|
|
 Âûïóñê 100
- Bitter I. L1 stability of transition densities of perturbed degenerate diffusions
In this paper, we derive a stability result for L1 perturbations of degenerate diffusions under weak regularity conditions on the coefficients. In particular, the drift terms we consider can be unbounded with at most linear growth, and the estimates reflect the transport of the initial condition by the unbounded drift through the corresponding flow. Our approach is based on the study of the distance in L1-L1 metric between the transition densities of a given diffusion and the perturbed one using the McKean -- Singer parametrix expansion.
- Agasandyan G. Collections of multidimensional option markets and optimization on CC-VaR
The work continues studying application of the continuous VaR-criterion (CC-VaR) in a collection of financial markets. This time the theoretical generality of the approach supposed before is tested on some more complicated collection of three multidimensional theoretical option markets, one of which is two-dimensional and two are two-dimensional. However, now some qualitative new in principle technical problems must to be solved. The randomization of basis structure for model feasibility is necessary as well, but is conducted for two-dimensional markets. At forming initial data with full analytical description, the econometric approach added by heuristic constructions is used. Here the more convenient for CC-VaR problem CB with the unknown initial investment amount and risk preferences functions not depended on scale parameter is solved. The regular combined portfolio that achieves the minimum of the general cost with fulfilling the CC-VaR need to be found. For purposes of methods illustration for marginal random values describing forecast and cost data of the problem, beta-distributions are used. In addition, an idealistic version of the optimal portfolio combined of instruments from markets of different dimensions is formed. It allows plotting two-dimension integrated surface income diagrams that overlap two-dimension parts of the optimal portfolio and arbitrary two-dimension sections of its three-dimension part.
- Nguyen Kh.T., Vlasov S. Adaptive disturbance compensation for mimo system with control delay
The paper considers the problem of compensation of multisinusoidal disturbances for linear MIMO system with delay in control. The problem of compensation of external disturbances for linear multichannel objects with delay at the input is important and relevant. A solution to this problem is proposed in problems of control of dynamic objects and in a number of others. The proposed method is based on the principle of indirect adaptation, where it is necessary to identify the perturbation parameters. At the first stage, a scheme for extracting a perturbation is described, which is represented as a sinusoidal signal with an unknown frequency, amplitude, and phase. At the second stage, the problem of identifying the frequencies of sinusoidal and multisinusoidal signals is solved. At the last stage, an object stabilization algorithm was developed, implemented using feedback. This paper presents a new scheme for compensating external disturbances for linear multichannel plants with input delay. A new algorithm for identifying the frequencies of a multisinusoidal signal is proposed. The analysis of the possibilities of the proposed estimation method using computer simulation in the MATLAB Simulink environment is carried out. The developed method can be effectively applied to a wide class of applied tasks related to the control of robots, manipulators for various purposes.
- Zhukov P., Fomin A., Glushchenko A. Implicit adaptation of mesh model of transient heat conduction problem
Considering high-temperature heating, the equations of transient heat conduction model require an adaptation, i.e. the dependence of thermophysical parameters of the model on the temperature is to be identified for each specific material to be heated. This problem is most often solved by approximation of the tabular data on the measurements of the required parameters, which can be found in the literature, by means of regression equations. But, for example, considering the steel heating process, this approach is difficult to be implemented due to the lack of tabular discrete measurements for many grades of steel, such as alloyed ones. In this paper, the new approach is proposed, which is based on a solution of a related variational problem. Its main idea is to substitute the adaptation process in the classical sense (i.e., to find the dependencies of thermophysical parameters on temperature) with ”supervised learning” of a mesh model on the basis of the technological data received from the plant. The equations to adjust the parameters of the transient heat conduction model, which are related to the thermophysical coefficients, have been derived. A numerical experiment is conducted for steel of a particular group of grades, for which enough both technological as well as tabular data are available. As a result, the ”trained” mesh model, which has not received explicitly any information about the physical and chemical properties of the heated substance, demonstrated an average error of 18.82 oC, which is quite close to the average error of the model adapted classically on the basis of the tabular data (18.1 oC).
