The objective of this paper was to justify the new synthesis method of stabilizing controller for parametrically perturbed systems,which often appear in mobile robots, aircrafts, engineering objects with non-stationary parameters, intellectual control systems with aself-learning etc. Due to the high complexity and uncertainty of these systems, the classical PID controllers are not applicable and soa full information about the object state vector is used. Controllers obtained in this way allow to minimize the integral quality criterionof the system with the worst case parameter perturbation. For this purpose, the methods of differential games and switching systemstheories were applied. Control laws are calculated by using the value function of the corresponding differential game, which can beobtained by solving the Hamilton-Jacobi-Bellman-Isaacs equations. A special set of basic functions was developed to approximate thevalue function and satisfy the boundary conditions. Finally, controller synthesis for a specific object with a nonstationary parameteris given. It significantly exceeds both the linear and fuzzy controllers in terms of quality. In the task of analyzing system qualitativecharacteristics under the worst parametric perturbation, our results are compared to the modern direct collocation methods of optimalcontrol. With the same accuracy, proposed method is two times faster for low order systems. To verify that developed controllers canbe employed in real time applications, we present computational time and memory usage in the end of the article.

Nonlinear discrete (finite-difference) system of equations subject to the influence of a random disturbances of the "white" noise type, which is a difference analog of systems of stochastic differential equations in the Ito form, is considered. The increased interest in such systems is associated with the use of digital control systems, financial mathematics, as well as with the numerical solution of systems of stochastic differential equations. Stability problems are among the main problems of qualitative analysis and synthesis of the systems under consideration. In this case, we mainly study the general problem of stability of the zero equilibrium position, within the framework of which stability is analyzed with respect to all variables that determine the state of the system. To solve it, a discrete-stochastic version of the method of Lyapunov functions has been developed. The central point here is the introduction by N. N. Krasovskii, the concept of the averaged finite difference of a Lyapunov function, for the calculation of which it is sufficient to know only the right-hand sides of the system and the probabilistic characteristics of a random process. In this paper, for the class of systems under consideration, a statement of a more general problem of stability of the zero equilibrium position is given: not for all, but for a given part of the variables defining it. For the case of deterministic systems of ordinary differential equations, the formulation of this problem goes back to the classical works of A. M. Lyapunov and V. V. Rumyantsev. To solve the problem posed, a discrete-stochastic version of the method of Lyapunov functions is used with a corresponding specification of the requirements for Lyapunov functions. In order to expand the capabilities of the method used, along with the main Lyapunov function, an additional (vector, generally speaking) auxiliary function is considered for correcting the region in which the main Lyapunov function is constructed.

The article discusses an original solution for designing an algorithm for selecting the most optimal technical and economic indicators for the operation of generating equipment of thermal power plants, taking into account the requirements of the wholesale electricity market, the day-ahead market and the balancing market. To design an algorithm for controlling generating equipment, the activity of a generating company in the wholesale electricity market was considered in terms of system dynamics. The proposed solution made it possible to select and interpret the state variables of the model, build flow diagrams describing the functioning of a technical-economic system, and visualize cause-and-effect relationships in the form of structured functional dependencies. In this work according to the norms of industry legislation and previously conducted scientific research the most important parameters were identified that form the flows of a dynamic technical and economic system, which are optimization criteria in fact. On the basis of this data, a stream stratification of the production processes of generating companies was carried out and a complex of mathematical models of system dynamics was developed to determine and plan the financial efficiency of the operation of thermal power plants and generating companies. The mathematical apparatus and the algorithm of its functioning are developed on the basis of the digraph of cause-and-effect relationships between the investigated technical and economic indicators. On the basis of the graph of interrelationships of system variables, a system of nonlinear differential equations has been built, which makes it possible to determine planned performance indicators when various technical and economic conditions change. The novelty of the proposed approach is the use of new model solutions based on the mathematical apparatus of system dynamics to represent the proposed model in simulation systems, in industry ERP and MES systems, for the development of DDS.

Mobile robots with walking propulsion devices operating in a "pulling" mode, which, as a rule, are unstable, are considered. It is explained to the jamming of propulsion device due to the orthogonality of the acting force to the virtual displacement of the point of application. The task is to develop such an algorithm for controlling the robot, which consists in purposefully changing the geometric orientation of the propulsion devices controlled by the swing drive, which will ensure stable motion. A method for controlling the orientation of the walking plane with its initial deviation from the programmed position is proposed, based on the implementation of a discrete control algorithm, which provides for the introduction of such a piecewise constant function at each step of the mover, which has received an initial perturbation, which will provide a stable motion mode in a finite number of steps. The change in the orientation of the walking planes of the propellers connected with the steering is controlled, and thereby the direction of movement of the robot body changes in the first step, as in the subsequent ones. The described algorithm assumes the fulfillment of two necessary conditions: the presence of an information-measuring system that controls the orientation of the walking planes and ensuring that the interaction forces of the feet controlled by the steering of the propulsion devices with the supporting surface are sufficient for the absence of slippage. An algorithm for controlling "dependent" propulsion devices (working out the programmed translational motion of the body) is presented, taking into account the fact that their orientation depends on the orientation of the controlled ones, which consists in changing the step length, which should also be determined to ensure movement stability. The main task of controlling "dependent" propulsion devices, which do not change the orientation of their walking plane at the initial moment of time, is to determine the points for setting the feet by changing the step length, in accordance with the established criteria and design constraints, in particular, energy efficiency, maximum efforts in drives, maximum and minimum stride length. The propulsion device will start to work in a stable "pushing" mode at the final stage of motion correction, by performing a sequence of actions. It has been established that the "pulling" mode of the walking propulsion device can be stable, with appropriate control.

