Sliding mode control (SMC) laws are commonly used in engineering to make a system robust to parameters change, external disturbances and control object unmodeled dynamics. State-of-the-art capabilities of the theory of adaptive and robust control, the theory of fuzzy systems, artificial neural networks, etc., which are combined with SMC, couldn’t resolve current issues of SMC design: vector design and stability analysis of a closed-loop system with SMC are involved with considerable complexity. Generally the classical problem of SMC design consists in solving subtasks for transit an object from an arbitrary initial position onto the sliding surface while providing conditions for existence of a sliding mode at any point of the sliding surface as well as ensuring stable movement to the desired state. As a general rule these subtasks are solved separately. This article presents a methodology for SMC design based on successive aggregation of invariant manifolds by the procedure of method of Analytical Design of Aggregated Regulators (ADAR) from the synergetic control theory. The methodology allows design of robust control laws and simultaneous solution of classical subtasks of SMC design for nonlinear objects. It also simplifies the procedure for closed-loop system stability analyze: the stability conditions are made up of stability criterions for ADAR method functional equations and the stability criterions for the final decomposed system which dimension is substantially less than dimension of the initial system. Despite our paper presents only the scalar SMC design procedure in details, the ideas are also valid for vector design procedure: the main difference is in the number of invariant manifolds introduced at the first and following stages of the design procedure. The methodology is illustrated with design procedure examples for nonlinear engineering systems demonstrating the achievement of control goals: hitting to target invariants, insensitivity to emerging parametric and external disturbances.

Asymptotic methods for analyzing large deviations in this work are used to convert information about the state of a controlled diffusion process into probabilistic estimates of the normal or abnormal development of the process. Thus, over the reflex contour of local stabilization a system of global semantic control is implemented, a kind of second signal system. A functional analytical approach similar to the weak convergence of probabilistic measures is used as an analysis tool, which makes it possible to significantly expand the conditions for applying the method. Global control is reduced to solving the Lagrange problem in the form of Pontryagin for the system of ordinary differential equations (system of paths), the Ventzel-Freidlin action functional (or "rate function" in some English literature), which is presented here as an integral-quadratic criterion for control functions in the system of paths, and the boundary condition in the form of the critical state of the system. A bounded solution of the Lagrange — Pontryagin problem on the half-line, which gives a prototype of the quasipotential of the system of paths, is called the A-profile of the critical state. The A-profile makes it possible to significantly simplify the procedure for analyzing large deviations, up to its implementation in real time and the implementation of the global control loop (2nd signaling system). The resulting two-tier architecture is positioned as a baseline to achieve the functional stability of the control system. It is speculated that this role of the apparatus of large deviations takes place in biological evolving systems, including the formation of languages and other attributes of the evolution of higher human nervous activity.

The task of controlling the manipulation robot movement in one direction has been considered. Such task appears at cutting, welding, painting and other similar operations, when the robot instrument performs a program motion along the working surface and at the same time, it is necessary to keep a definite distance from this instrument to the surface automatically without excessive correction. A new algorithm of controlling the linear object of the second order of the general form has been obtained by dynamics and perturbations compensation method, which takes precedence over well-known decisions. The algorithm provides a zero static error of the system regulation and movement in acquisition of external effects within the accuracy of standard filters of the second order that is convenient for practical use. The first filter indicates movements of the system during the task performing; the second one provides perturbations compensation on state variables. A step-by-step procedure of the algorithm synthesis has been represented for the second order controlled object of the general form. Formulae for calculating regulator coefficients have been obtained. The obtained equations defining processes in a closed control system allow performing the analysis of the control quality and the dynamics of control changes depending on external influences. A method of equations identification of the robot motion in conditions when we know the maximum speed of its instrument movement and a dynamic error of the robot servosystem regulating has been developed. By this method, the robot equations are brought up to the Vyshnegradskiy’s form and then on the computer model a fundamental frequency and a decay factor can be easily chosen. The application of the obtained algorithm has been reviewed to create a system of automatic regulation of the robot instrument position. It has been clarified that defining free coefficients of these filters on position of filter fundamental frequency equation and a controlled object provides the given system operation speed at moderate amplitude of controlling actions. A mathematical modeling method has shown the advantages of regulation program quality, parametric and structural robustness of the obtained control system.

The article presents a solution to the problem of calculating the parameters of a mathematical model of an electric hybrid stepper motor based on an analysis of the picture of its magnetostatic field. The main disadvantage of such an engine described. Is the mid-frequency resonance, which occurs due to the coincidence of the natural frequency of the rotor with the frequency of the supply voltage pulses. The necessity of taking this factor into account when designing a discrete electric drive system based on the executive motor of this type by calculating the values of resonant frequencies and using them in developing the drive control algorithm is shown. The task of developing a mathematical model of the engine is formulated, which allows to analyze the influence of its design parameters on the spectrum of resonant frequencies. The method of calculating the parameters of a given mathematical model is formed. The variants of the mathematical description of this electric machine are considered and the selection of its known mathematical model is made based on the equivalent electric circuit. The numerical calculation of the spatial pattern of the magnetostatic field of the electric motor is performed. Based on the analysis of the calculation results, a system of assumptions has been formed to develop an equivalent magnetic circuit of an electrical machine. An equivalent magnetic circuit and the corresponding system of equations has been developed. Formed a system of equations of a mathematical model based on the equivalent circuits of the electric and magnetic circuits.On the basis of the obtained system of equations, a simulation model of a discrete electric drive was developed in the Simulink software package. Using the obtained simulation model, the calculation of transients on the angle of rotation of the rotor and the electromagnetic moment is carried out and the influence of one of the design parameters on the natural frequency of the rotor is analyzed. Based on the simulation results, it is shown that with an increase in the air gap height of a hybrid stepper motor, the resulting electromagnetic moment decreases, and the natural oscillation frequency of the rotor decreases, and the frequency at which medium-frequency resonance occurs also decreases. This mathematical model can be used at the stage of the correct calculation of the selected engine, since allows you to analyze the effect of a specific design parameter of the machine — in particular the size of the air gap on the natural frequency of the rotor, and, consequently, on the spectrum of the resonant frequencies of a discrete electric drive.

