The problem of constructing common solutions to terminal control problems of nonlinear systems is considered here. Previously proven positions are used that the optimal trajectory is an envelope of a parametric family of surfaces (a parametric family of singular curves), and that optimal control can be found on this family. The fact that at each point of the optimal trajectory the vector-function of Lagrange factors is tangent to it, but also tangent to the singular curve, is played out here. A constructive method of constructing singular curves based on conditional separation of variables in the Hamilton-Jacobi equation is given. The " free" parameters of singular curves are based on the condition of minimizing the terminal functionality, which avoids an explicit solution to the boundary problem for a class of nonlinear dynamic systems, and simplifies computational algorithms. Singular curves are described by a reduced (abbreviated) mathematical model. Thus, to synthesize the law of optimal control, we must use the complete (original) mathematical model of the dynamic system, but to calculate it at one time or another, it is enough reduced model. This consideration defines the principle of informational dualism. An illustrative example is given. It has been shown that this approach can be used to solve some classes of differential games.

We consider the problem of organizing the control process in adaptive systems, in which it is required to ensure the preservation of the optimal state of the system when external conditions change. The analysis of existing approaches to its solution showed grea t promise in the synergistic effect of using machine learning and computer vision technologies. A system analysis of the management process using these technologies has been carried out. Its prim ary objects have been formalized, and the research task has been set. To solve it, a method is proposed, the novelty of which lies in the usage of machine learning and computer vision technologies for recognizing and obtaining a compresse d idea of the state of the observed environment, objects of observation and control. And also, the choice of the control team was unified, based on three approaches: a system of rules, a neural network with classification, and machine learning with reinforcement. All stages of the method are formalized, and the possibility of using machine learning technologies (neural networks) for their i mplementation is theoretically substantiated. The practical significance of the developed method lies in the possibility of automating the activities of a human operator in complex adaptive systems through the use of machine learning and computer vision technologies. The method was tested on the example of an adaptive running platform control system. Experimental stu dies have been carried out to assess the efficiency of the method, its perfor mance and accuracy of work in determining the state of objects of observation using computer vision technologies. The result of the work is the proven high efficiency of the proposed approach. The usage of computer vision and machine learning technologies made it pos sible not only to control the adaptive running platform but also to determine critical situations (falling or sudden stop of a person), which increases the safety of the control system, expands its functionality in monitoring the state of the environment and objec ts of observation

A distributed electrical network (DEN) with a voltage of 0.4 kV operating in an unsymmetric mode is considered as an object of automated control. The problem of identification of places and control of unauthorized power take-offs (UPTO) in the DEN in the conditions of functioning of the automated system of control and accounting of electricity (ACMSE) is formulated. The primary source information for its solution is the data obtained from the head and subscriber electricity meters by synchronized remote measurements at discrete points in time. This problem belongs to the class of problems in which there is significant uncertainty about the current state of the object under study and the parameters of external disturbing influences, which are unauthorized consumers of electricity. Under these conditions, the primary measurement data on the characteristics of the network subscribers’ loads received from the counters of the automated system and recorded in its database are insufficient to solve the problem under consideration. In this regard, in order to reduce the level of uncertainty and obtain additional necessary information about the state of the object, the concept of a virtual DEN model is introduced into consideration, designed to describe its desired state, which is determined by the absence of these external random disturbances in the network. A new method for solving the formulated problem is proposed, based on the concept of a virtual DEN model. The conditions for identifying the current state of the DEN have been obtained. For this purpose, the desired input phase currents of the virtual network are determined by introducing equivalent complex resistances of certain parts of the three-phase network. The vectors of the effective values of currents and voltages on the loads of subscribers and inter-subscriber sections of the virtual network are identified. Criterion functions are introduced that determine the deviations of the corresponding components of the stress vectors on the loads of subscribers of the real DEN and its virtual model. Based on these functions, an identification criterion and an algorithm for monitoring unauthorized power take-offs in a three-phase distributed network are formulated. The obtained results are oriented for the creation of algorithmic and special software for the subsystem of automated control of UPTO as part of the ACMSE.

A method is proposed for solving the problem of planning the movement of a group of ground-based robotic platforms (UGR) with the requirement to maintain a given formation of the system in the presence of stationary obstacles and sources of disturbances. The task of calculating the trajectory of the leading UGR, coupled with the use of a displacement planner and subsequent smoothing of the resulting trajectory according to the method considered in the first part of this work, is highlighted. The trajectories of the slaved elements of the group are determined by constructing offset spatial curves along which these elements should move, taking into account a given configuration or the requirements of preserving some average kinematic parameters of the elements along their trajectory. To solve the problem of evading the group from the influence of sources of disturbances, the method considered in the previous works of the authors is proposed. It is based on the calculation of the probabilities of successful passage of the elements of the group of their trajectories. These probabilities can be found after evaluating the parameters of the characteristic probability functions of the sources describing the nature of their impact on moving objects over small time intervals. In this article, this method is modified by additional optimization of the resulting spatial trajectory along the length for each UGR, taking into account a given degree of permissible deviation from the original curve. A technique has been developed that allows to find the target trajectories of the leading and driven UGR of the group, the probability of successful passage of which exceeds the specified target value. The methodology is generalized to the case when the optimization criterion is the probability of successful completion of only part of the UGR group. Simulation results confirms the effectiveness of the proposed method of planning the trajectories of robots forming a group in the field of repeller sources.

Currently, various possibilities for obtaining energy from renewable sources, in particular, flows of water or wind, are intensively investigated. The most widely used wind power harvesters are those where the working element rotates (a propeller or a vertical axis turbine, such as a Darrieus or Savonius rotor). However, the possibility of using the flow-induced oscillations of elastic structures in order to generate energy is now actively considered. One of the types of such oscillations is galloping, i.e. vibrations of bluff bodies in the direction perpendicular to the incident flow. The occurrence of galloping is due to the fact that aerodynamic forces acting on a bluff body, under certain conditions, create a negative damping. In this paper, we consider a mechanical system consisting of three bodies that can move in a direction perpendicular to the flow. One of these bodies is a square prism, and the other two are material points. The bodies are connected in series with each other and with a fixed support by linear elastic springs. A permanent magnet is rigidly connected to the prism. This magnet moves inside an induction coil. As a result, an electric current is generated in the electrical circuit connected to the coil. For such installations, on the one hand, it is required that galloping occurs at the lowest possible flow speed. On the other hand, at high flow speeds, it is necessary to reduce the amplitude of oscillations so that the device would not be damaged. The influence of the system parameters (in particular, the spring stiffness coefficients) on the stability of the equilibrium and on the characteristics of periodic solutions is studied. It is shown that by changing the stiffness of the springs, it is possible to significantly expand the range of flow speeds where the galloping occurs. The amplitudes of oscillations of bodies increase as the flow speed grows. In order to increase the limit flow speed, at which the amplitudes of oscillations start exceeding the maximum permissible value, a regulating algorithm is proposed. Within the framework of this algorithm, the displacement of one of mass points with respect to the prism is locked/unlocked depending on the current flow speed.