The method of a research of roughness of dynamic systems based on a concept of roughness according to Andronov—Pontryagin and named with "method of topological roughness" is considered. The concepts "roughness" and "bifurcation" of dynamic systems formulated at a dawn of formation of the scientific direction of mathematics — topology, are given by the great French scientist A. Poincare. Also the concept of roughness according to Andronov—Pontryagin is formulated and conditions of accessibility of required roughness of a dynamic system are defined. The definitions of concepts of the maximum roughness and minimum non roughness of dynamic systems entered by the author earlier are given. The corresponding theorems of necessary and sufficient conditions of accessibility of the maximum roughness and the minimum non roughness and also emergence of bifurcations of topological structures of dynamic systems, which were proved in the fundamental works of the author given in the list of references are formulated. At the same time it is claimed that sets of rough and not rough systems make roughnesses of a set, continuous on an indicator. As a roughness indicator in a method the number of conditionality of a matrix of reduction to a diagonal (quasidiagonal) type of a matrix of Jacobi in special points of phase space of a system is used. The method allows to controling roughness of control systems on the basis of the theorem formulated with use of the matrix equation of Sylvester and proved in works of the author which is also provided in this work. The main stages of researches of roughness and bifurcations of systems by means of the considered method are formulated in the form of the corresponding algorithm. In work questions of synergetic systems and chaos (strange attractors) in them, founders of science of synergetics — H. Haken, I. Prigozhin are briefly stated. The method can be used for researches of roughness and bifurcations of dynamic systems and also synergetic systems and chaos of the different physical nature. In works of the author the method is approved on examples of many synergetic systems, such as Lorenz attractors and Rössler, Belousov-Zhabotinsky’s systems, Chua, "predator-prey", Henon, Hopf’s bifurcations, etc. In this work of a possibility of a method are illustrated on examples of synergetic system Chua and also a technical system in the form of the nonlinear servomechanism.

Robust algorithms for synchronizing a network of nonlinear plants with time delay are proposed. A network of control plants in the Lurie form with Lipshets nonlinearities is considered taking into account the time delay under the conditions of constantly operating external uncontrolled disturbances. Taking into account nonlinear and delayed components in mathematical models of plants makes the system close to real. In each local network plant, the input of the leading subsystem is monitored. Dynamic compensation of disturbances in each of the plants is carried out by extracting a signal that carries information about these disturbances, and then suppressing it using an auxiliary circuit and two observers of the system variables. The use of variable observers is due to the need to obtain estimates of the derivatives of the system variables, the measurement of which is not available. A numerical example of the synchronization of a network consisting of four nonlinear control plants with a delay in state under conditions of uncertainty of the parameters of their mathematical models and the action of external bounded disturbances is considered. For the network of plants, the proposed control algorithms are applied. The numerical simulation in the Simulink Matlab package was carried out, the graphs of transient processes for tracking errors for each of the four subsystems are presented. The simulation results confirmed the theoretical conclusions and showed good performance of the proposed synchronization algorithms in the conditions of constantly operating external and internal disturbances.

We consider the problems of implementing control actions on the object in the ergatic system "man—machine", combined through the control body of the human-machine interface apparatus, in order to effectively distribute the control functions between the human operator and the system’s control automat. Peculiarities of technical realization of operating influences on object ergatic system using the apparatus combines new type of control, through a management body of which is communication between a human operator and automatic system. The principle of construction of joint control devices is shown with the help of pictorial models of discrete and continuous operation devices that have an Electromechanical drive device that reacts to signals from the control machine due to the movement of the control body. The devices provide for the possibility of moving the control body and the muscular effort of the human operator. For the verbal model of actions and responses of the human operator and the machine, adopted in engineering psychology, mathematical models of joint control of the object of the ergatic system, describing the movements of the control body, are developed. The mathematical model of the response of the controlled object of the system is represented by a normal system of ordinary differential equations. As a result of composition of models of actions and reactions for the system "man—machine" obtained a finite set of incomplete representations of the elementary movements depicting point in the state space, which is constructed for controlled movement of an object in a sequence of elementary movements. Virtual discrete control signals corresponding to specific positions of the control bodies of the joint control devices of the human-machine interface of the system, which are used for sequential transitions from one elementary movement to another, are determined. The results of approbation of joint traffic control of vessels using a mathematical model of actions and responses in full-scale experiments with increased requirements for safety and accuracy of movement are presented. Conclusions are formulated about the effectiveness of the use of Sov-local management in transport ergatic systems "man—machine". It is shown that in this case, the advantages of management partners are most used and combined.

To the present days, the scientific direction of computer science metaphorically called "Artificial Intelligence" (AI) as well as corresponding information technologies is becoming of strategic value as the theoretical and the technological basis of digital economy of the 21-th century. The leading economies of the world invest huge money in R&D of AI area. In many countries, e.g. in the USA and Europe the standardization effort in AI scope are initiated. In Russia, the President issued a decree "On development of artificial Intelligence in the Russian Federation" dated 10 October 2019. One must acknowledge, however, that up to the current days there is no common opinion, among AI scientists and engineers, on what is the research subject of AI, which are its R&D goals, scientific contents, methodology and technologies. In the paper, Artificial Intelligence is considered as a scientific discipline that is a section of Computer Science. In it, the knowledge acts as the main research subject and its scientific contents is composed of methodologies, methods and algorithms of the three AI subsections those are knowledge acquisition, knowledge representation and knowledge usage for decision making. This point of view is justified in the paper by analysis of AI historical issues, composition of its scientific topics and technologies. The aforementioned analysis is underway with regard to the basic R&D problems that should be in the focus of the AI roadmap of the Russian scientific and industry communities in context of the Presidential decree on the strategy of the development of Artificial Intelligence in Russian Federation.