- Mukhin A. Interception of matrix inequalities solution sets in problems synthesis of static feedback controllers
The article considers some possible descriptions of Lyapunov matrix inequalities solutions sets in the problems of synthesis of static state and static output feedback controllers for linear continuous stationary controlled systems. For each inequality with a given matrix of the system, in general, there is its own set of solutions, which is a set of positive definite matrices of the Lyapunov function. The conditions for the solvability of Lyapunov inequalities in different bases are shown, depending on the selected non-degenerate transformation matrices. If we perform a similarity transformation for the matrix of the system, then for the solvability of the Lyapunov inequality, it is sufficient that in the corresponding basis the matrix of the Lyapunov function is congruent to the matrix of the same name in the original basis. It is shown that in some cases, the matrix inequalities solutions sets for a static state and static output feedback controllers may coincide, which allows us to reduce the static output feedback controller synthesis task to the static state feedback controller synthesis task. The conditions for the implementation of such cases imply a certain structure of the input and output matrices, as well as the presence of one stable diagonal block of nonzero dimension in the original matrix of the linear system.
- Kutyakov E. Developing and analysis of a quadratic approximation of a nonlinear two-area power system model in the state space
We present the results of mathematical modeling of a two-area four-generator electric power system (EPS) in the state space, with accounting the second order terms. Software for construction of quadratic approximations of the EPS was developed. The model is based on a 6-th order nonlinear synchronous generator model that integrates the electromechanical equations of the rotor motion, the excitation winding electromotive force (EMF) dynamics, and the dynamics of the three damping windings. Automatic voltage regulators and system stabilizers are not considered. For construction of the quadratic approximation, the Carleman linearization method is used, which is widely used for representation of nonlinear dynamic systems models in bilinear form. A detailed analysis of the dynamics matrix spectrum of the obtained quadratic approximation is presented. The results of numerical experiments are presented to demonstrate that in comparison with the traditionally used linearized model the developed quadratic approximation gives qualitatively new information about the transient processes of the initial EPS model, arising both at the deviation of some state variables and at the disturbance through system inputs. The resulting model can be used for analytical studies of the nonlinear behavior of the EPS near its operating point, in particular, for the analysis of interarea oscillations and parametric resonances. It should be noted that the method for constructing a quadratic approximation (Carleman linearization) applied in this work can be extended to EPS of larger sizes, and the developed software allows upgrading for taking into account terms of the third and higher orders of smallness.
- Roslyakova N., Trenev N. Differentiation of inequality dynamics in different types of regions
The aggravation of crisis phenomena around the world raises issues of social inequality extremely acutely. As the main theoretical construction, the authors used the hypothesis of S. Kuznets that inequality changes over time and is consistent with the processes of economic growth. To date, the literature has received many confirmations of the Kuznets hypothesis and justifications for other types of connection between economic growth and inequality. In this work, five model regions of Russia (Ulyanovsk Region; St. Petersburg; Karachay-Cherkess Republic; Magadan Region; Voronezh Region) acted as objects of research. Based on data from 1998-2020, using regression modeling, the classical specification of the Kuznets curve was evaluated. The hypothesis was not confirmed for St. Petersburg, the Karachay-Cherkess Republic and the Magadan region. There is a reverse situation, when a certain level of the economy is reached, the growth of inequality accelerates. At the same time, real data indicate that only St. Petersburg is in a state of economic growth with a decrease in inequality. For the Ulyanovsk and Voronezh regions, the Kuznets hypothesis was confirmed. The results obtained confirm the initial hypothesis about a high level of differentiation of regions both in terms of inequality parameters and in terms of the main mechanisms of interaction between economic growth and inequality.
