No 5 (2023)

Исследуемая гибридная аффинная система возникает при применении импульсного управления специального вида к цепочке четырех интеграторов. Цель управления – стабилизировать систему в начале координат так, чтобы система приближалась к состоянию равновесия по заданной желаемой (целевой) траектории. Целевая траектория определена неявно как траектория интегратора второго порядка, стабилизируемого с помощью обратной связи в виде вложенных сатураторов. Задача исследования – найти диапазон изменения коэффициентов обратной связи, при которых система глобально устойчива. Показано, что задача сводится к более простой задаче установления устойчивости линейной системы второго порядка с переключениями с зависящим от состояния законом переключений. Доказано, что последняя устойчива при любом законе переключений.

The problem of the speed of performance (speed, performance) of a group of controlled objects is considered, the initial state of each of which is given, and the final state is selected from a fixed set of possible terminal states (targets). For each object, it is required to assign a target and find the control that ensures that the group simultaneously reaches all the selected targets in the shortest time. Since the speed-optimal controls of individual objects do not solve the problem of group speed, the so-called minimally delayed trajectories are used. A technique for solving the problem is developed, which includes an algorithm for solving the minimax assignment problem and a procedure for using the optimal and minimally delayed trajectories. The problem of the speed of a group of objects, whose planar motion is represented by Markov–Dubins trajectories, is solved.

In the class of discrete enumeration problems, an important place belongs to the problems of searching for frequently and infrequently occurring elements in integer data. Questions on the effectiveness of such a search are directly related to the study of the metric (quantitative) properties of sets of frequent and infrequent elements. It is assumed that the initial data are presented in the form of an integer matrix, whose rows are descriptions of the studied objects in the given system of the numerical characteristics of these objects, called attributes. The case is considered when each attribute takes values from the set {0,1,...k-1}, k>2. Asymptotic estimates for the typical number of special, frequent fragments of object descriptions, called correct fragments, and estimates for the typical length of such a fragment are given. We also present new results concerning the study of the metric properties of the minimal infrequent fragments of descriptions of objects.

We consider a chain of several bodies that can move translationally along a horizontal line. The neighboring bodies are connected to each other by springs. One end of the chain is fixed, and on the other there is a body, which is a rectangular parallelepiped of a square section. The system is placed in a horizontal stationary medium flow perpendicular to the specified straight line. Under the assumption that the flow affects only the parallelepiped, the dynamics of this system are studied as a potential working element of an oscillatory wind power plant using the galloping effect. For a different number of bodies in a chain, different values of flow velocity and external load, periodic regimes in the system are studied. It is shown, in particular, that an increase in the number of bodies in a chain makes it possible to increase the maximum power that can be obtained using the device and to reduce the critical speed at which oscillations occur. A scheme for regulating the load resistance is proposed, aimed at ensuring the transition to an oscillatory mode with maximum power.

Balancing strategies for control flows and resources are studied in computational experiments on a mathematical model of a multiuser network. An algorithmic scheme for sequentially solving a chain of lexicographically ordered problems of finding nondiscriminating the maximin distributions of flows is proposed. A procedure for step-by-step equalizing the splitting of internodal flows along all the existing shortest paths is developed. At each iteration, a part of the available resource is distributed equally among all pairs of correspondent nodes for which there is a possibility of flow transmission. The results obtained in the course of the experiments make it possible to trace the dynamics of changes in the capacity of the edges, up to reaching the maximum network load. Bottlenecks in various networks are analyzed and compared with a monotonic increase in the flows. Special diagrams are given.

The article discusses the information technology of a robust intelligent control system design based on quantum fuzzy inference. The application of the developed design methodology is based on the quantum self-organization of fuzzy controller’s imperfect knowledge bases and leads to an increase in the robustness of intelligent control systems in unpredicted situations. The results of mathematical modeling and physical experiment are compared using the example of an autonomous robot in the form of a “cart – pole” system. Experimental confirmation of the synergetic effect existence in the robust self-organized fuzzy controller formation from a finite number of non-robust fuzzy controllers in on-line has been demonstrated. The resulting effect is based on the existence of hidden quantum information extracted from the classical states of the controller’s time-varying gain coefficients processes schedule. The derived law of quantum information thermodynamics establishes the possibility to forming a thermodynamic control force due to the extracted amount of hidden quantum information and performing additional useful work, that guarantees the achievement of the control goal based on increasing the robustness of a self-organized quantum controller. At the same time, the amount of useful work performed by the control object (at the macro level) exceeds the amount of work spent (at the micro level) by a quantum self-organized controller to extract the quantum information hidden in the responses of imperfect knowledge bases without violating the second thermodynamics information law for open quantum systems with information exchange of entangled super correlated states. A concrete example of an autonomous robot is given, demonstrating the existence of a quantum self-organization synergetic effect to imperfect knowledge bases.

The information technology developed by the authors to ensure the possibility of operation without downloading information by the ground control complex while improving the accuracy of the ephemerides of the existing global navigation satellite systems (GLONASS) midaltitude segment and its promising additions is described. Achieving the stated goals within the framework of the technology under discussion involves the formation of precise ephemerides by solving the following interrelated tasks: improving the accuracy of determining and predicting the ephemerides of navigation satellites in the inertial coordinate system; improvement of methods and algorithms for forecasting and updating the evolution of the Earth’s rotation parameters onboard satellites; and precise synchronization of onboard clocks. The primary attention is paid to the first of the listed tasks, i.e., prediction and refinement of the ephemerides of navigation satellites in the inertial coordinate system, including in the mode of operation of satellite constellations without updating the ephemerides-temporal information. As a base for its solution, it is proposed to use advanced onboard hardware for intersatellite measurements. The basic limitations related to the implementation of intersatellite measurements and their subsequent processing for both midaltitude and advanced space segments of the GLONASS are discussed. The results of the design-ballistic analysis and processing of real and simulated measurements, as well as the preliminary characteristics of the accuracy of the ephemerides estimates obtained in this case onboard, are presented.