The paper presents the description of developed hardware, algorithms and software of the system for measuring of radial clearances between stator and blade tips in the compressor of gas-turbine engine. The measuring system implements the method with self-compensation of temperature effects on the eddy-current single-coil sensor with a sensitive element in the form of a conductor segment. Due to the self-compensation the number of used sensors and related mounting holes in the power plant stator was reduced. The core operations of the self-compensation are realized in real time on hardware-and-software level. This makes it possible to use the system for the detection of dangerous states of gas-turbine engines during power plants operation. The previously unexplored phenomenon of "not-complete compensation" of temperature effects is considered. The phenomenon is related to the special features of the conversion of the single-coil eddy-current sensor’s informative parameter in the measuring circuit. It manifests in the difference of conversion functions of the system’s measuring channels under normal and nominal temperatures. The paper provides the way of the effect elimination by means of program correction. The results of experimental researches of the working model of the measuring system are given. They characterize the metrological appropriateness and efficiency of the system. The experimentally obtained calibration characteristic approximated by polynomial function was used to determine the systematic part of the error as a difference between the given and the calculated radial clearance. The random error was evaluated by the deviation of measured codes from an average value in the sample that was obtained at the specified value of radial clearance for the fixed blade’s position relatively to the sensor’s sensitive element. The efficiency of the working model was evaluated on the laboratory equipment during the rotation of the electrically driven compressor wheel. The quantitative estimates of speed and accuracy of the working model of the measuring system were obtained during experimental researches. They confirmed the possibility of using the system for the detection of dangerous states of gas-turbine engines applied in the electrical power industry.

Stereotactic operations are actively used in modern minimally invasive medicine. During such operations, a flexible needle is inserted into the internal organs, with the help of which a biopsy or a local treatment is performed. The application of such approaches in neurosurgery requires the accurate positioning of the needle tip at the target point. The present study is related to the creation of a robotic system that delivers the needle to a given point and uses drives compatible with magnetic resonance imaging devices that visualize the position of the needle. In this paper, we propose a finite-dimensional mathematical model of a mechatronic system that uses a piezoelectric drive (PED) to move the needle (cannula) along a given line. To describe the contact between the cannula and the soft tissue, a mathematical model of their interaction is developed. The contact problem involving two processes occurring during the introduction of the needle into the biological tissue is solved: the introduction of a rigid (compared to the tissue) indenter and its retention at a certain depth. Relaxation properties of the tissue are taken into account. The behavior of tissue is described using a phenomenological approach based on a modified Kelvin-Voigt model. This allowed for reducing the solution of the contact problem to the integration of a system of ordinary differential equations. One of recognized ways to develop medical robotic systems is to test their functioning using phantoms of biological tissues. For this purpose, a phantom of a porcine brain based on agar-agar is made. Experiments are carried out to indent a standard cannula into the phantom body. Based on the obtained experimental data, the parameters of the contact model are identified. An algorithm is proposed for controlling the PED frequency, which ensures the introduction of the cannula into the soft biological tissue to a given depth. Numerical simulation of the insertion of the cannula into the soft tissue using this algorithm is performed. The influence of feedback coefficients on the position and speed of the indenter on the nature of the implementation process is investigated.

The problem of a two-wheeled balancing robot control is the scope of this research. Such plants are unstable, and their mathematical description includes several types of nonlinearities: rising to the power of the robot state coordinates and the trigonometric functions application. Moreover, such objects are non-stationary, i.e. they change the values of their parameters (mass, position of the center of mass and the coefficient of friction of the wheels on the road surface). The existing control systems of balancing robots (in most cases, these are optimal LQ algorithms and PID controllers) are not able to provide compensation of significant parametric disturbances, although they have a certain robustness with respect to them. All above mentioned problems make it reasonable to apply adaptive control algorithms to such plants. So we propose an adaptive control system based on the second Lyapunov method and the use of a reference model. To build such an adaptive controller in this study: 1) a mathematical description of the reference dynamics of the robot (at nominal values of its parameters) is made; 2) the LQ regulator parameters are calculated according to the theory of optimal control; 3) an adaptation loop of the parameters of the obtained controller, which does not require the plant model, is developed on the basis of the second Lyapunov method. The resulting adaptation loop is supplemented with a variable step size, which is recalculated on the basis of data about the current and previous values of the reference of the robot state coordinates. Experimental validation of the adaptive controller is made with the help of both mathematical and physical models of the balancing robot. Considering the experiments with the mathematical model, the mass of the robot is increased from two to 13.5 times. As for the physical model, the mass is doubled. The experimental results show the efficiency of the developed system in comparison with the optimal LQ-regulator in terms of the integral quadratic transient quality index.