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 Âûïóñê 107
- Kotyukov A., Pavlova N. complex system, equilibrium, covering map, coincidence point, elastisity
The paper is dedicated to complex systems analysis, in particular, the question of searching a coincidence point for two mappings. A coincidence point is a point at which the image of one mapping coincides with the one of another mapping at this point. This notion is a generalization of fixed point concept. It can be applied to information processing, artificial intellect and system analysis. Besides, this concept may be applied in economical problems such as resourse management, production volume calculation and price regulation. In this paper coincidence points theory is applied to the question of equilibrium in market system. An equilibrium is a state at which the supply of all goods on the market equals to thier demand. We developed a search algorithm of coincidence point for covering and Lipschitz-continuous mappings. The work of this algorithm is demonstrated on open market model. In this model supply and demand mappings are restored by their price elasticities. Elasticity is a measure of change for one variable under the change of another. We consider partical equilibrium in this model. It is a state at which supply equals demand for some subset of goods, not all of them. Equilibrium is conisedered as a coincidence point of supply and demand mappings. We complement the results with the example of partial equilibrium in the model of two goods.
- Matyushenko S., Samouylov K. The Laplace – Stieltjes transformation of the distribution function of the peak age of information in a transmission group modeled by a two-node network
In this paper, we consider a two-node information transmission group consisting of a peripheral node (sender node), a control center (recipient node) and two serial communication channels between them. The process of transferring information from the sending node to the receiving node is modeled by means of a two-node queuing network with an arbitrary function for distributing intervals between requests and arbitrary service durations at each node of the network, i.e., a network that, according to Kendall's designations, is usually encoded as G/G/1 – G/G/1. In this case, the transmitted packets of information are modeled by requests, and the process of transmitting packets through the system channels is modeled by the maintenance procedure at the network nodes. The paper provides an expression for the Laplace – Stieltjes transformation of the stationary distribution function of the peak age of information – a metric that allows quantifying the "freshness" of information entering the receiving node in order to accept management decisions. This work continues the cycle of works by the authors devoted to the problem of analyzing the age of information, summarizing the results of the work of other authors, which is achieved through the most arbitrary assumptions about the distributions of the durations of generating and servicing applications in the network nodes. The correctness of the obtained results was verified on a number of special cases considered earlier, as well as by comparing the analytical results with the results of simulation modeling.
- Krasnov D., Antipov A. Implementation of combined control in the tracking system of a single-link manipulator with an uncertain input
As a control plant, we consider a single-link manipulator with a flexible joint that functions under parametric uncertainty and external uncontrollable disturbances. The dynamic of the current loop is not introduced. The armature current of the DC motor is considered as the control, which can be converted into torque applied to the gearbox shaft. We pose the problem of synthesizing dynamic feedback that provides specified changes in the angular position of the manipulator under the following atypical assumptions: 1) only the current deviation of the manipulator position from the reference signal (tracking error) is available for measurements; 2) the multiplier before the control (input matrix) is not known exactly. The first factor motivates the use the transformation to the block form of input-output with respect to the tracking error for solving the problem of observation and synthesis of dynamic feedback based on mixed variables (combinations of state variables, external influences and their derivatives). The main contributions include, firstly, a method for designing a mixed variable observer of minimum possible order with piecewise linear corrective actions. This observer recovers mixed variables from tracking error measurements. To simplify its tuning, both the principles of construction of the state observer and the differentiator of external signals are simultaneously used in one algorithm. The second main contribution is a method for the formation of combined control with compensation of matched disturbances under conditions of uncertain multiplier before control. The numerical simulation results are presented. They demonstrate the robustness of the closed-loop system and guaranteed stabilization of the tracking error with a given accuracy when external disturbances, reference actions, and uncertain parameters change within acceptable ranges.
- Zhukov P., Glushchenko A. Stability of numerical method of implicit adaptation of transient heat conduction model to rigid body thermophysical parameters
This study is devoted to the analysis of algorithmic stability and complexity of the model of transient heat conductivity with implicit adaptation to the thermophysical parameters of the heated solid body. The implicit adaptation method is based on the substitution of such parameters as heat capacity, thermal conductivity and density in the transient heat conduction equation by two dimensionless adjustable coefficients, uniformly discretized over the entire model lifetime, with their further adjustment using a modified stochastic gradient descent method. In order to ensure the stability of calculations of such a model using a computer, some conditions have been defined in previous studies, which allowed us to obtain stability equal to 64%. It was assumed that the remaining 36% was a consequence of violation of these conditions in the process of adjustment. In this paper we propose algorithmic constraints that allow us to solve this problem. The repetition of experiments shows that the application of the proposed approach allows one to increase the stability from 64% to 98%. Also, an analytical comparison of algorithmic complexity classes for models with implicit adaptation and with "group-explicit" adaptation is made. As a result, it is found that the proposed numerical method has a lower complexity in comparison with the finite-difference method with "group explicit" adaptation.
