Abstract A new method for attenuation of external unknown bounded disturbances in linear dynamical systems with known parameters is proposed. In contrast to the well known results, the developed static control law ensures that the phase trajectories of the system are located in an ellipsoid, which is close enough to the ball in which the initial conditions are located, as well as provides the best control accuracy in the steady state. To solve the problem, the method of Lyapunov functions and the technique of linear matrix inequalities are used. The linear matrix inequalities allow one to find optimal controller. In addition to the solvability of linear matrix inequalities, a matrix search scheme is proposed that provides the smallest ellipsoid in transition mode and steady state with a small error. The proposed control scheme extends to control linear systems under conditions of large disturbances, for the attenuation of which the integral control law is used. Comparative examples of the proposed method and the method of invariant ellipsoids are given. It is shown that under certain conditions the phase trajectories of a closed-loop system obtained on the basis of the invariant ellipsoid method are close to the boundaries of the smallest ellipsoid for the transition mode, while the obtained control law guarantees the convergence of phase trajectories to the smallest ellipsoid in the steady state. 

We analyze the known problems of optimal control of speed (OCS) and methods for their solution. It is shown that the use of the one criteria in these tasks (the speed criterion) does not sufficiently reflect real situations. The solution of the OCS problem in real situations leads to a deviation from the nominal or optimal values of a number of other indicators. Proceeding from this, a generalization of the OCS problem is considered taking into account other indicators as a criterion for optimal control. In this aspect, three generalized statements of the OCS problem are analyzed, where in the first formulation, the OCS task is expanded with additional constraints on other indicators; in the second setting, other indicators were used as criteria alongside with the performance criterion; and in the third formulation, the expansion of the formulation is considered with the introduction of restrictions also on the criteria themselves, formed from other measured indicators. In the article, the most general — the third multicriteria problem is considered as the subject of research and the necessary condition for optimality of its solution in the form of the maximum principle is obtained. A traditional and iterative scheme for solving the generalized by OCS problem is presented, based on the obtained necessary optimality condition, in contrast to the traditional criteria, which are also dependent on the degree of preference. 

The parameters of the object of regulation during operation due to various reasons may vary. These changes can lead to a change in the performance indicators of the automatic system, as well as its stability. This article proposes an approach to determine the range of acceptable values of the parameters of the control object of an automatic system with a PID controller, in which the system will remain stable. Thus, the problem arises of analyzing an automatic control system given not only by a single model with clearly defined parameters, but by a family of models belonging to a given set — the task of robust regulation. The search for ranges in which the parameters of the regulated object can change is based on the solution of the nonlinear programming problem in this paper. The conclusion of the objective function and constraint system using the theorem of V. L. Kharitonova on the robust stability of linear systems. The main idea is that each parameter of the regulatory object can be changed by some value hi1 in the direction of decrease and by hi2 — in the direction of increase. Replacing the notation used in the theorem of V. L. Kharitonov, the lower and upper boundaries of the change of parameters by the sum and difference of the nominal values of the parameters and the corresponding hi1, hi2, we get a system of restrictions. Moreover, for the stability of Kharitonov polynomials, it is most convenient to use the Lienar-Shipar criterion. The larger the values of hi1, hi2, the wider the ranges of variation of the parameters, and the smaller the inverse of the sum of these values. Based on this statement, the objective function is formed. It should be noted that the condition for the considered automatic system on which the proposed approach is based is sufficient, but not necessary, since the coefficients of the polynomial are interdependent. An example with the help of which the proposed approach is demonstrated is considered. This approach can also be applied to other linear systems for which theconditions of V. L. Kharitonova. 

