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“Informatics and Applications” scientific journalVolume 20, Issue 1, 2026Content Abstract and Keywords About Authors MULTIPLICATIVE OUTPUT CONTROL UNDER A QUADRATIC CRITERION: DYNAMIC PROGRAMMING AND THE OPTIMAL SOLUTION
Abstract: The paper addresses an optimal control problem for a quasi-linear output of a stochastic differential system driven by an Ito diffusion process. In contrast to the traditional additive control formulation, the controlled linear output is assumed to include multiplicative control resulting in a quasi-linear differential system with feedback. The problem is formulated using a general quadratic performance criterion which defines control objectives identical to those in the additive control model. This allows for a direct comparison of control strategies as alternative architectural solutions within the same application context. The study focuses on two multiplicative control configurations: one where the control acts as amultiplier of the system state, and another where itmultiplies an uncontrolled disturbance. The third possible case — output-multiplicative control — leads to a bilinear system; since its analysis requires a different methodological framework, it is excluded from this study. The solution is derived using a dynamic programming approach. Similar to the additive control case, the Bellman function is shown to take a quadratic form with respect to the output variable. However, in the state-multiplicative control configuration, the solution — characterized by three coefficients of the Bellman function — is substantially more complex. This complexity motivates the problem of synthesizing practically implementable approximations.While the disturbance-multiplicative control case is considerably simpler, its practical relevance is found to be limited. Keywords: stochastic differential equation; optimal control; quasi-linear systems; multiplicative control; dynamic programming; Bellman function; Riccati equation; linear parabolic equations NORMAL FILTERING METHODS FOR OBSERVED HEREDITIARY STOCHASTIC SYSTEMS WITH UNSOLVED DERIVATIVES
Abstract: The paper presents analytical synthesis methods for normal conditionally optimal and suboptimal filters (NCOF and NSOF) based on the mean-square criterion (i. e., in the Pugachev sense). These methods are developed for information processing in interconnected, observable hereditary stochastic systems with unsolved derivatives (HStSUSD). Abrief survey of publications on the analysis, modeling, and nonlinear filtration in HStSUSD is also provided. The NCOF are based on a dual procedure of HStSUSD reduction to finite-differential stochastic systems using the methods of normal approximation and statistical linearization. The analytical reduction methods of first and second stages are discussed. To illustrate the approach, examples are presented where NSOF for HStSUSD is generalized throught the application of the second-stage Kalman-Bucy filtering techniques. The NCOF and NSOF peculiarities for real time filtering in reducible HStSUSD are outlined. Future generalizations are discussed. Keywords: hereditary stochastic systems with unsolved derivatives (HStSUSD); normal conditionally optimal filter (NCOF); normal supoptimal filter (NSOF); stochastic process (StP) THE TIME-OPTIMAL PROBLEM FORA SWITCHED MODEL OF A CONTROL PLANT ON A PLANAR ROUTE
Abstract: The paper addresses the time-optimal control problem for a mobile object moving along a prescribed planar route. The route is defined as a continuous curve composed of standard segments (straight lines, circular arcs, etc.) and may contain nonsmooth junctions at angular points. During motion, the control system model undergoes changes (switches) due to differences in the equations of motion across distinct segment types. General constraints across the entire time-optimal problem include limits on linear velocity, linear acceleration, and angular velocity during turns. Due to these switches, the problem cannot be reduced to a classical time-optimal control formulation. A solution to the stated problem is derived in the article. The optimal control along the entire route is achieved through optimal traversal of all its standard segments. This requires maximizing the magnitude of linear velocity on each segment of bounded curvature and maximizing the magnitude of angular velocity during on-the-spot turns at angular points. The effectiveness of the proposed approach is validated through numerical simulations. Keywords: switchable model; time-optimal problem; planar motion ON NORMAL VARIANCE-MEAN MIXTURES AS STATIONARY DISTRIBUTIONS OF A STOCHASTIC DIFFERENCE EQUATION WITH RANDOM COEFFICIENTS
Abstract: It is shown that an arbitrary normal variance-mean mixture can be a stationary distribution of a stochastic difference equation (that is, in the first-order autoregressive scheme) with random coefficients. An example is presented of what the random drift and diffusion coefficients should look like in order that a specified mixture is a stationary distribution. It is demonstrated that one and the same stationary distribution can occur with different forms of the coefficients. In terms of the closeness of coefficients, some estimates are presented for the closeness of the distributions of random autoregressive sequences of the first order. It is also shown that the stationary mode of the first-order autoregressive process with random coefficients possesses the property of stability in the sense that small deviations of the distribution of the initial term of the autoregressive sequence from the stationary distribution corresponding to the given coefficients guarantee small deviations of the distributions of the rest terms of the sequence from this distribution. Keywords: stochastic difference equation with random coefficients; first-order autoregression with random coefficients; stationary distribution; normal variance-mean mixture METHODS FOR GENERATING METRICS ON OBJECT SETS IN THE CONTEXT OF THEORY OF TOPOLOGICAL DATA ANALYSIS. PART 1. METRICS BASED ON DISTANCES BETWEEN FEATURE VALUES
Abstract: Distance metrics on object sets are widely used in various machine learning algorithms. However, generating such metrics for specific application tasks is a nontrivial challenge. Typically, researchers are limited to selecting from established empirical metrics and, in some cases, fine-tuning their parameters. The paper proposes several theoretical approaches developed within the context of topological data analysis. These approaches include metrics derived from distances between feature values, analysis of multidimensional spaces, the implications of Urysohn's embedding theorem, and the introduction of a lattice of feature combinations.