- Shiroky A. The influence of the structure of a complex system in risk management
Risk management problems are often addressed using game-theoretic models such as the "Defender – Attacker" and "Defender – Attacker – Defender". Players employ sets of acceptable distributions of limited resources as strategies. In the classical problem settings, the Defender is unable to reduce risk by changing the composition or structure of the system to be protected, as most real systems cannot be altered in such ways or cannot be altered at all. However, the question of the influence of the system structure on its overall risk is still relevant when designing one. Therefore, there is a need for methods to compare structures with each other. This article proposes a modification of the classical formulation of the problem of minimizing the integral risk of a complex system. This modification allows one to quantify the influence of the placement of system elements within a given structure on the value of risk. The study provides a solution to the problem for a simple chain, which is the simplest specific case, as well as an algorithm to build a structure minimizing the risk of a complex system. The result obtained can be used in the future to find solutions to this problem in the case of structures of more complex topologies, such as tree-like ones.
- Dabas M., Saraev P. Modeling of the temperature regime of the strip and roll in the stands of the hot rolling mill with interval parameters
In the development of the theory of expert assessments, the exceptional role of the position and the median of ranking, known as the Kemeny median, has been revealed. However, there is no optimal solution method for finding the median of the rankings represented by the matrices of binary relations according to the distance matrix criterion. The validity of the optimal solution to the problem of choosing the median in the space of the rank scale of measurement is due to the fact that there is a one-to-one correspondence between the rankings represented by binary relation matrices on a set of pairs of objects and the rankings in the rank scale. It is also an important task to check the consistency of the opinions of the expert group. The existing statistical methods and methods of rank correlation do not measure the consistency of expert opinions, if by which we mean the measure of proximity between expert assessments of objects. The article shows by concrete examples that the Kendal concordance coefficient, which is still found in the works of some authors, does not allow for a realistic assessment of the consistency of expert rankings, which can lead to erroneous management decisions. A method is proposed for evaluating the opinions of both a pair of experts and a group of experts, in the form of an average agreement of experts with respect to the median of rankings presented in the ranking scale.
- Poleshenko D., Korenev A. Development of the method of early recognition of the slag of the steel ladle of the continuous casting machine
The article deals with the problem of early recognition of the slag of the steel casting ladle of a continuous casting machine. In this paper, the vibration method of slag recognition was investigated, since it is the most informative. A number of methods were tested for analyzing the vibration acceleration signal of the protective tube manipulator for timely cutting off of slag and preventing it from entering the intermediate bucket, such as averaging it using a moving average filter, entropy calculation, construction of the signal spectrum envelope, as well as the power spectrum envelope. The analysis of the results of the approbation showed that not all methods can be applied to solve this problem. The highest efficiency, equal to 93 percent, was provided by an approach based on the analysis of the power spectrum of the vibration acceleration signal. In addition, in this paper, a neural network method for detecting anomalies in the vibration acceleration signal using various autoencoder architectures is considered and tested. This approach was tested on both "synthetic data", where it confirmed its efficiency in detecting anomalies, and on real data, where an accuracy of 73 percent was achieved. Further research will be aimed at a more thorough elaboration of this method.
- Kokunko J. Dynamic differentiation and smoothing of noisy signals specifying the trajectory of an unmanned aerial vehicle
The problem of developing a complex approach to filtering and smoothing of reference trajectories, which are signal reference actions, and to recovery of their derivatives is considered on the example of an unmanned aircraft of the airplane type. To solve this problem, methods of design and algorithms for setting up a dynamic generator of acceptable trajectories are developed. The system of differential equations, which describes the generator of tasks, corresponds to the canonical model of the control plant "input - output". The output variables of the generator track the reference noisy and non-smooth vector signal of the reference actions. Thus, the generator is a tracking differentiator. To design its local links and corrective actions, smooth and bounded sigmoidal functions with bounded derivatives are used. This approach allows considering the restrictions on the speed and acceleration of a particular aircraft, so the output variables of the tracking differentiator generate a naturally smoothed spatial curve and its derivatives, which are used in the plant control system as a realizable reference trajectory. Numerical simulation results demonstrated the efficiency of the developed approach to dynamic differentiation and smoothing of vector signals both in the deterministic case and in the presence of noise. A comparative analysis of dynamic generators with different variants of additional low-pass filters is performed. The application of the developed approach is possible for processing the reference actions of various control plants, it is only necessary that their dynamic model be reduced to the canonical form.
- Tretyakova E. Compensation of interference in airborne electromagnetic systems and solution of the problem of relative positioning in the electromagnetic two-dipoles field
The solution of the problem of relative positioning of the alternating magnetic field transmitter and the receiver is to determine the radius vector between the objects under consideration and their mutual orientation. In this paper, algorithms for the relative positioning of two dipoles in an electromagnetic field in three-dimensional and two-dimensional formulations are considered. The results obtained during the processing of real data from the airborne electromagnetic system EM4H are compared. Compensation has been carried out by measuring of two dipoles for the EQUATOR and “ÅÌ4Í” airborne electromagnetic systems in several modifications: with a transmitter loop attached to the fuselage of a Mi-8 helicopter, with a loop attached to the fuselage of an An-3 aircraft, and with a loop towed by a Eurocopter AS350B3. A comparison with the traditional method of compensation based on measurements of the field of three dipoles has been caried out. The signals remaining after interference compensation have been analyzed. It has been shown that the quality of compensation in the field of two dipoles is equatable to the traditional one.
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