Nº 4 (2025)

Abstract-For linear systems with discrete time, an approach to constructing the law of limited controls as functions of the current state is proposed. The idea is based on using information about the 0-controllability sets.

This article presents a general algorithm for the synthesis of an optimal, on average, fast dynamic regulator, performed sequentially in time and obtained in the first part, with a selectable order for the case of inaccurate measurements of the output of a nonlinear stochastic controlled object. Its application to a particular control problem for a linear-Gaussian object with a variable quality criterion, which is quadratic in the control and regulator state but quadratic-biquadratic in the object state, is demonstrated. It is shown that the optimal nonlinear structural functions of the controller state equation and its output formula in this case are expressed in terms of the first three initial moments of the conditional probability density obtained by solving the Cauchy problem for a nonlinear partial differential equation obtained from the Fokker–Planck–Kolmogorov equation. To find the approximate analytical form of these functions, the Gaussian approximation method is used, which reduces the problem to obtaining the coefficients of some nonlinearities, which depend only on time, by the sequential Monte Carlo method. It is shown that the biquadraticity of the criterion leads to a useful polynomial form up to the third degree for the structural functions of the Gaussian regulator, while for the quadratic criterion, a linear regulator satisfying Wonham’s separation theorem is obtained, and its order is equal to the object order.

The problem of vehicle’s translation to a certain landing location above the surface of the planet is considered. Using the Pontryagin maximum principle, the optimal control problem is reduced to a boundary value problem for a system of nonlinear differential equations. A qualitative analysis of the optimal phase trajectories of the system is carried out, their properties are established, illustrated by the results of numerical modeling. The domains in the plane of phase variables are analytically described, from which it is possible to achieve a terminal set. A synthesis of optimal control is constructed.

The paper proposes a constructive method of solving the linear-quadratic problem of optimal control of hyperbolic systems with distributed parameters under the conditions of estimation in a uniform metric of the target sets of final states of the controlled variable and the rate of its v variation in time. The previously developed alternance method of constructing program control algorithms is applicable to the considered range of problems. The corresponding methodology uses the procedure of parameterisation of the desired control actions on a finite-dimensional subset of an infinite number of final values of conjugate variables and the subsequent operation of exact reduction to a parametric problem of semi-infinite optimization, which is solved according to the scheme of application of the alternance method generalised to the situations under consideration. It is shown that the sought equations of optimal regulators are reduced to linear, with non-stationary coefficients, feedback laws on the measured output of the object. An example of the solution of the problem of energy-optimal control of an object described by a wave equation of mathematical physics, which is of independent interest, is given.

Сonstructing convex combinations of predictors is an effective method for building ensembles in solving regression problems. Herewith it seems possible to improve the final quality of the algorithm if an initial set of predictors is constructed in a special way. In this paper, we study two techniques that allow us to achieve such an improvement: bagging in combination with the random subspace method, and optimization of the divergence of predictors. The effectiveness of resulting methods is verified in applied problems.

The maximum indicators of the functionality of a multiuser communication system are investigated under a change in the capacity of network edges. Based on the transmission routes of the maximum flows of the same type, the minimum cuts of the network are determined. The influence of changes in the capacity of the cut edges on the maximum allowable internodal flows under monopoly control modes is studied. The maximum values of the internodal flows correspond to the corners of the set of allowable flows satisfying the constraints of the model. A convex combination of vectors corresponding to the corners is used to estimate the relative changes in network characteristics during deformation of the set of feasible flows. Multi-criteria guaranteed estimates of the maximum feasible deviations from the reference indicators of the network functioning are formulated. Summary diagrams for networks with various structural features are provided.

Recommendation systems are finding increasingly wide application, encompassing a variety of domains and diverse data types. However, in scenarios with a limited number of items, traditional approaches often prove to be insufficiently effective. In such cases, methods based on boosting algorithms offer a more efficient solution. This paper proposes a way to improve recommendation quality within this approach by incorporating users’ negative interactions with items. Integrating these data enables more accurate modeling of both preferences and avoidances. The presented method enhances recommendation personalization even under conditions of high interdependence and limited item availability.

The article proposes a new algorithm for measuring the texture characteristics of objects in images. The novelty of the algorithm lies in using pairs of images obtained in raking light and combining their Fourier spectra. The application of the developed algorithm is demonstrated in solving the problem of counting the threads of woven bases of paintings from images. A computational experiment showed that the error in measuring the canvas density does not exceed 0.4 threads per centimeter. The accuracy of measuring the canvas density using different methods was compared. The proposed algorithm measures the characteristics of painting canvases with a texture distorted by pollution, ground penetration, or treatment with restoration materials, and is superior in accuracy to previously used algorithms. Using a new algorithm, the density of the canvases of seven paintings from the collection of the State Historical Museum was measured.

The task of improving the characteristics of GLONASS in the context of the prospects for the development of global satellite navigation systems is described. The authors consider as key areas of research and development related to the advanced laser and quantum optical hardware integration into orbital constellation’s technological processes. The main factors that currently hinder the joint processing of measurements generated on board and on the ground from various sources are discussed. Ways to eliminate these factors are proposed by developing and implementing special information technologies for comparing time scales and digitizing measurements and clarifying delays in the functioning paths of optical hardware. Experimental results are obtained and estimates of the measurements formed in this way are presented, and conclusions are drawn about their possible use in the interests of improving GLONASS accuracy characteristics.