the problem of energy-saving AM control are considered. Variants of control of an asynchronous electric drive with IM on the basis of predicting its state are considered. The analytical de-sign of the predictor (ADP) is an asynchronous motor control algorithm based on the mathematical theory of optimal control (L.S. Pontryagin's maximum principle). The control algorithm (ADP) ensures the achievement of the minimum value of the target functional, which (functional), in contrast to the structure of the classical pre-dictive control system (Model Predictive Control - MPC), is clearly not part of the ADP. Calculations of the movements of an electric drive with an IM in the control modes of its state, taking into account delays along the channels for assessing its state and control, as well as using predictors, are given. The effectiveness of the in-troduction of predictors to improve the stability and quality of control of an electric drive with an IM has been established.

Aviation radio control systems as complex technical systems. Part 1. Analysis of the possibilities of multicriteria optimization

The need to take into account the increasing requirements for expanding the field of application conditions, taking into account an increasingly wide range of possible conditions, increasing requirements for the volume and reliability of the information used, combined with increasing requirements for improving the efficiency of operation, predetermined the emergence of a new type of information management systems, called "complex technical systems" (CTS). In general, the CTS is understood as a set of functionally related control and information subsystems united by a common goal of joint solution of a group of tasks. The most striking example of CTS is aviation radio control (RC) systems, which are able to solve the general task of destroying targets in several stages, using various methods of route control and guidance on them in conditions of high initial uncertainty due to a variety of possible objects of influence of varying degrees of importance and the random nature of their spatial location. At the same time, the task of destroying objects of the opposing side is solved, as a rule, in several stages, including long-range (command), short-range guidance (homing) and the use of weapons. It should be emphasized that the choice of indicators of excellence that reflect various aspects of the functioning of the CTS (aircraft RC systems) is by no means a trivial task. Within the framework of the "system – environment" approach, which takes into account the specific conditions of the use of the CTS, in addition to performance indicators that reflect the degree of compliance of the system with its purpose, such indicators as functional stability (survivability), dynamism and informativeness are increasingly in demand, which, as a rule, contradict each other. It should be noted that due to the heterogeneity of the tasks being solved and the inconsistency of the requirements, it is necessary to take into account the need to use a multicriteria approach to the synthesis of control methods and information support algorithms. However, the methods of multicriteria optimization used in practice have a number of significant drawbacks that make it difficult to use them in the development of promising CTS (RC systems). At the same time, it is very tempting to use the mathematical apparatus of the statistical theory of optimal control (STOC) for multicriteria optimization of the CTS, which allows to avoid the above disadvantages to some extent. The expediency of using STOC for solving multicriteria problems is due to the fact that the very formulation of the STOC problem and the resulting optimization procedures already contain a solution to the two-criterion problem of obtaining a system that is jointly the best in both accuracy and costeffectiveness of management. The analysis of various approaches to solving multicriteria problems has shown that the most rational is to reduce them to a singlecriteria problem with further use as a basic variant of local STOC optimization.

Aviation radio control systems as complex technical systems. Part 2. Multicriteria optimization based on a local modification of the statistical theory of optimal control

The analysis of the known modifications of the statistical theory of optimal control (STOC) in the application to the problem of multicriteria optimization of radio control (RC) systems showed that for its solution, a variant that takes into account the measured perturbations in the state model can be used as a basis. The physical meaning of this approach is that of all the alternatives, one is chosen, conditionally the main one, for which a state model is formed. The remaining participants in the general synthesis procedure are considered as a set of perturbations acting on this model. Accordingly, in the quality functional used, the terms that ensure the minimization of these perturbations should be taken into account in the form of an additional linear combination of quadratic forms. Management that minimizes such functionality, to one degree or another, will be jointly the best for the entire set of requirements. The choice of the local optimization option is based on the desire to avoid the need to solve a very computationally expensive twopoint boundary value problem, which is characteristic of the optimization procedures of systems for the entire time of operation, and to ensure invariance to the time of operation. The analysis of the obtained control law allows us to formulate the following conclusions. The control contains two terms, one of which implements the main purpose of the system, providing an approximation of the real state to the required one, and the second takes into account the influence of alternative requirements. The optimized system should include optimal filters that form estimates of the necessary state coordinates, and a controller that forms a control signal. The obtained result indicates that it is possible to optimize management within the framework of solving a multicriteria task (MCT) without solving a complex two-point boundary value problem. If necessary, you can choose another version of the main model with a different set of auxiliary tasks and the corresponding functionality as the main task, with a different control option. In the process of comparing the obtained control options, you can choose the best solution to the general optimization problem. Considered as an example, the law of controlling a group of three initially geographically separated and moving in different directions unmanned aerial vehicles used for radar monitoring of large areas of the earth (water) surface, which at the same time should provide the collection of the group, the required trajectory of its flight and the required topology of participants implementing a given control band, confirmed the possibility of solving the MCT based on STOC.

Method of controlling the parameters of the pulse-Doppler onboard radar station while ensuring the energy stealth of its operation on radiation

In the article, based on the mathematical apparatus of the statistical theory of optimal control in the state space, the synthesis of a method for controlling the parameters of the pulse-Doppler onboard radar system (BRLS) of a fighter aircraft is presented, in the interests of ensuring the energy stealth of its operation on radiation with a given probability, when detecting an air target-the carrier of a radio intelligence station, the optimal minimum local quality functional. The efficiency of the synthesized method is also evaluated on the basis of modeling. As part of the synthesis, the quality functional was determined and control signals were obtained for the parameters of the radar operation, which make it possible to ensure the energy stealth of the fighter's radar operation with a given probability in the process of approaching the radar carriers and the radio intelligence station (RTR). The indicators of the control signal efficiency determine the probability of correct detection of the radar of the air target carrier of the RTR station and the probability of non-detection by the RTR station of the sounding radar signal in the process of their approach. Based on the simulation, the effectiveness of the control signals is evaluated, which shows that in the process of approaching the fighter and the RTR carrier station, the energy stealth of the radar operation is provided with a given probability by controlling the parameters of the radar operation.

The Guidance Algorithm of Air-to-Air Guided Missile with an Active Radar Target-Seeking Head to a Helicopter with Various Modes of its Flight

On the basis of the mathematical apparatus of the statistical theory of optimal control, the method and algorithm of guidance of an air-to-air guided missile with an active radar target-seeking head when aiming at a «helicopter» class air target with various modes of its flight, including when hovering have been developed. The synthesis has been carried out as a result of flight experimental studies of radar signals reflected from a real helicopter. Also, recommendations for ensuring continuous tracking of a helicopter in an active radar target-seeking head have been presented

MATHEMATICAL MODELLING OF IMMUNE PROCESSES AND ITS APPLICATION

The aim of the study was to develop a mathematical model to research hypoxic states in case of simulation of an organism infectious lesions. The model is based on the methods of mathematical modeling and the theory of optimal control of moving objects. The processes of organism damage are simulated with the mathematical model of immune response developed by G.I. Marchuk and the members of his scientific school, adapted to current conditions. This model is based on Burnet’s clone selection theory of the determining role of antigen. Simulation results using the model are presented. The dependencies of infectious courses on the volumetric velocity of systemic blood flow is analyzed on the complex mathematical model of immune response, respiratory and blood circulation systems. The immune system is shown to be rather sensitive to the changes in blood flow via capillaries. Thus, the organ blood flows can be used as parameters for the model by which the respiratory, immune response, and blood circulation systems interact and interplay.