The paper considers the problem of constructing null-controllable sets for stationary linear discrete-time systems with a summary constraint on vector control, i.e. sets of those initial states from which the system can be transferred to the origin in a fixed number of steps. The generalized Minkowski sum of convex compacta is introduced to solve this problem. The main properties of this operation are studied, in particular, its connection with the classical Minkowski sum is demonstrated. It is proved that each null-controllable set can be represented as a generalized Minkowski sum of linear mappings of a set of constraints on control actions. Based on this fact, expressions for the support point, support function and the normal cone of nullcontrollable sets are explicitly constructed. Conditions are formulated under which these sets retain compactness, convexity, and relatively strict convexity. The effectiveness of the developed theoretical results is tested for a three-dimensional satellite motion control system. It is assumed that the spacecraft is a material point whose movement occurs in a small neighborhood of a circular orbit. Control is carried out by low-thrust engines and has a relay nature, which makes it possible to consider the state vector only at moments when the control changes. For the discretized in this way system, numerical simulation of the null-controllable sets is carried out for various parameter values. The results are presented graphically.

The paper is devoted to the problem of interval observers design for technical systems described by non-stationary linear dynamic equations under unmatched disturbances and measurement noise. The problem is to design the observer with fewer dimensions than that of the original system; such an observer must generate upper and lower bounds of admissible values of the prescribed linear function of the original system state vector. To construct the interval observer, the reduced-order model of the original system insensitive to the disturbances is designed. It is assumed that the reduced-order model is realized in the diagonal Jordan canonical form. The main advantage of such a form is that it has the main properties which are necessary to the interval observer design and to take into account non-stationarity of the system. As a result, the model is stationary and nonlinear. Besides, such a model allows to reduce limitations on the system under which the interval observer can be designed. The interval observer consists of two subsystems: the first one generates the lower bound, the second one the upper bound. The relations describing both subsystems are given. To take into account the nonlinearities, the notion of monotony of the output variables entering in the nonlinear term on the model is introduced. This notion allows finding out how the upper and lower bounds of these variables will appear in the interval observer. To reduce the interval width, the sliding mode observer is suggested to use. Such an observer is intended to estimate the value of the external disturbances; this estimate is used then in the interval observer to compensate the disturbances. Theoretical results are illustrated by practical example of the electric servoactuator for which the interval observer is designed.

The work is devoted to the problem of controlling the movement of robots in a social environment in crowded places. An algorithm for planning the movement of mobile robots among stationary and moving obstacles using reinforcement learning has been developed and studied. The GA3C-CADRL algorithm was chosen as a prototype, in which the robot and obstacles are considered as interacting agents. The algorithm was modified and implemented using an LSTM recurrent neural network to approximate the value and policy functions simultaneously. The neural network was trained on a common data set obtained through actor-critic reinforcement learning. Additionally, the rl_ planner and social_msgs components have been developed to integrate a pre-trained planning algorithm into a robot control system on the Robot Operating System 2 software platform. The first component implements processing of input data, calculating the robot’s actions and generating the required speed of movement, and the second contains messages with information about neighboring agents. To test the algorithm, experiments were carried out with three different scenarios: – with static obstacles, – mixed, – with dynamic agents. The number of episodes for training the algorithm with 5 agents reached 1,500,000. Simulation of the movement of a robot on two tracks in the environment Gazebo showed that in conditions of static obstacles the robot reaches the goal in the shortest time. In the presence of dynamic obstacles, the time increased by 2 times due to collision avoidance. At the same time, the distance to the nearest agent remained safe (more than 2 meters).

A key factor in enhancing the efficiency of navigation systems across various domains is the development of novel approaches for determining the location of mobile objects within heterogeneous signal propagation environments. The non-uniform nature of wireless environments necessitates a comprehensive positioning strategy, integrating diverse technologies, algorithms, and data processing methods. Wireless positioning relies on the presence of mobile nodes, whose locations must be determined relative to fixed reference wireless nodes (base stations) with known and precise positions within the adopted coordinate system. This research aims to develop an algorithm for estimating the location of a mobile object in a heterogeneous environment utilizing range measurement and trilateration techniques. The paper presents a process for determining the coordinates of a mobile object based on measuring signal propagation time between network nodes and employing a triangulation algorithm to calculate the agent’s coordinates. To pinpoint the agent’s location using measured distances from base stations, the research employs geometric methods for estimating the agent’s location, the least squares method, and the received signal strength indicator, depending on the quantity of data received from various base stations. Numerical studies reveal that the developed comprehensive algorithm for determining the agent’s location enables the estimation of its coordinates in a two-dimensional heterogeneous environment when measurements are available from two or more base stations. The obtained results hold potential for application in the design of positioning systems for wireless sensor networks, utilized in tasks involving monitoring, navigation, logistics, and other areas.

Most vehicles: cars, buses, motorcycles, airplanes, etc. are currently equipped with an automated braking control system. Its purpose is to shorten the braking distance while maintaining vehicle stability and controllability. The presence in the design of a wheeled vehicle of an automated braking control system leads to the need to simulate movement taking into account this system. Because the real change in time of vehicle motion parameters is continuous, and the calculated is discrete, the problem of verifying such models arises. The purpose of this work is to maintain solution accuracy and ensure solution stability of equations in the numerical simulation of the vehicle movement with an automated braking control system. A selection has been made of a validated mathematical model of vehicle motion equipped with an automated braking control system and its software implementation. Calculation experiments were carried out to verify the mathematical model of vehicle movement. Its motion parameters in different modes were obtained and their correspondence to experimental values was determined. It has been established that the integration step of the calculated motion parameters significantly affects at the calculating results then vehicle trajectory parameters in braking modes (straight-line and curvilinear). The direction of this influence is ambiguous. It is determined that the solution instability is given by: the equation for calculating the longitudinal wheel slip and the related equation of the every braking wheel. This is especially true for small value of slip in the wheels-road contact, which are critical in accordance with the algorithms automated control system. A method for obtaining the objective function as a result of solving the problem of choosing a integrating step for the motion parameters of a wheeled vehicle with an automated braking control system has been developed and implemented while ensuring the necessary solution accuracy and solution stability. The study results can be used in design modeling of the vehicles movement on elastic wheels. 

This study investigates the problem of the spatial monotonic rendezvous of two spacecraft, initially orbiting Mars in distinct circular paths. The maneuvering spacecraft is tasked to rendezvous with a passive spacecraft, which strictly adheres to its orbit without executing any maneuvers. The aim of this study is to numerically model and analyze the conditions that facilitate the spatial monotonic approach of these spacecraft. The mathematical modeling of their relative motion employs the linearized Hill-Clohessy-Wiltshire equations, which have a known analytical solution when the passive spacecraft sustains a constant orbital motion. The analysis involves using expressions for the first and second derivatives of the distance between the spacecraft, calculated through differential calculus of functions of several variables. The boundary problem of achieving a rendezvous between the maneuvering and passive satellites in Mars orbit is addressed by utilizing solutions to the linearized Hill-Clohessy-Wiltshire equations. This study also explores the use of a control strategy based on a PD (Proportional-Derivative) regulator integrated with a genetic algorithm to ensure precise and optimal monotonic rendezvous. From a practical standpoint, this rendezvous could facilitate the remote recharging of the passive satellite’s battery, where the maneuvering satellite employs an onboard LED lamp to beam light to the solar panels of the passive satellite. The light transmission device consists of a parabolic emitter with a powerful LED lamp positioned at its focal point, enhancing the efficiency of the energy transfer.