The paper deals with the development of algorithms for calculating the high-order moments of the noise of noisy signals and their use in the analysis of the technical condition of industrial facilities. It is shown that for monitoring and controlling the onset of an emergency at oil production facilities, random vibration signals are used, which, in addition to the noise caused by external factors at the time of the initiation of the malfunction, also contain additional noise. The characteristics of this noise contain certain information about the technical condition of the drilling rig. Earlier, algorithms were developed for calculating the variance, standard deviation, and density distribution function of the noise that cannot be separated from the noisy signal. In this paper, it is shown that high-order moments of the noise can be used as a diagnostic indicator for determining the presence and degree of damage development in drilling rigs during the latent period of damage initiation. Possible options for calculating the high-order moments of the noise are analyzed. Recursive algorithms are developed for expressing high-order moments of a normally distributed noise through its variance. The possibility of calculating the high-order moments of the noise through the distribution density functions is also shown. A matrix consisting of estimates of the high-order moments of the noise calculated at different instants of time is built. It is shown that at the first stage, it is possible to determine the presence and degree of the damage based on the values of the matrix elements. At the second stage, the intensity of damage development is determined by comparing the values of the noise characteristics at different instants of time. Calculations are performed for all signals coming from the sensors. Training is carried out and, the correspondence is established between the values of the high-order moments and degrees and intensity of damage development. The possibility of using the proposed algorithms and technologies in the system of noise control of the beginning and development dynamics of accidents at drilling rigs is shown. It is noted that even if the estimates of the high-order moments of the sum noisy vibration signals change within a wide range during drilling, their high-order noise moments do not exceed a predetermined value in the absence of a malfunction. In the event of a malfunction, the estimates of the highorder moments of the noise exceed the predetermined threshold level and, as the defect develops, their values also change. If adverse processes are stabilized, the variation of these estimates stops as well. Moreover, depending on the degree and intensity of stabilization of the technical condition of the drilling rig, the change in the estimates of the moments, starting from the highest to the lowest or vice versa, stops one by one. This specific feature of estimates of high-order noise moments of vibration signals allows us to identify the beginning and to control the development dynamics of the latent period of an emergency state of the drilling process. 

The article describes radiation power control of industrial CO₂ lasers of Lantan series excited by а nonself-sustained glow discharge in the automatic mode. These lasers are closed-cycle fast gas-transport lasers excited by a nonself-sustained glow discharge with ionization by periodic-pulsed capacitively coupled auxiliary discharge. In this case, ionization and conductivity are provided by periodic-pulsed capacitively coupled discharge. The energy contribution to molecular oscillations is provided by the passage of the main discharge current through the plasma with electron density given by ionization. This permits easy laser power control, provides excellent optical homogeneity and stability of an active volume together with high laser efficiency. A system of a nonself-sustained glow discharge with ionization by periodic-pulsed capacitively coupled auxiliary discharge, the stages of creation and brief characteristics of the Lantan series lasers is presented. The method of controlling the power of laser radiation by changing the frequency of the ionization pulses is determined. This control method allows operating of the laser in continuous and in pulse-periodic modes with adjustable pulse ratio and pulse duration, and also provides switching from one mode to another. In the continuous mode, the radiation power is controlled by changing the frequency of ionization pulses, which are high voltage pulses with duration of 100 ns, given with the frequency of 1-5 kHz. Pulse-periodic radiation control is performed by modulating ionization pulses that consists of pulses being delivered in batches. The frequency of the pulses in a batch determines the radiation power in a pulse. The frequency of the batches following is the frequency of the pulse mode, and the length of the batch determines the pulses duration. Based on the experimental data, the dependence of the radiation power on the ionization pulses frequency was determined. An experimental system is presented and the measuring accuracy of the laser radiation power and the frequency of ionization pulses is determined. Data acquiring and processing of experimental results were performed using the NI 6008 USB data acquisition device in the LabVIEW programs of National Instruments. To study the dependence of the laser power on Мехатроника, автоматизация, управление, Том 21, № 4, 2020 231 the frequency of the ionization pulses, a regression analysis method was applied. Studies have shown that the dependence of the laser power on the ionization pulses frequency is linear in a wide range of parameters. The equation of the direct regression is calculated. The confidence estimates of the coefficients of the direct regression and the confidence estimates of the deviation of the theoretical direct regression from the empirical one are calculated with a confidence level of 95%. 

