A theoretical result is presented in the form of a new algorithm for the synthesis of a control system over a non-linear object, whose mathematical model represents a stochastic matrix difference equation having noise with a zero mean and finite dispersion in the righthand part. The new algorithm for synthesizing stochastic control for such an object is based on a three-stage procedure. In the first stage, the structure of the control system is formed in accordance with the classical method of analytical design of aggregated regulators (ADAR) in a fixed-noise assumption. In the second stage, the conditional mathematical expectation of the resulting expression for the first-stage control is determined. In the third stage, the control model is refined by excluding the noise variable from the control formula based on decomposing the initial control system affected by the new control. It is shown that the proposed control strategies minimize the target macro variable dispersion and ensure a stable, on average, achievement of the target manifold. A detailed example of an application of the algorithm for synthesizing control over the motion of an immobile center of mass is given, whose analog is represented by the objects such as by robot-manipulators, is given. The results of numerical modeling are presented, which confirm the operability of the constructed controller. Numerical simulations of the designed control system was performed using the authentic working equipment data.

There is development of the well-known sliding mode, which in the classical formulation didn’t find the development to be applied to control systems discussed. Alternatively, there is method of organizing one of the uniformity of the sliding mode called the "point sliding mode" proposed. The distinctive feature of this mode is that here the control gaps occur at time-equal points of the switching line (hyperplane) which allows the origin of coordinates for a finite number of switches. The possibility of changing the time interval between these points makes it possible to obtain various modes: a finite mode, in which a given point is reached from any initial state in one switch, and in this mode the switch line is "isochronous"; point sliding mode in which a given point is reached in a finite number of switchings; limit mode, when the length of time intervals tend to zero, and the switching frequency to infinity. Considering this feature the concept of "degree of slip" is introduced. It is shown that in the case of forced movement in the SPS, a sliding motion is observed, which does not allow for ensuring invariance with respect to external disturbances. There are two ways to eliminate the forced component of the movement offered. One of the advantages of using a point sliding mode is that, in order to improve performance, it is not necessary to use a boundary layer, which is realized by entering various logical conditions into the control algorithm. The practical significance of a point sliding mode lies in the fact that, with a small switching frequency, it is possible to maintain the quality indices of an undefined object within an acceptable interval. The studies were conducted for onedimensional second-order linear systems (SISO). Results can be generalized for higher order multidimensional systems. Solution of model problems on MATLAB / Simulink allows us to make a number of positive conclusions that are of great practical importance in terms of expanding the area of use of skipping modes, especially in relation to the management of undefined objects.

The article is devoted to the problem of developing a digital algorithm for operational harmonic analysis of complex vibration signals. The basis for solving this problem was the generalized equation of statistical measurements, which defines the measurement procedure as the sequential execution of interrelated measurement and computational transformations. During the development of the algorithm, special attention is paid to analog-to-digital conversion because it directly affects the computational efficiency of digital procedures for obtaining the final result. As such a conversion, the use of binarysign analog-stochastic quantization is justified, which allows performing two-level quantization without systematic error regardless of the statistical properties of the analyzed signals. The discrete-event model of the binary-sign analog-stochastic quantization result allowed for the analytical calculation of integration operations in the transition to estimating the amplitude spectrum in digital form. As a result, the developed algorithm of harmonic analysis does not require performing digital multiplication operations typical for classical algorithms, which are based on the calculation of the direct discrete Fourier transform. The execution of the algorithm is reduced to the implementation of the addition and subtraction arithmetic operations of the cosine-function values in the time moments determined by the result of the binary-sign analogue-stochastic quantization. The exclusion of digital multiplication operations provided an increase in the computational efficiency of amplitude spectrum estimation. Laboratory studies of the developed algorithm were carried out using simulation modeling. The simulation results showed that the algorithm allows calculating estimates of the amplitude spectrum of complex signals with high accuracy and frequency resolution in the presence of additive noise. In real conditions, the testing of the developed algorithm was carried out during bench studies of the operational status of the MAZ-206067 bus, designed for the transportation of passengers on urban and suburban routes of average workload. Analysis of the results of experimental studies confirmed the possibility of using the algorithm as part of the diagnosability provision for operational monitoring of vibration signals in a complex noise environment.