- Storozhev S. Adaptation of a fuzzy group controller to changing operating conditions
An aircraft gas turbine engine (GTE) of aircraft from the point of view of control theory is a complex nonlinear object, the frame mathematical description of which is known a priori. During the operation of a gas turbine engine, continuous monitoring of parameters is required (gas temperature behind the combustion chamber, the rotor speed of the low-pressure compressor (free turbine), the rotor speed of the high-pressure turbocharger (gas generator). Further development of the control of the gas turbine engine can be associated with the use of fuzzy control. The aim of the study is to improve The adaptive fuzzy group controller allows taking into account the values of several circuits by the weighted average method when forming the control action on the fuel dispenser into the combustion chamber of the gas turbine engine. changing operating conditions. The developed adaptive fuzzy group controller allows you to replace the standard selector and ensure adaptability to changing operating conditions of the gas turbine engine. The new controller is characterized by the best values for assessing the probability of failure-free operation of the electronic engine controller. The results of the research can be used to control the fuel dispenser into the combustion chamber of the gas turbine engine. The resulting adaptive fuzzy group controller will significantly reduce the uncertainty in the operation of the combustion chamber, providing a guaranteed thrust of the aircraft.
- Krygin A., Kupriyanov B. Identification of critical nodes of the transport network
The paper considers the problem of finding critical objects of the transport network. A mathematical model of the transport network is constructed, taking into account the cost of trips and the need for movement between network nodes. The method of determining all parameters of the mathematical model is described and its correctness is justified. The optimization problem is formulated, which is reduced to a linear programming problem.
- Shulpin S. Agent control in a dynamic environment based on fuzzy inference system
The paper considers the task of control a mobile agent in a dynamic unknown environment. To solve this problem, it is proposed to use a neuro-fuzzy controller. To adjust the parameters of the controller, a genetic algorithm is used. The paper also proposes a modification of the genetic algorithm that allows to configure not only the parameters of the membership functions of linguistic variables, but also their type. This allows to fine-tune the controller and, as a result, improve the quality of the system. The effectiveness of the proposed approach was confirmed by computer simulation in the developed virtual environment. The resulting controller was used in a physical experiment with a mobile agent implemented on the basis of Arduino Uno, in an environment with dynamic and static obstacles.
- Aleksanin A., Scherbatyuk A. On monitoring of marine fishing areas using satellite data and information from marine robotic systems
Satellite data provide a significant amount of information for assessing fishing areas, and modern autonomous uninhabited surface and underwater vehicles make it possible to conduct commercial reconnaissance, collecting information about both bottom aquatic organisms and the presence of schools of pelagic fish. Their use increases the efficiency of the search for fishing aggregations by estimating the volume of aggregations and the size of fish. The use of such systems in commercial fishing will significantly reduce the load on fishing vessels by obtaining knowledge about fishery objects from the above systems, as well as reduce the impact on the environment by reducing fuel consumption during their search. The article deals with the problem of providing short-term fishing forecasts. There are two tasks of organizing an effective fishery: the assessment of promising areas and the search for fish concentrations. To solve them, the use of a combination of satellite remote sensing and autonomous robotic systems is considered.
- Zverkina G., Koshelev A. On the search for the optimal step in the simulation of random variables using intensity
It is not always possible to determine the characteristics of the system under study by theoretical methods in queuing theory and related areas. Therefore, it is important to be able to model the behavior of such complex systems with the help of computers. To do this, one must be able to model random variables corresponding to periods of work / repair / waiting, etc. In complex technical systems, these periods essentially depend on the behavior of the system components, while their distributions can change already during the operation of such periods. Such behavior of the system can be described using variable intensities of distributions (hazard functions), and modeling of such random variables is impossible by classical methods. Previously, the authors considered a new approach to modeling random variables with a variable intensity unknown in advance. The quality of such modeling is analyzed and the issue of optimizing the modeling procedure is solved in the presented work -- so far for the case when the intensity of the simulated distribution does not turn to zero.
|
|