The actual tasks of 3D-reconstruction of the industrial-urban environment and navigation models are considered by solving the identification of textured linear objects in the process of movement according to the onboard complex and technical vision system consisting of a mutually adjusted 3D laser sensor and a video camera with a common viewing area. For a complete solution of the navigation task (determination of three linear and three angular coordinates of the control object), it is necessary to select and identify at least three mutually non-parallel flat objects in the process of moving in a sequence of point clouds formed by a 3D laser sensor. In the case of the allocation of less than three flat objects (for example, in environments subjected to destruction), the navigation problem is not fully solved (not all coordinates are determined unambiguously, and some coordinates are related by linear or non-linear dependencies). In these cases, it is proposed to additionally use the texture of the selected flat objects formed by the video camera. In the paper is given the analysis of the features of the solution of the navigation problem is carried out depending on the number of allocated and identifiable textured linear objects in the current integrated images and algorithms for solving the navigation problem are evaluated for selecting and identifying the process of movement of one textured linear object and of two textured non-parallel linear objects. It is shown that in the first case, the use of texture makes it possible to reduce the solution of the navigational problem to a three-dimensional one, and in the second case to a one-dimensional optimization problem (finding the global optimum of a functional three and one variable, respectively). The proposed algorithms for processing complexed images provide a complete solution to the navigation task even if less than three linear objects are selected, which significantly increases the reliability of solving the navigation task and building an environmental model even in industrial-urban environments that have been destroyed, and therefore, the reliability and survivability of the ground ones and airborne robotic tools in autonomous modes of movement. The results of the corresponding software and hardware solutions in real industrial-urban environments, confirmed the accuracy and effectiveness of the proposed algorithms.

The problem of optimal reorientation of the spacecraft orbit is considered in quaternion formulation. Control (vector of the acceleration of the jet thrust) is limited in magnitude. It is required to determine the optimal orientation of the vector of the acceleration in space to solve the problem. It is necessary to minimize the energy consumption of the process of reorientation of the spacecraft orbit. We used quaternion differential equation of the orientation of the spacecraft orbit to describe the motion of the center of mass of the spacecraft. The problem was solved using the maximum principle of L. S. Pontryagin. We simplified the differential equations of the problem using known partial solution of the equation for the variable conjugated to true anomaly. The problem of optimal reorientation of the spacecraft orbit was reduced to a boundary value problem with a moving right end of the trajectory described by a system of nonlinear differential equations of fifteenth order. For the numerical solution of the obtained boundary value problem the transition to dimensionless variables was carried out. At the same time a characteristic dimensionless parameter of the problem appeared in the phase and conjugate equations. We constructed an original numerical algorithm for finding unknown initial values of conjugate variables. The algorithm is a combination of Runge-Kutta 4th order method and two methods for solving boundary value problems: modified Newton method and gradient descent method. The using of these two methods for solving boundary value problems has improved the accuracy of the solution of the investigated boundary value problem of optimal control. Examples of numerical solution of the problem are given for the cases when the difference (in angular measure) between initial and final orientations of the spacecraft orbit is equals to a few (or tens of) degrees. Graphs of changes component of the quaternion of the spacecraft orbit orientation; variables characterizing the shape and dimensions of the spacecraft orbit; optimal control are plotted. The analysis of the obtained solutions is given. The features and regularities of the process of optimal reorientation of the spacecraft orbit are established. We found that when the difference between initial and final spacecraft orbits is small there is a one point of extremum for the eccentricity of the spacecraft orbit and for modulo of the vector of orbital velocity moment of the spacecraft. And there are a few points of local extremum for these functions when the difference between initial and final spacecraft orbits is large.

It is shown that the known limitations on the measurement of air parameters on board the helicopter due to significant aerodynamic disturbances introduced by inductive flows of vortex column of main rotor. This determines the need to create the means of measurement, taking into account the aerodynamics and dynamics of the helicopter flight. The known direction of overcoming these limitations is the use for measuring the information of aerodynamic field of vortex column of main rotor and its perception by means of the stationary multi-functional aerometric receiver. However, the need to protect a large number of full-pressure tubes installed in the flow channel of the multifunctional aerometric receiver, strict requirements for the identity and stability of the characteristics of the large number aerometric channels, complicate the design, reduce reliability, increase cost, inhibit the use of the air parameters measurement system on helicopters of various classes and purposes. Principles of construction, functional scheme, features of perception of primary information of measuring system of air parameters of the helicopter with the stationary receiver of a stream, ion-label and aerometric measuring channels are showed. Algorithms for processing primary information at various stages and flight modes, including: in the parking lot before the launch of the power plant and when rotating the rotor, when taxiing and maneuvering on the earth’s surface, on takeoff and landing modes and when flying at low speeds, at flight speeds, when the stationary receiver of primary information leaves the zone of the vortex column of the rotor using ion-label and aerometric measuring channels, are presented. It is shown that the proposed approaches to the construction, models and algorithms for processing the primary information of the measuring system air parameters of helicopter with ion-label and aerometric measurement channels allow to determine the speed and direction of the wind vector, altitude-velocity parameters of motion relative to the environment and atmospheric parameters in a wide range of helicopter operation, which determines its competitive advantages in solving problems of piloting and provide the flight safety of helicopters of different classes and purposes.