A group of mobile agents on a straight line is considered. Agents are understood as numbered points that can change their position. It is assumed that the dynamics of agents is modeled by second-order integrators, with each agent receiving information from one of its left and one of its right neighbors (not necessarily nearest neighbors). It is required to provide a given nonlinear-uniform (uniform with respect to a prescribed nonlinear function) deployment of agents on a straight line segment. It is worth mentioning that, in numerous applications such as optic, acoustics, physiology, information theory, thermodynamics, etc., instead of linear scale, nonlinear ones (for instance, logarithmic) are used. In addition, it should be noted that an important class of formation control problems is synchronization of processes with respect to certain functions of phase coordinates. To solve the stated problem, nonlinear decentralized protocols are proposed. The conditions on the control parameters are determined, under which the agents converge to the required positions. The robustness of the constructed control protocols with respect to communication delay and network topology switching (replacing chosen neighbors by the other ones) is investigated. In this case, it is assumed that information about the magnitude of the delay and about the switching law may be absent. It is shown that for any constant non-negative delay and any admissible law for switching connections, a given deployment of agents is guaranteed. The proofs of the stated statements are based on the application of the Lyapunov direct method and a special form of the decomposition method. Original constructions of Lyapunov functions and Lyapunov—Krasovskii functionals are used. The results of numerical simulation are presented, confirming the obtained theoretical conclusions.

For linear stationary one-dimensional control objects, the inverse problem of analytical design of optimal controller (ADOC) is considered, which consists in determining the weight coefficients of the quadratic functional of the optimality of the control process, providing a closed control system with the set values of primary quality indicators (static error, transient time and overshoot). It is analyzed in relation to both the ADOC problem in the Letov-Kalman formulation. A method of its solution is proposed based on the transformation of the ADOR problem to a canonical form in which the control object is described by a matrix differential equation in the Frobenius form, and the quality functional is defined as an integral of the sum of the products of the canonical phase coordinates of the object with the corresponding weight coefficients, as well as the square of the control signal. It is shown that the solution of the inverse canonical ADOC Letov-Kalman problem is determined by the values of only three non-zero weighting coefficients of the criterion, and one of them has a single value. The values of the other two coefficients are proposed to be found in the process of modeling the synthesized optimal control system from the conditions of ensuring for it the values of primary quality indicators no more than the specified ones. The results obtained, presented in the form of Theorems 1 and 2, are extended to the synthesis of astatic control systems, in which an additional integrator is connected to the plant output to obtain astaticism. Since such an "extended" control object is described using a state vector that has the first two phase coordinates of the canonical form, the synthesis of the optimal system is carried out without converting the object description to the canonical form of the phase variable and vice versa. The construction of an astatic control system is illustrated by an example.

The paper discusses the development of a platform for distributed energy resources management based on digital twins. The platform use cases include demand response, electric vehicle charging, peer-to-peer energy trading, storage scheduling, virtual power plant, and so on. Thanks to the digital twin, the platform can perform the use cases controlling either real operation-stage equipment or virtual design-stage simulation models. The platform offers mass distributed energy resources owners and operators to improve the power supply quality (including stability), reduce costs (including transaction overhead), and gain emerging market opportunities (including participation in various aggregators' programs). Software and equipment vendors are interested in the platform's capability to quickly assemble distributed energy management systems almost without programming. The digital twin and the platform are designed with the viewpoint-based approach established by the international systems engineering standard ISO/IEC/IEEE 42010. The typical power system digital twin architecture is described. The major kinds of mathematical models as part of digital twins are presented: physical models based on numerical solutions of differential equations and optimization problems, machine learning models, knowledge-based models. The interoperability of such heterogeneous models is ensured on the basis of the ontological model of distributed energy. The platform architecture is represented from three key viewpoints: functional, information, and software. To formalize and ultimately automate the integration of heterogeneous models, we propose novel mathematical methods of model-based system engineering based on category theory, including universal constructions and the multicomma. The multicomma category is shown to be constructed using standard product, exponent, and pushout constructions, which makes it possible to establish a number of its practically significant properties.

