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 Выпуск 103
- Vishnevsky V., Klimenok V., Larionov A. et al. Perforamnce evaluation of the priority multi-service system MMAP/PH/M/N using the Monte Carlo method
In this paper, we present the results of a study of a priority multiline queuing system with a marked Markov arrival process (MMAP), phase-type service time (PH), and a buffer with finite capacity. Priority traffic classes differ in the probability of joining the queue, which depends on the number of customers in buffer, and in the service time PH distribution. If the buffer is full, customers don't join the system. An analytical model has been developed and studied for a particular case of a queueing system with two priority classes. We present an algorithm for calculating stationary probabilities of the system state, loss probabilities, the average number of customers in the queue, and other performance characteristics for this particular case. For the general case of a system with K-classes, a simulation model is constructed, with the help of which various characteristics of the system are studied.
- Korepanov V., Chkhartishvili A., Shumov V. Basic combat models
The paper presents three approaches to the description of combat operations and the modeling results: game-theoretic models of the optimal distribution of forces and means of the parties in directions and echelons (tasks) in tactical models of oncoming combat offensive and defense; expansion of the Osipov-Lanchester models of the dynamics of combat operations; simulation models of combat units. As an indicator of the effectiveness of combat operations, it is proposed to use the probability function of the victory of one of the parties, depending on their numbers and the combat superiority of one of the parties. Game-theoretic models of "offensive-defense" (oncoming combat) are solved in two stages. At the first stage, according to one of the three criteria (breakthrough of the weakest point, breakthrough of at least one point, weighted average probability of a breakthrough taking into account the value of the points), the optimal distribution of the forces and means of the parties by points (along the front) and the value of the game are found. At the second stage, according to two criteria, the optimal distribution of forces and means between tactical tasks (echelons) is found under the assumption that when solving the immediate task, the parties are guided by the criterion of breaking through the weakest point of defense. The formulation of the masking problem using the approach of reflexive games is also given. The last section proposes a discrete-time algorithm for simulating units combat. It is proposed to take into account the characteristics of the battlefield, the dynamics of the position of combat units of the parties, the types of units (which determine the average speed of units, the range of detection and effective defeat), UAVs, the angle of fire, the effect of camouflage. To test the proposed algorithm, a simulation model of an oncoming battle was built, with the help of which the dependencies of the victory of one side on the decisiveness parameter were obtained. The perspectives of the approaches are discussed.
- Bubnova E. Reachability sets and the generalized h_2-norm of a linear discrete descriptor system
The paper focuses on a linear discrete noncausal descriptor system on a finite horizon under consistent initial conditions and bounded external disturbances, i.e. a bounded l2 norm. The notion of the generalized H2-norm for a linear discrete descriptor system is introduced as the induced norm of the linear operator generated by the system under consideration. This norm is characterized in terms of difference projected generalized Lyapunov equation solutions. It is demonstrated that if the sum of the quadratic forms of the initial and final states and the sum of the quadratic forms of the disturbance over a finite time interval is bounded by a given value from above, the reachability set of this system is a time-varying ellipsoid whose matrix satisfies the difference projected generalized Lyapunov equation. It is established that the generalized H2-norm of the system under non-zero initial conditions coincides with the value of the maximum half-axis of the reachability ellipsoidal set for a given output of the system. An example of a fourth-order descriptor system is provided as an illustration of the results. For this system a generalized H2-norm is calculated and reachability sets are constructed. The paper demonstrates the results of numerical simulations and projections of reachability sets on the plane corresponding to the forward and backward subsystems.
- Belov I., Kustov A. On the application of Kalman filter for the estimation problem with weakly coloured noises
The anisotropy-based estimation problem for linear discrete time invariant system is considered in the paper. The asymptotic formulas for estimator matrices, estimation error covariance matrice and anisotropic norm of estimation error system under the condition of small values of mean anisotropy of input disturbance are demonstrated. Also the maximum edge of external disturbance anisotropy, providing the prescribed accuracy of anisotropy-based estimator approximation by Kalman filter, is determined in the article. The stated problems solution is demonstrated in the graphical results of numerical modelling for linear discrete time invariant stable system.
- Mukhin A. The static output feedback existence criterion
The problem of finding criteria for the existence of stabilizing static output feedback for linear continuous stationary systems is considered. The fact is that the existing rank criteria for the existence of static state feedback are applicable only in cases where one of the input or output matrices has full rank. In all other cases, as a rule, frequent in practice, these criteria are not applicable. To solve the problem, a class of linear systems is introduced, for which a criterion for output feedback also exists and can be formulated as necessary and sufficient conditions. The main idea is to reduce the output matrix by means of a non-degenerate linear transformation to a certain block form.
- Korneenko V. Methods for selecting the median ranking and evaluating the consistency of expert assessments by the proximity criterion
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.
- Stetsyura G. Synchronization of a distributed experiment with feedback (based on IEEE 1588 – PTP and WHITE RABBIT)
We propose a method decentralized executed synchronous initiation of actions of a group of physical objects participants of a controlled experiment. Here, the objects detect the occurrence of events, which require joint actions of all objects, and without the participation of the control center create a common command to initiate the actions of the objects simultaneously or with additional delays prescribed for each object. For this purpose, objects exchange messages via a signal repeater that does not contain computational means, form a common command in it, and perform auxiliary calculations. Necessary for these actions the simultaneous arrival in the repeater messages objects with the alignment of their binary digits of the same name is provided. In general, in the method, a group of objects functions as a distributed control system, which corrects the execution of the experiment with minimum delays in response to the appearance of unforeseen or expected at unknown points in time events.
- Garakoev A., Gladyshev A. Identification of the dynamic system "aircraft + pilot" when performing airborne geophysical survey
The solution of the problem of the structure determining of a controlled dynamic system and the formation of the corresponding control laws requires a detailed analysis of real experimental data, identification methods. Methods for identifying models of behavior of <<aircraft + pilot>> systems have been successfully developed since the 60s of the last century. Manned aviation occupies a leading position in relation to unmanned systems, respectively, the relevance of such tasks remains to this day. When performing flights, the pilot relies on navigation information displayed on various indicators located in the cockpit of the aircraft. An example of such a pilot indicator is an indicator of type <<Arrow>>. This article is devoted to the analysis of real flight data of four aircraft, the pilots of which flew according to information from the <<Arrow>> indicator. According to the results of the analysis and with the help of computer simulation, the parameters of four dynamic models <<aircraft + pilot>> were identified. The models are linear closed (pilot-regulator closing control loop) dynamic systems of the 1st order, described in the form of transfer functions. The results of experiments performed on the simulator using each of the models are presented.
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