Information and Control Systems

Stability analysis of a Lurie system with scalar retarded control and switching

Nataliya Romanovna Andriyanova — 2023-12-19

ntroduction: To ensure the stability of switched linear systems, M. S. Branicky proposed a method for finding conditions on the switching law. It is also known that the presence of delays can disrupt stability. It is advisable to extend this method to a nonlinear control system, which makes it possible to set arbitrary concentrated delays during control or switching. Purpose: To investigate a nonlinear system with subsystems composed of linear parts and control assumed to be a scalar nonlinearity with a greater than one rational degree. Also, for an arbitrary delay in control, to obtain conditions for the switching law that would guarantee the stability of the solution. Results: Cases of both synchronous (simultaneous for all parameters of the system) and asynchronous switchings have been studied in connection with the occurrence of delays when developing a controlling action, as well as receiving information about active subsystem changing. Multiple Lyapunov – Krasovsky functionals were constructed for each system under discussion, which made it possible to find conditions on the switching law under which the solutions will be locally asymptotically stable. As we have found out it is sufficient for this to choose the switching moments so that the duration of the subsystem should unboundedly tend to infinity over time. We also demonstrate that in the discrete case, similar conditions also ensure stability at a sufficiently small discretization step. We have carried out numerical modeling for both synchronous and asynchronous switching between continuous and discrete subsystems. The graphs presented in the paper are consistent with the theoretical conclusions.

Minimization technique for the amount of computation for land clutter simulation

Margarita Valerievna Oreshkina — 2023-12-19

Introduction: Land clutter simulation is an important step in testing and evaluating the performance of radar stations. A surface simulation model is an area within the radar field of view divided into many small sites. Each of these sites is a point reflector. The echo signal from the surface area is a set of signals from the point reflectors this area contains, which requires significant computing resources. Purpose: To substantiate the techniques of minimizing the amount of computation when calculating reflected signals for the simulation of radar station operation. Results: The land clutter modeling requires the calculation of the convolution of the sequence describing the structure of the earth's surface and the sequence describing the probing signal. The calculation of the convolution is efficient according to the overlap-save method, where the entire sequence is divided into several sections. The study shows that when computing partial convolutions with the use of the Fourier transform, some harmonics have low energy and can be ignored without significantly affecting the accuracy of the calculations. The land clutter properties change depending on the distance of the particular area from the radar station. In an area which close to the radar station, the contribution of reflections from areas is highly dependent on their location. Reflections actually are formed only by nearby areas. We obtain the expressions for estimating the errors that arise due to the neglect of reflections from remote areas. At a considerable distance from the radar, the reflective areas take on a point character, which makes it possible to calculate the convolution without using fast algorithms. Practical relevance: The presented computational optimization techniques can be used to develop echo signal simulators.

Mathematical model and control algorithms for a group of ground robots with energy resource redistribution

Konstantin Dmitrievich Krestovnikov — 2023-12-19

Introduction: Applying several homogeneous or heterogeneous robots for solving target problems provides advantages in terms of time reduction or increased functionality compared to a single robot. At the same time, the amount of resources required to ensure the operation of a group of robots also increases. Purpose: To increase the efficiency of a group of robots operating in rough terrain by redistributing energy resources within the group. Results: We present mathematical model and control algorithms for a group of robots, with some of the robots defined as workers, and the other part as chargers. Worker robots are aimed solely at completing assigned tasks, and charging robots replenish their energy resources. The proposed approach takes into account the limited energy resource of charging robots and losses during energy transfer between robots, which makes it possible to apply the developed solutions for robots equipped with contactless energy transfer systems. The selection of points at which energy is transferred takes into account the topography of the surface of the working space, which simplifies the process of robots positioning and increases the efficiency of contactless energy transfer. Using simulation modeling in the Gazebo environment, we have compared the total time for performing tasks by groups operating with traditional principles and that for groups based on the presented approach. In the group without redistribution of resources, all robots were workers and performed target tasks. The second group was divided equally into worker robots and charger robots. The results obtained in the simulation show a general trend towards faster completion of tasks by a group operating with a redistribution of resources when the distance to tasks and their number increases. Practical relevance: The proposed approach of the resource redistribution expands the operation area of a group robots and makes it possible to apply it for potentially more energy-intensive tasks.

