The problem of plasma stabilization in a magnetic field is considered. The plant is described by the hydrodynamics model of a weightless potential ideally conducting fluid in a cylindrical coordinate system. The deviation of the perturbed surface, the velocity of deflection of the perturbed surface, the acceleration potential are the functions of state. The acceleration potential on the outer generatrix of cylinder surface is used as the control. The state and control functions depending on the radial and axial coordinates are presented as series with respect to orthonormal systems of functions. Via the spectral method of the distributed systems analysis and synthesis the theoretical positions for the transition from the initial mathematical model described by PDE system to an infinite descriptor system are done. The components of state and control vectors of the descriptor system are the time-varying amplitudes of the spatial harmonics of the series. Expressions for the calculation of the operational differentiation matrices, the operational matrices of factors depending on spatial coordinates depended vectors, the matrices of boundary conditions are given. The matrices of the descriptor plant representation are obtained. The questions of existence, uniqueness, and convergence of the solution of the received descriptor system are investigated. For the plant represented by the descriptor system, a control low described by the differential system is constructed. The solution of the problem is based on the variational approach. The H2 optimization criterion is used. The analysis and synthesis of the closed-loop system via Matlab is done. The results of the analysis indicate that there is no overshoot and oscillation in the system. Calculations based on a limited number of equations show that with the increase in the number of differential and algebraic equations and, respectively, the spatial modes of the expansion of the control functions and the state of the process, the obtained result tends to a certain limit.

A complete pole placement method for linear MIMO systems with the use of state feedback is presented. The method is based on specific decomposition of representation in the state space of the original MIMO system. The converted representation of the MIMO system contains explicit elements, changing of which with the help of the feedback, enables a specified complete placement of the closed-loop system's poles. The method does not require special solving of matrix equations (like Sylvester equations), which are expressed in the same form for both continuous and discrete cases of the MIMO system description, and does not place restrictions on the algebraic and geometric multiplicity of the specified poles.

In this paper obtain the general solution of terminal control problem with a set of initial perturbations. Propose conditions of the general solution existence to discrete linear control systems. Also give the optimal solution of the terminal control problem minimizing the distance between the trajectory and fixed points. Constraints on the trajectory of the system are selected for certain points. Describe the set of all solutions to the control problem of trajectories ensemble with discrete time. The problem of optimal displacement of a discrete system from the initial state to the final one is solved. The problem of optimal displacement of a discrete system from the initial state to the final state with restriction to phase coordinates is solved. The trajectory of the system with optimal terminal control will pass next to the predefined points. The problem of control a set of trajectories for linear discrete systems is formulated and solved. The obtained control of the set trajectories is optimal. Necessary and sufficient conditions for solving this problem are obtained. Consideration is given to the mathematical problem on constructing general solutions of the problem concerning the terminal control for the set of initial perturbations. The existence conditions of the general solution of this problem for linear dynamic systems with the discrete argument is given. The obtained function of control is based on filtration of linearly independent rows and columns of the matrix. The optimal controls for linear dynamic discrete systems will solve of practical important problems.

It is known that if problems do not dare at that level where they have appeared - it is necessary to rise on level above, on a higher step of understanding of laws of the nature. Optimum control problems cannot be solved purely matematicheski: the mathematics without physics - is silly, the physics without mathematics - is blind. It is offered to look at problems of a method of dynamic programing of R. Bellman having methodological value, at least still from outside the physical phenomena. It allows to solve optimum control problems multidimensional installation of a high order, in that count also nonlinear. The principle of R. Bellman has a methodological importance - it is possible to control everything or everybody if three conditions are met: the object of control is known, the ultimate goal of control is known and the criterion of an estimation of quality of control is known. If there is no at least one of them - there is no sense to get down to the solution of a control problem. It is meant that there are at least two co-operating blocks in control tasks: the control object and the subject of control, i.e. a person (manual control) or a control system - an automatic steering block which often called a regulator. Questions of the optimum control theory with reference to technics and, in particular, to electric drives are considered in this paper. Ways to solve the problems of control systems optimum on accuracy for nonlinear objects of high order are offered. By example of a direct-current drive it is shown that usage of the physical and mathematical theory will allow to achieve small errors (no more than 20 arc sec.) on minimal speeds of tracking (up to 0,01 deg./sec.) with friction torque and load fluctuations during operation, with presence of a reducer backlash that is 10 times greater than admissible error, with a nonrigid and unbalanced design of an actuator. The theory also allows to create a hi-tech industrial equipment (for ex., precision rigs) and prospective types of weapons and military equipment (for ex., high-precision radar tracking stations).