Today, climate change, the limited availability of natural resources, coupled with an increase in total consumption, constantly increase the requirements for agricultural facilities. One of the urgent tasks in the field of robotic agricultural automation systems is the task of developing methods and approaches to precise irrigation and fertilization, characterized by a high level of autonomy, a wide working area and the ability to perform tasks in a continuous mode. Thus, within this study, a method of precise fertilizer application was proposed, based on the use of a group of heterogeneous robotic means. The heterogeneous composition of the system provides the possibility of replacing batteries and replenishing the solution tanks of the robotic means, which carry out the application of fertilizers in the areas of operations through the use of specialized ground robots. Approbation of the proposed method was carried out in the Gazebo virtual environment on the example of a garden of columnar apple trees with an area of several hectares, which includes more than 8000 trees. The final consolidated assessment of the proposed solution, averaged over all selected groups of tasks, was 74.6 %. The average proportion of trees missed in the experiment was: 7.8 %. According to the results of the experiment, the proposed solution allows not only to successfully carry out the tasks of fertilizing large agricultural facilities in a continuous mode of operation, but also to carry out autonomous identification of potential zones where fertilization is required.

This article is about the technologies of simulation modeling of mobile robotic complexes. The basic demands for a simulation environment are defined such as realistic results, open-source code, extensibility, performance of system, possibility of usage of low-level code for simulation. Moreover, the most significant characteristics for physics engines are described in the article, specifically solid-state physics, torque setup, stability of "axle" connection, stability of the simulated many-body system. The frequently used physics engines such as PhysX, ODE, MuJoCo, Bullet, Havok are analyzed and the search of modeling services is made in order to make the comparative table. The platform Unity is in focus of this work to show its abilities in modeling of mechanical and electronic parts of mobile robots. The aim of this work is minimizing mobile robots development outgoings. Programming product is given as result of simulation modeling of robotic complexes. The Unity platform is used as the engine for development of simulation tools for mechanical and electronic parts of robotic complex. The set of tools based on Unity engine is developed in order to create virtual models of mobile robots. The architecture of the project was developed in order to determine aspects of creating mobile robots in a simulation modeling environment. The logic of scripts for modeling the solid-state physics, kinematic chains and joints with different degrees of freedom is presented as a result of developing architecture of the project. The package was tested, a model of a mobile four-wheeled robotic platform was built as a result of the test.

The paper considers the task for simulation of final stage spacecraft landing on the Moon in virtual environment systems. To solve this task, methods and algorithms are proposed for the lunar module motion control with the implementation of fast attitude maneuvers and minimum fuel consumption during its deceleration. The spacecraft control is based on virtual sensors feedback and makes it possible to implement stabilization, reorientation, deceleration, maneuvers, hovering and soft landing of the spacecraft on the Moon. The work involves virtual reality technologies with the implementation of human interaction with a computer-synthesized environment. In this case, to control the spacecraft in manual mode, virtual hands are used that copy the movements of the operator’s hands and act on the elements of virtual controls (joystick, buttons, etc.) inside the spacecraft model. Approbation of methods and algorithms proposed in the paper was carried out in our software package of virtual environment system on the example for landing simulation of virtual model Orel spacecraft in semi-automatic mode. In this software package the spacecraft control in manual mode is implemented by data which transit from Oculus Rift CV1 VR headset and Oculus Touch controllers designed for tracking the operator’s head and hands, as well as displaying synthesized stereopair to his eyes. The simulation of spacecraft landing on the Moon was carried out for stages that begin immediately after the basic deceleration at an altitude of about 2 km and including the free fall of the lunar vehicle, its verticalization, horizontal and vertical deceleration, hovering, and soft landing. The results of approbation showed the adequacy and quality of the solutions proposed in the paper, which can be further used to create simulators designed to train cosmonauts how to control a spacecraft during landing on the Moon.