A software package for studying problems of asymptotic combinatorics of Young diagrams and Young tableaux

Vasilii Sergeevich Duzhin — 2023-12-19

Introduction: It is often impossible to solve fundamental problems of asymptotic combinatorics without conducting massive computer experiments. However, carrying out such experiments usually requires significant computational costs. In this regard, the task of developing effective software tools is relevant. Purpose: To develop a software package for working with Young diagrams and Young tableaux. Results: A software package has been implemented in C++ which makes it possible to work with two- and three-dimensional Young diagrams and Young tableaux, as well as model various Markov processes on graded graphs. Numerous operations on Young tableaux have been implemented, including the Robinson-Schensted-Knuth algorithm and the Schützenberger’s jeu de taquin. The software tools also include rich functionality for visualizing various combinatorial objects. Practical relevance: The software package is written in C++, which gives an advantage over traditional approaches using computer algebra systems in terms of efficiency, with the specifics of many problems of asymptotic combinatorics taken into account. The developed software package was used to conduct numerous computer experiments in the process of modeling the dynamics of the behaviour of various objects of asymptotic combinatorics. The modeling results have formed the basis for a number of scientific publications.

Secure data transmission method for the movement of autonomous vehicles

Roza Ravilevna Fatkieva — 2023-12-19

Introduction: Current vehicle monitoring and management systems, as well as methods for route optimization do not permit modeling cyberattacks on the transportation infrastructure nor assessing the disruption of traffic flow. Purpose: To develop a method for transmitting information messages using a discrete situational network device to improve the safety of autonomous vehicles. Results: We develop models of route construction and autonomous vehicle movement. Compared with traditional algorithms for finding the shortest paths, the route optimization for autonomous vehicles is carried out dynamically by evaluating the characteristics of the segment of the path encountered on the route and the time it takes to reach the destination. This is ensured by the proposed method of transmitting information messages in a discrete situational network, where the correction of route information is carried out on the basis of active and passive solvers accompanied by the formation of information messages about the disruptions of the current traffic situation as well as control messages for changing the route of movement. To improve the security of the transmission of information messages, we develop algorithms that ensure the confidentiality and reliability of the transmitted messages. Practical relevance: The results of the study can be used in the design and construction of control systems for autonomous vehicles, as well as for modeling their movement under the conditions of cyberattacks. Owing to the possibility of software implementation of the algorithm to ensure the reliability of transmitted messages, a practical result of protection against denial-of-service attacks is achieved.

Sufficient conditions for the stability of a locally admissible dynamic system with constraints on phase coordinates and controls

Artem Aleksandrovich Efremov — 2023-12-19

Introduction: The synthesis of systems for the stabilization of program motions of objects is an urgent task of control theory. Projection operator methods of mathematical programming are adequate methods of control synthesis for this class of problems. Purpose: To develop the methods for synthesizing locally admissible controls for stabilizing programmed motions of linear and nonlinear dynamic objects with restrictions. Results: The linear stationary control object is specified in the form of a difference operator controlled according to Kalman criterion. For the specified control object, transformations of the projection operator for solving problems of stabilization of program movements with restrictions have been carried out and equations for the transition and stationary states of the system under study have been synthesized. The compression condition is obtained from an estimate of the norm of deviation of the phase coordinates of the system from the stationary state. Based on the principle of compressive mappings, a sufficient condition for the stability of a projection-operator dynamic system with restrictions on phase coordinates and controls is obtained. The derivation of a sufficient stability condition made it possible to determine the projection operator feedback parameter and ensure the stability of the projection operator of the dynamic system obtained earlier. As a control object, a vector-matrix model of a synchronous generator in the Cauchy form was used for the computational experiment. A computational experiment confirmed the theoretical generalizations obtained in the study. Practical relevance: The fulfillment of the inequality condition to determine the feedback parameter guarantees the stability of the projection operator dynamic system.

Information about the authors

Unknown — 2023-12-19