The proposed framework enables the systematic generation of problem-oriented metrics on object sets Keywords: topological data analysis; distance functions on objects; algebraic approach to algorithm design; theory of feature value analysis MATHEMATICAL MODEL FOR THE ANALYSIS OF THE DATA TRANSMISSION PHASE IN INTERNET-OF-THINGS SYSTEMS
Abstract: The paper develops a mathematical model for a massive machine-type communication (mMTC) system on Cellular Internet-of-Things (CIoT) designed for phase analysis of data transmission. The random access phase is treated as an input traffic generation mechanism and is not the subject of the detailed study. Instead, the focus is on the uplink and downlink traffic service processes accounting for limited frequency and time resources. The model observes asynchronous packet generation by loT devices as well as the emergence of new traffic in the form of group software updates. A Markov model with field-based tools is used for analysis allowing for the capture of stationary system characteristics. Analytical expressions are provided for the average number of packets, mean transmission delay, and resource utilization. Numerical results demonstrate that static resource allocation between transmission phases significantly limits system efficiency. These findings justify the necessity for adaptive resource management in 5G/6G CIoT networks. Keywords: 5G; 6G; mMTC; CIoT; data transmission; delay; optimal resource allocation FUNCTIONAL CHARACTERISTICS OF VERTEX CLUSTERS OF A MULTIUSER NETWORK SYSTEM
Abstract: Within computational experiments, internodal transmission modes and resource distribution in a multiuser network system are investigated. The concept of a vertex cluster of outgoing flows is introduced. For each network vertex, the vector of outgoing internodal flows transmitted simultaneously from a source node to all cluster recipients is computed and analyzed. Two internodal dispatching methods are examined: shortest-path routing and maximum-flow routing between source-destination pairs. For each cluster, relative edge-utilization metrics and specific network resource consumption are determined. Based on the obtained numerical characteristics, a comparative multiparameter analysis of various routing strategies is performed. Furthermore, normalized flow vectors are compared for both individual and simultaneous transmission from source to destination. The position of each cluster's central vertex within the network is evaluated. The calculations were performed for networks with different structural features and the same total capacity ofedges. The experimental results are illustrated with special diagrams. Keywords: streaming model of the communication network; vertex clusters; unit cost of resources ORDERING OF MULTIVARIATE LONGITUDINAL DATA BASED ON COINTEGRATION ANALYSIS
Abstract: In the processing of longitudinal data, multivariate cointegration analysis methods deserve for special attention identifying long-term relationships between several nonstationary time series. In relation to the problems of econometrics, the article discusses the application of cointegration analysis to the ranking of objects based on a single indicator: the degrees of connectivity between the components of an observed multidimensional time series.
Keywords: regression analysis; spurious regression; cointegration analysis; relate coefficient; regional economy; investments; gross regional product; number of employed persons; statistics with R; tests for stationarity; object ordering ON RELATIONAL FORM TO SOLVE THE NETWORKING COOPERATIVE GAMES
Abstract: Relational statement of networking game is investigated. It has applications to multiagent and cooperative robotics problems. A model with a large number of intellectual players capable of cooperative behavior is studied. The conflict rational resolution is based on the agents networking and data transition. The networking structure is generated by agents themselves in the process of stable coalitions formation. To achieve this goal, players apply generalization of their preferences and possibilities relations. For equilibrium situation and optimal communication network search, game reduction is used. It is based on the game compositionality property in the category of binary relations. The distributed polynomial method to solve the networking cooperative game is contributed. Effective or stable parallel coalitions are to be found in it by players' collective efforts. Possibility to split all players into union of stable coalitions is proved. Parallel coalitions classification is given depending on the degree of their stability. Keywords: relational game; relation: preferences, possibilities, characteristic; preorder; network structure; game reduction; effective coalition; stable parallel coalitions: strong; tiered; mixed; weak
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The paper presents a rigorous analysis of the theoretical transition from metrics on feature value sets 
to 
. Experimental validation of the various branches of the proposed formalism is deferred to future publications.
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