Numerical simulation is widespread method to investigate machines and robotic mechanisms in different applications. Program complexes such as MATHLAB Simulink and similar ones are based on the assumption that mechanism kinematics can be described by kinematic scheme and it does not change on time interval of simulation. This is used to generate equations of dynamics automatically and then calculate the mechanism motion. Formulated assumption does not take place for numerous applications cause a set of contact points between mechanism parts is not permanent. This circumstance restricts application area of simulation method and accuracy of investigations. "Physical drives" are software systems for motion simulation of interacting bodies in real time. This restricts the complicity of dynamics model that are used in simulation. The paper describes the simulation method in which mechanism is represented as mechanical system of geometrical bodies. Their motion is defined by Lagrange virtual movement principle. Simulation algorithm generates equations automatically when all contact points between mechanism parts and with external environment are found. Simulation program was been used to investigate the motion of cylindrical shaft in assembly operation. It was been became all scenarios of shaft motion relatively hole. Each of them is defined by initial position of shaft and hole and also mechanical features of assembly device units or features of assembly manipulator servo control system. Simulation algorithm calculates assembly force, forces and moments are acted in mechanism and between mating surfaces. Developed simulation program can be used for choosing of constructive parameters and defining acceptable deviation in initial shaft position.

The article proposes a mathematical model of a hybrid system installed on board of a moving object and represented by an inertial sensor of the vector of specific forces — a three-component newtonometer with orthogonal sensitivity axes and a network of receivers of a navigation satellite system (HSS). The purpose of this hybrid system is the temporal estimations of the nearEarth gravitational field on the trajectory of the object. Within the Newtonian mechanics the possibility of choosing an inertial reference system with a beginning at the center of mass of the Earth is assumed; сomplementary to the PZ-90 (Russia) and WGS-84 (USA) standards, the following are introduced: 1) an ellipsoidal (geodesic) coordinate system, rigidly connected with the solid Earth; 2) two movable accompanying right-angled trihedrals with a common origin as a point whose movement forms the trajectory of the object; the instrument one, is rigidly connected with the object as a solid body, and is thus freely oriented, other one are geographic, and permanently oriented to the cardinal points (East, North, Zenith). In the presentation of kinematics, attention is drawn to the fact that the variability of the absolute linear velocity in inertial space explained by the motion of an object relative to solid Earth and its own rotation is characterized by rotational vectors of relative and portable velocities which identify the vectors of relative and portable angular rotational velocities of the undeformable geographic trihedron and are represented projections on its axis. The causality of the trajectory is determined by Newton’s second law; in projections on the axis of the moving geographic trihedron, component-wise recording of the equations of dynamics is performed, which are resolved with respect to the components of the strength of the gravitational field. It is noted that the previous article by the authors is devoted to the problem of a high-precision estimate of the kinematic parameters of motion equations. In such a context it is indicated that direct calculation of the gravitational field strength requires the convertting of Newtonometer measurements from the instrument trihedron to the geographic one. The required linear transformation for this is constructed considering the possibilities of multiposition of the NSS object. A computational experiment is described and some of its results are presented.

A method has been developed for constructing three-dimensional models of rigid objects on the earth’s surface using one satellite image using the example of railway infrastructure. The method consists in step-by-step processing of satellite images with sequential application of two convolutional neural networks. In the first processing step, a satellite image is segmented by a neural network to select a plurality of objects of predetermined classes. At the second stage of processing with the help of neural network local analysis of image areas detected by results of the first stage of processing is performed. The results of the second processing step are used to estimate the parameters of the 3D model of the object. The possibilities of the method are shown by the example of processing a satellite image of the railway infrastructure. The following classes of informative areas are considered: building, wall edge, roof edge, building shadow, railway infrastructure, car, highway; rails, poles and shadows from poles (taken as reference objects for estimating scaling coefficients in certain directions). An example is given of using the developed method of highlighting typical railway infrastructure objects and for subsequent evaluation of the parameters of a three-dimensional building model partially obscured by trees.