No 3 (2023)
Mathematical Problems of Control
On a Decomposition Method for Designing Communication Networks
Abstract
This paper presents a communication network design algorithm for finding a guaranteed trans-portation plan of a given volume under uncertain factors. The volumes of production and the capacities of communication lines are expressed as linear functions of invested resources. The well-known Dantzig–Wolfe decomposition algorithm is applied to solve the dual problem due to its stepped block structure. In view of their specifics, the linear problems arising in iterations are solved using effective network and graph theory methods: the maximum flow, the minimum cutset in the network, the connectivity components, and the minimum spanning trees of the graphs are found. The existing algorithms for these problems have the complexity estimates О( ), О( ), and O(n + m), where n is the number of graph vertices and m is the number of edges.
Control Sciences. 2023;(3):3-11
3-11
Analysis and Design of Control Systems
Peak-Minimizing Design for Linear Control Systems with Exogenous Disturbances and Structured Matrix Uncertainties
Abstract
A major characteristic of transients in linear dynamic systems with non-zero initial conditions is the maximum deviation of the trajectory from zero, which has a direct engineering meaning. If the maximum deviation is large, the so-called peak effect occurs. This paper completes a series of research works devoted to the peak effect in linear control systems. We consider a linear control system with non-random bounded exogenous disturbances and system uncertainties. A regular approach is proposed to design a stabilizing static state-feedback control law that minimizes the peak effect. The approach is based on the technique of linear matrix inequalities and reduces the original problem to a parameterized semidefinite programming one, which can be easily solved numerically. The proposed approach can be extended to new classes of problems, in particular, to the case of output feedback using an observer or a dynamic controller.
Control Sciences. 2023;(3):12-19
12-19
Control in Social and Economic Systems
Parametric Control of Agricultural Development Based on Cognitive Modeling
Abstract
The concept of parametric control is used to prove the existence of a contradiction between the growth of agricultural production and the lack of conditions for expanded reproduction in Russian agriculture. This contradiction is the main limitation of agricultural growth in the country. The theoretical foundations of parametric control are specified for socio-economic systems and the parameterization stage of the controlled system is included in the control process. A control action should be chosen by comparing the estimates of two blocks of parameters. The first block assesses the potential of an external control action affecting the system. The second block of parameters shows the internal potential of the controlled system. If the estimates do not match, the control process has a contradiction, and the control action should be corrected. Fuzzy cognitive modeling is used to determine the contradiction in the control of agricultural development. A fuzzy cognitive map of Russian agriculture is constructed using expert assessments and correlation-regression analysis according to statistical data for the period 2000–2020. The structural-target analysis of this map is performed and its system indicators are calculated to identify the main limitations in agricultural dynamic processes. Agricultural development is forecasted through the scenario analysis of the fuzzy cognitive map. According to the cognitive modeling results, the control action potential exceeds the agricultural growth potential. Therefore, for sustainable long-term agricultural growth in Russia, it is necessary to change approaches to agricultural management.
Control Sciences. 2023;(3):20-39
20-39
Models of Joint Dynamics of Opinions And Actions in Online Social Networks. Part II: Linear Models
Abstract
Based on VKontakte data, we study the influence of various factors on the dynamics of opinions and actions both at the macro level (“public opinion”) and at the micro level (the opinions and actions of individual agents). A model of collective decision-making is briefly considered; in this model, interconnected parameters reflect both the mental and behavioral components of the agents’ activity. Identification results are presented for two special modifications of the model, namely, linear macro- and micro models of the dynamics of opinions and actions in a social network. We estimate the influence of various factors on the opinions and actions of agents: aggregated social influence (public opinion), the agent’s individual opinions and actions, the opinions and actions of the social environment, and the mechanisms of the agent’s trust in information sources and information content.
Control Sciences. 2023;(3):40-64
40-64
Scenario-Cognitive Modeling of Complex Systems Based on Event-Driven Identification of Factor Dynamics
Abstract
This paper is devoted to methodological problems of increasing the effectiveness of scenario analysis and modeling of development processes in socio-economic systems. The corresponding results can be used in management decision support systems for proactive evaluation of their effectiveness. Several limitations of the traditional approach to scenario-cognitive modeling are considered; due to these limitations, the resulting scenario neglects key events directly affecting the assessment of the current situation and decision-making. A novel approach is proposed to identify and analyze the dynamics of factor values when studying the model as well as to form additional scenario-event relationships between the factors in order to increase the adequacy of the model to the situation. A computational algorithm is developed to analyze the dynamics of factor values of the model. This algorithm is implemented and tested within the program-analytical complex of scenario modeling. Finally, an example of using the algorithm is given.
Control Sciences. 2023;(3):65-76
65-76
Control of Moving Objects and Navigation
An Adaptive Aiding Algorithm for Pedestrian Navigation
Abstract
This paper presents a novel aiding algorithm for pedestrian navigation using foot-mounted inertial measurement units (IMUs). Autonomous pedestrian navigation with foot–mounted IMUs is based on the integration of simplified navigation equations and the correction of the navigational solution with zero velocity. Additional aiding algorithms are needed in the absence of external information such as GNSS or Wi-Fi and Bluetooth signals. There are two main groups of such algorithms: aiding based on information about bounded step length (two IMUs on both feet are required) and aiding based on straight-line path detection (heuristic drift elimination, HDE). The first method does not consider different accuracy of IMUs whereas the performance of the second one strongly depends on trajectory form. An attempt to eliminate the drawbacks of both algorithms is undertaken below. The novel algorithm is an adaptive version of the method based on bounded step length. Adaptivity is provided by tuning the measurement matrix for the less accurate IMU. The accuracy is assessed through the trajectory analysis based on information about straight-line motion. The novel algorithm is tested on experimental data. According to the testing results, this algorithm has better performance in the experiments with complicated trajectories. It can be used within an integrated pedestrian navigation system in the absence of external information.
Control Sciences. 2023;(3):77-87
77-87