The article discusses the movement of a three-link crawling robot on a horizontal rough surface, while changing its configuration. The robot contacts the surface in four points where active bearings are in place. The active bearings are designed in such a way that their dry friction coefficient is a controlled quantity, which allows periodically fixing these bearings to the surface. The robot consists of modules, each of which is a translational pair, and the modules are interconnected by two-axis hinges. It is proposed to consider these modules as links of variable length. In the paper, the basic kinematic relationships for this robot were found, a vector of generalized coordinates was specified, and the constraints imposed during the movement were described. The studied here motion corresponds to a scenario where two outer bearings are fixed on the surface, while links execute planar movements from a given initial to the desired final position. The implementation of such a movement requires a change in the lengths of the links (in the simplest case, a change in the length of one link is enough, in the most difficult case, all three are required to change length), for the implementation of which a correction system is proposed. The method considered in the work consists in varying the length of one link, which is the robot body, the movements of the other two links are determined by the operation of the corresponding drives. As a result of numerical simulation, the range of allowable values for the elongation / shortening of the robot body is determined by varying the relative angle between the body and one of the side links in a given range. In addition, four intervals of changes in the relative angles were revealed, at each of which the nature of the variation in the length of the central link differs in the number of maxima and minima achieved. Also, the dependences of the change in the angle of rotation of the side link, at which the length of the body reaches its maximum and minimum lengths, from the previously specified relative angle and time of movement, are constructed. The temporal laws of changes in the rotation angles of the links are given and analyzed. 

Modern air targets are characterized by low visibility, high maneuverability and high survivability. In addition, for some specific targets, for instance ballistic missiles, in order to defeat them the missile need tobe guided and carried out direct hit, i.e. "hit to kill". Therefore, in this paper, we present a high-precision missile homing system (MHS) using the proportional guidance method for firing at the highly maneuverable targets. Specifically, we propose a parametric optimization method for choosing a set of optimal parameters of the missile homing system for each dynamic parameter set of the missile. In addition, the paper gives the recommendations of choosing the initial conditions for the synthesis of missile homing system. In our experience, we should choose the small initial condition for synthesizing the missile homing system. Finally, the article also investigates the influence of systematic error in determining the speed, normal acceleration of missiles and the angular velocity of the line of sight of the missile and target on the accuracy of the missile homing system. We implement the proposed missile homing system and the parametric optimization method in Matlab. The experimental results illustrate that, using proposed system and the parametric optimization method, the missile can defeat the modern air targets with low visibility, high maneuverability and high survivability. 

Different directions of creation high reliability integrate spacecraft control system are discussed on base of robust diagnostic models and division principle in parity space. Problems of synthesis spacecraft control system algorithms are examined with incomplete apriory and distorted current information, action of uncontrolled and random factors, information losses and equipment failures. The structure of onboard attitude control system is synthesized and control algorithms are chosen, which guarantee robust stability and failure stability in presence indignant factors and obstacles. An instrumental structure and operational modes of spacecraft attitude control system are described. Methods of dynamic research, computer technology and modeling particularities are indicated. Diagnostic and reconfiguration algorithms for onboard complex of connection, navigation, geodesy satellites and earth inspectoral satellite in prolonged space flight utilization are proposed. Testing procedure is contains two stage: discovering and eliminating faults. Given mathematical system model is researched by means of difference signals, which forms with arise at fault emergence. The failure character is established by deciding rules on base difference signals and measures to it eliminating are took. Questions of onboard spacecraft control system failure stable improving are discussed on base principle reconfiguration with apply to adaptive logic in testing and diagnostic algorithms. The mathematical system model is researching with implementation of analytic reserving. Difference signals are formed, which arise at fault appearance. The adaptive approach to development testing and diagnostic systems provide for realization of flexible logic of control system function to take into account factual onboard equipment state. Special attention is devote to problem influence liquid fuel reactive engine agility on spacecraft control attitude system dynamic characteristics and precision. The effectiveness of prepositional approaches and algorithms is confirmed by mathematical modeling results for several actual technical systems. Recommendations to their practical applications are given.