Some aspects of the development of the theory of linear matrix inequalities are considered. A number of results obtained at the initial stage of the development of this theory, both in the development of numerical methods and in obtaining analytical conditions for their solvability, are highlighted. The main attention is focused on the system of linear matrix inequalities arising in solving the absolute stabi lity problem. E. S. Pyatnitskiy and his followers showed that the solvability of this system is a criterion for the existence of a quadratic Lyapunov function and a sufficient condition for absolute stability. The prerequisites leading to this result are considered here. The use of the considered system of inequalities for studying the stability of hybrid systems described by differential inclusions and switching systems is shown. An analysis is given of citing some works of Pyatnitskiy’s school on the theory of stability and the theory of systems of linear matrix inequalities, from which the relevance of the results of these works at the present time follows.

In developing numerical methods, it was first shown in the work of Pyatnitskiy and Skorodinskiy that the solvability problem for a system of linear matrix inequalities reduces to a convex programming problem. An interesting gradient algorithm for finding solutions to such a system is also presented. In analyzing analytical conditions of solvability, an unsolvability criterion for the system of our interest obtained by Kamenetskiy and Pyatnitskiy is noted. In modern terms, this result can be considered as a description of an admissible set in the dual semidefinite programming problem. A similar result is given in the famous book by S. Boyd et al. The paper shows that the result of Boyd et al. is a simple corollary of the unsolvability criterion. Here the unsolvability criterion is generalized and refined.

This article is devoted to research and design of relay systems with control of data sampling. It is shown that the time sample has a significant effect on the parameters of periodic oscillations. We propose an exact method for analyzing periodic modes in digital self-oscillatory control systems with a two-position relay element and a linear piecewise-linear part is proposed. The proposed approach extends the phase hodograph method to the class of systems operating in discrete time. Two approaches have been developed to assess the stability of periodic motions in such systems. In the first approach, a discrete representation of a plant is considered and areas of stability are defined for each possible limit cycle. The sampling of the control system causes a delay in the switching of the relay in a batch mode in comparison with the continuous case. The second approach assumes the replacement of a discrete system by an equivalent continuous system with a time delay. Further, the asymptotic orbital stability of self-oscillations in a relay control system (RCS) with a delay is estimated. We consider the linearization of relay systems with digital control of the input signal. It is also shown that when linearizing a relay element in a digital RCS using a useful signal, the relay transfer ratio will belong to a certain range of values. Synthesis of corrective devices for relay control systems with regard to digital implementation has been reviewed. At the stage of optimization of parameters of the relay control system, the sample is taken into account. The model example demonstrates an advantage in the synthesis of digital technologies. It is shown that when optimizing the controller parameters with regard to time discretization, it was possible to provide the desired frequency of self-oscillations, which ensures the best accuracy of the tracking mode.

The article deals with the problem of nonlinear synthesis of the laws of motion control of an autonomous underwater vehicle (APA) in the vertical plane. The tasks of the synthesis are the output of the underwater vehicle to a predetermined depth at a given speed. Based on the non-linear mathematical model of the APA, the control laws are synthesized by two different approaches: using the classical automatic control theory method, the proportional-integral-differential controller (PID controller), and using the synergetic control theory, the analytical design method for aggregated regulators (ADAR). Classical methods of the theory of automatic control assume a linear or linearized mathematical description of controlled processes and scalar control, which cannot but affect the adequacy of the mathematical description of processes and the efficiency of the developed algorithms. Such structures are ineffective because they do not allow to obtain the necessary stability margin of the system and are approximate. In addition, the scalar control principle often limits the ability to effectively influence the system, ignoring potential control channels. The vector control principle used in the work allows to more effectively influence the system through various control channels. The assumed laws of synergetic control endow the object in question with properties of asymptotic stability in the entire admissible region of change of state variables.

The results of computer simulation of the APA motion, which confirm the achievement of control goals, are considered.

In this paper, two issues are discussed in a PV pumping system. Firstly, an evaluation of super capacitor is studied to reassure the storage of electrical energy and solve the intermittence problem of photovoltaic energy production in dark periods. Secondly, a fuzzy logic controller (FLC) is proposed to stabilize, on the one hand, the DC motor speed around a preferred level by the control of duty cycle of DC buck boost converter. On the other hand, FLC serves to control the charge and discharge of super capacitor according to the sunlight levels and its state of charge. In this framework, a complete photovoltaic pumping system model is simulated in MATLAB Simulink to discuss the run results at different levels of sunshine.

