No 2 (2024)

The solution of many practical problems leads to the calculation of the values of probabilistic criteria, the most common of which are the quantile and probability functionals. It is known that, under fairly general assumptions, methods suitable for solving problems of finding the values of a probabilistic criterion can be used to solve the problem of quantile analysis. The proposed method for solving the problem of quantile analysis is based on the use of the method of numerical multidimensional integration described in the previous works of the author. One of the important properties of this integration method is universality (when using it, we can set an arbitrary number of variables n and an arbitrary number of linear constraints r). The only limitation is the case of an unacceptably long solution time. Thus, the indicated universality is transferred to the solution of the considered problem of quantile analysis.

The problem of estimating unknown probabilities of transitions of a random Markov binary input signal of a nonlinear one-dimensional discrete system based on estimating the expectation and variance of the output signal is considered. The defined expressions are built on the basis of considering equally probable transitions and the steady-state mode of the algorithm for assessing the state of the system, obtained by approximating the probability density of its output signal by the Pearson type I distribution. An example of comparison of theoretical calculations with the results of imitation mathematical modeling is given.

We consider the problem of the time-optimal movement of a rigid body moving translationally along a horizontal straight line and carrying n-linear oscillators. The only control force is applied to the platform and is limited in magnitude, there is no friction. The system is transferred from a state of rest to a specified distance with vibration damping. The evolution of optimal control functions depending on the distance of movement is investigated. A general approach to constructing a visual diagram reflecting such evolution is proposed. To do this, a geometric interpretation of the necessary optimality conditions is used as properties of an auxiliary “control” curve in n-dimensional space. Numerical examples of constructing diagrams of optimal control functions for a platform with three oscillators are given.

An inverse problem with distributed parameters for the process of the self-focusing of cylindrical X-ray pulses in a plasma is considered, and a mathematical model of the studied process in a cylindrical coordinate system is described, taking into account the symmetry of the pulse relative to the direction of its propagation. A similar process in the case of plane pulses is compared, a computational method for solving the direct problem of interaction between the plasma and pulse for the given parameter values is presented, the second order of approximation and the asymptotic stability of the constructed difference scheme are proved. It is proposed to use the equivalence set method to solve the inverse problem of determining the initial parameters of the plasma and pulse from the shape of a cylindrical X-ray pulse passing through it and the dynamics of its maximum intensity. Using this problem as an example, an algorithm for using the equivalence set method to solve inverse problems is described.

This paper proposes optimization models for the production and financial activities of an enterprise, which make it possible to increase the efficiency of its functioning in the modern market environment. The novelty of the proposed tools is due to taking into account the peculiarities of the processes of consumption and storage of finished products, as well as lending and expansion of production. To implement the proposed models, the generalized reduced gradient method is used, built into the MS Excel toolkit (the “Solver” add-on). Solving problems of choosing a production program is also possible using other methods of this add-on, including the simplex method.

The article formulates a problem of compliance of time inter-frame delays via video frames decoding from input cyclic-structured video stream. Implementation of software buffer or buffers set is reviewed as a general approach to solving this problem. Some methods of implementation of such buffers for video processing and transmission systems are proposed. Experimental research of these methods is conducted; recommendations for use are offered.

The motion control of the advanced manned spacecraft “Orel” is considered. For maneuvering and angular stabilization, a propulsion system is used as an actuator. In order to ensure simultaneous control of the motion of the center of mass of the spacecraft (SC) and its stabilization with the help of engines at each moment of time, it is necessary to solve the problems of determining the required change in the speed of the SC, choosing the optimal configuration of the engines, and the problem of predicting the motion parameters of the SC. Methods for solving these problems, applied in the development of the control system of the manned spacecraft “Orel”, are presented. The operability of the described algorithms is confirmed by the results of mathematical modeling on a ground test bench for onboard software.

In the context of group interaction among mobile robots, there arises the challenge of task distribution within the group, considering the robots' characteristics and the working environment. This study aims to modify the Hopfield neural network and develop methodologies for its application in solving the task allocation problem for an arbitrary number of tasks within a group of mobile robots. To achieve this, the Hopfield neural network is represented as a graph. An algorithm is presented, demonstrating the transition from the initial problem to the Traveling Salesman Problem (TSP). The application of the Hopfield model to the task distribution problem in a group of robots is described, along with the development of an optimization function calculation algorithm. An assessment is conducted to evaluate the impact of neural network parameters on the quality and speed of solving the optimization problem. By comparing it with other heuristic methods (genetic and ant colony algorithms), the domains of application for the modified algorithm are determined.