This paper considers development of positioning systems for manipulator links to solve the forward kinematics problem (FKP) and inverse kinematics problem (IKP). Here we study a robotic manipulator with four degrees of freedom. It should be noted, that one of the relevant research problems of modern modular robotic devices consists in the lack of the universal algorithms, that would ensure kinematics problem recalculations in the cases of reconfigurations of the whole system. Challenges, the researchers are facing with when solving this problem, have to do with geometrical and non-linear equations (trigonometric equations), finding of inverse matrix of the Denavit—Hartenberg presentation, as well with other problems, such as multiple solutions when using the analytical approach. Common mathematical solutions of the inverse kinematics problem, such as geometric, iterative and algebraic ones, may not always lead to physically appropriate solutions. It’s also noteworthy, that, trying to introduce physical solutions for the manipulator, we need to take into account, that the number of calculation formulas increases, what, in turn, causes further computing power consumption increase. If the manipulator acquires additional degrees of freedom, analytical modeling becomes virtually impossible. One of relevant inverse kinematics solution methods consists in implementation of neural networks to that end. To solve this problem various sources were analyzed, considering alternative ways of target point discovery. Considering the analyzed papers, we propose to use a perceptron. Before training the network, we compose an algorithm, calculating the Denavit—Hartman presentation matrix and check for correctness of target point reach by the terminal manipulator link. We did calculations for a thousand positions of manipulator and object in the environment, fed to the neural network. When solving FKP we obtain object coordinates as network output, whereas in the case of IKP — manipulator link angles. We present kinematic scheme testing results, as well a control scheme for a manipulator with four degrees of freedom.

The flow of the fluid in an elastic cylindrical microchannel, the central part of which is located inside the piezoelectric ring, is simulated numerically. It arises as due to channel deformation by piezoelement according to the harmonic law, and pressure drop at the inlet and outlet to the microchannel. The aim of the work is to create a three-dimensional computer model of controlling the flow of a fluid by means of a pressure drop and a tube compression piezoelectric element. The model of an element of a computational bench that allows you to find fluid flow using specified analytical formulas, built using an approximation of the calculation results for the full model for individual sets of parameters. Modeling an element of a computing bench will allow real-time calculations with direct integration into the control system of a technical device. The model is based on the obtained analytical dependencies taking into account the restrictions introduced, which can significantly reduce the amount of computation and improve the quality of the result. The solution of the full equations of elasticity for the tube and the equations of hydrodynamics in the microchannel was carried out numerically by the finite element method in the package of numerical simulation FreeFem++. Numerical results are obtained for the flow rate of a fluid as a function of time, the physical properties of the fluid (dynamic viscosity and density) and external influences (the magnitude of the pressure gradient, the amplitude and frequency of compression of the piezoelectric element). The variants of using the obtained results in practical applications are shown. For example, in a liquid cooling system, the obtained relationship between the system parameters allows one to determine the flow regime that prevents the flow of heated liquid through the channel outlet. It is planned to use the results in the development of a computing stand for capillary micro-capture, containing two tubes (at the input and output) with piezoelectric elements, dividing the device into two parts (with dynamically changing and unchanged geometries) which will greatly simplify the full simulation.

A mathematical model of a hybrid navigation system (GNS) consisting of a three-component block of linear newtonometers (accelerometers) physically simulating a vector-based measurer of non-gravitational nature forces and on-board GLONASS receivers that positioning a moving object in an ellipsoidal coordinate system is presented and investigated. The absence of a gyroscopic angular velocity sensors unit, traditional for the classical schemes of the inertial navigation method, and the presence of no more than two onboard satellite positioning devices (receivers) make it possible to characterize the considered GNS as a partial structure system. As a basic element of a mathematical model for estimating linear and angular parameters of an object’s motion, the developed procedure of multiple numerical differentiation of temporal data acquired from on-board satellite receivers, which functions stably irrespective of the magnitude of the discretization step of the problem in time, was used. The developed GNS makes it possible to qualitatively evaluate both the trajectory parameters (location, velocity, acceleration and forces causing the trajectory) as well as the parameters of the spatial orientation of the object (Euler-Krylov angles and its derivatives) with a two-positioning technique. The results of the computational experiment are given. The field of application of the research results is numerical-analytical planning of trajectories, determination of motion parameters and control of moving objects for various purposes and basing.

To address the navigation issues of the planetary rover and construct a map for the unknown environment as well as the surface of the planets in our solar system, the simultaneous localization and mapping can be seen as an alternative method. In terms of the navigation with the laser sensor, the Kalman filter and its improving algorithms, such as EKF and UKF are widely used in the the process of processing information. Nevertheless, these filter algorithms suffer from low accuracy and significant computation expensive. The EKF algorithm has a linearization process, the UKF algorithm is better matched in a nonlinear system than the EKF algorithm, but it has more computational complexity. The GP-RTSS filtering algorithm, based on a Gaussian filter, is significantly superior to the EKF and UKF algorithms regarding the sensor fusion accuracy. The Gaussian Process can be used in different non-linear system, does not need prediction model and linearization. However, the main barrier in the process of implementing the GP-RTSS algorithm is that the Gaussian core function requires a lot of computation. In this paper, an algorithm, so-called DIS RTSS filter under a distributed computation scheme, derived from the GP-RTSS Gaussia n smoothing and filter, is proposed. The distributed system can effectively reduce the cost of computation (computation expense and memory). Moreover, four fusion methods for the DIS RTSS filter, i.e., DIS RTP, DIS RTGP, DIS RTB, DIS RTrB are discussed in this paper. The experiments show that among the four algorithms described above, the DIS RTGP algorithm is the most effective solution for practical implementation. The DIS RTSS filtering algorithm can realize a high processing rate and can theoretically process an infinite number of data samples.