One of the topical areas of research in modern robotics is the problem of local navigation of mobile robots (MR), which ensures the movement of the robot to the target with the bypass of obstacles in the process of movement. The navigation process includes the following steps: mapping the environment, localization of the robot and planning the route leading to the goal. Among the popular methods of local navigation of robots is the method of artificial potential fields (PF). The essence of the PF method is to implement the movement of the MR in the field of "information forces" using the forces of "attraction" to the target position and the forces of "repulsion" from obstacles.

This article addresses the issues of local navigation and motion control of the MR based on the method of PF.

When using traditional attracting potential forces, the structure of virtual forces near the obstacle depends on the distance of the MR from the target, and the robot movement will slow down at the end of the route, which will inevitably lead to an unjustified tightening of the total time of moving the robot to the target position. To eliminate this undesirable effect, the authors propose to use attracting potential fields of special type.

The authors propose new methods of PF allowing to solve the key problems for the control of MR — "traps" (potential pits) and bypass obstacles: the method of two maps of potential fields and the method of "fairway" on the map of potential fields. The methods of "beetle" for solving the problem of bypass obstacles in the condition of the absence of a priori information about the working space of MR are discussed. A modified method of "beetle" having a number of advantages in comparison with classical methods is proposed. 

The article discusses the system of dialogue control manipulation robots. The analysis of the basic methods of automatic speech recognition, speech understanding, dialogue management, voice response synthesis in dialogue systems has been carried out. Three types of dialogue management are considered as "system initiative", "user initiative" and "combined initiative". A system of object-oriented dialog control of a robot based on the theory of finite state machines with using a deep neural network is proposed. The main difference of the proposed system lies in the separate implementation of the dialogue process and robot’s actions, which is close to the pace of natural dialogue control. This method of constructing a dialogue control robot allows system to automatically correct the result of speech recognition, robot’s actions based on tasks. The necessity of correcting the result of speech recognition and robot’s actions may be caused by the users’ accent, working environment noise or incorrect voice commands. The process of correcting speech recognition results and robot’s actions consists of three stages, respectively, in a special mode and a general mode. The special mode allows users to directly control the manipulator by voice commands. The general mode extends the capabilities of users, allowing them to get additional information in real time. At the first stage, continuous speech recognition is built by using a deep neural network, taking into account the accents and speech speeds of various users. Continuous speech recognition is a real-time voice to text conversion. At the second stage, the correction of the speech recognition result by managing the dialogue based on the theory of finite automata. At the third stage, the actions of the robot are corrected depending on the operating state of the robot and the dialogue management process. In order to realize a natural dialogue between users and robots, the problem is solved in creating a small database of possible dialogues and using various training data. In the experiments, the dialogue system is used to control the KUKA manipulator (KRC4 control) to put the desired block in the specified location, implemented in the Python environment using the RoboDK software. The processes and results of experiments confirming the operability of the interactive robot control system are given. A fairly high accuracy (92 %) and an automatic speech recognition rate close to the rate of natural speech were obtained.

Seismic prospecting is one of the crucial components for an effective use of oil and gas fields on offshore. Since the costs of drilling a well on the shelf is hundreds of times more expensive than drilling a well on land, preliminary marine seismic exploration can help avoid unnecessary costs. High quality data of marine seismic surveys can only be obtained from bottom technologies: special bottom stations are lowered into the investigated area of the seabed. These bottom stations collecting direct and reflected acoustic signals (generated on the surface by an acoustic radiator) from the seabed. After all data is recorded, bottom stations are lifted to the surface, the recorded data is downloaded for subsequent interpretation. As a result, based on the obtained data, a 2D or 3D detailed map of the potential oil and gas deposits is complied. The resulting maps are used to determine the exact coordinates of the installation of drilling stations. The most common technology of marine seismic exploration is the use of bottom stations on a halyard rope. First development of this technology began in the 1970s and did not assume the means of automation work with bottom stations. All operations of removal and attachment of rope to station, diving and lifting stations, as well as a number of other operations were performed manually. Nowadays, there has not been any automation in working with stations on the halyard rope. In addition, the use of halyard rope has a number of disadvantages such as: Hooking of halyard rope for obstacles on the sea bottom; The breakage of the halyard rope; The need to have additional space on the vessel to store the halyard rope and all accessories, which leads to the use of larger vessels that can not operate at shallow depths; The halyard rope that is connected to the bottom stations generates a seismic noise, which degrades the quality of the received data; Impossible to conduct seismic prospecting in places with high shipping traffic. Developed over the past few years, a new Russian technology of marine seismic exploration GEONOD allows us easily solve many of mentioned problems. Many of these problems do not rise at all, since the GEONODE technology does not use halyards, and the work is carried out by the autonomous self-popup bottom stations (ASDS). In this paper a number of problems on applied mechanics and control in connection with technology GEONOD are considering.