There is considered a vibratory robot, presented by a rigid box and a physical pendulum inside it. The robot moves along a horizontal plane in the gravity field. There is a Coulomb friction between the box and the surface. Control of the robot is defined by the choice of angular acceleration of the pendulum. In the paper there is considered a certain class of motion and a control low that insures sliding of the robot in the desired direction within all given restrictions. The control insures periodic motion of the robot with two phases: sliding phase, where the main body of the robot is moving in the desired direction, and resting phase, where the box of the robot is standing still. On the sliding phase on the maximum interval within the given restrictions there is no friction between the body and the plane. In the paper there is proved that such control law is optimal in terms of maximum velocity for a certain motion class. First, there is shown that for the case when the box is sliding, when the pendulum is in one half of the period it is best to insure its maximum acceleration, and in the second part the angular acceleration should be at its minimum value. Then there is shown that for the motion within all given restrictions when there are set certain starting conditions and ending conditions on phase variables then the considered control law insures maximum average velocity of the robot. After that there is shown that there should be set conditions on phase variables for only one position of pendulum on the period. Lastly there is proved that for a certain angle there is needed to define only the speed of the box, optimum value of angular velocity of the pendulum appears to be as desired.

The article considers aspects of using the based on fuzzy logic ISA in agriculture. It is shown that in the real world knowledge of a qualitative nature, are often much more useful than quantitative knowledge. It shows on statements of fuzzy controllers, that the most of problems man must solve initially based on fuzzy knowledge. Especially for agricultural production, where a wide range of uncertainty dictated by the participation in technological processes of living organisms. Shows a brief sketch of the mathematical apparatus of fuzzy knowledge, with explanatory examples from the field of agriculture. It is shown that the characteristics of a fuzzy set acts as a accessory function. In addition to the fuzzy sets Apparatus uses the concepts of fuzzy variable and linguistic variable, which is at a higher level than fuzzy variable. There are over a dozen typical forms of curves to define the membership functions. The most used are: triangular, trapezoidal and Gaussian accessory functions. Globally the logical inference mechanism consists of four steps: introduction of fuzziness (phasification), fuzzy inference, composition and bringing to clarity, or dephasification. The most common method of inference in fuzzy controllers - Mamdani inference. It uses the min-max composition of fuzzy set to intelligent ACS had close to human ability to work with knowledge requires their formalization and representation in the technical system by means of a description language knowledge categories which the system could operate in the same way as people with words. It is also clear that to achieve greater effect of intellectualization of the technical system, this language must describe all possible types of knowledge: quantitative and qualitative, crisp and fuzzy. In conclusion given a brief review of the practical application of IMS on the fuzzy logic basis in agricultural production by bringing the calculated dependencies of the algorithm for temperature control using fuzzy modeling.

In the paper, the automation water distribution system for high location territories which are got from the underlying water source and consisting a sequence of water pipe-warehouse pump-segments of the stations on the slope and partitioned equipment's - parts of channel on high location plain with an alarm reset in the end of the channel, removing excess water is considered. For effective work of such a system a new formulation and solution of the optimal management of water supply problems is offered. For solving the problem, the method of linear programming mathematical package "Matlab" is used. The problem solution is given for the system with 3 pump stations - pipeline segments - warehouses and 2 channel baffle structures, portions of each channel and water storage area which is powered by a single point of consumption. To solve this problem the method of optimization mathematical package of Matlab is used and the results are analyzed. As a result, the problem of operative control for 13 water supply facilities during 2 consecutive intervals of constancy of parameters where the duration of each of which-12 hours is made. Total instead for the optimal values for managing the system with 26 variables are searched. In addition, the costs in the emergency facility in both intervals are completely converted to 0. This proves the acceptability of the considered problem for the control of such objects. The machine time spent for solving this problem is much less, and the problem can be applied to complex objects.

This paper presents a voice activity detector (VAD) which uses the data from the compact linear microphone array and a video camera, so developed VAD is robust to external noise conditions. It is able to ignore non-speech sound sources and speaking persons located out of the area of the interest. A deep convolutional neural network processes images from the video camera for searching face and lips of the speaking person. It was trained using the Max-Margin Object Detection loss. Pixel coordinates of found lips are converting to directions to lips in camera coordinate system using optical camera model. The sound from the microphone array is processing using the weighted GCC-PHAT algorithm and Kalman filtering. VAD searches for speaking lips on the video. It becomes activated only if the video camera finds lips and the microphone array confirms that there is a sound source in this direction. A prototype of the system based the linear microphone array with 30 mm spacing between microphones and the video camera was developed, manufactured using a 3D printer and tested in the laboratory conditions. The accuracy of the system was compared with the open source VAD from the WebRTC project (developed by Google) which uses only audio features extracted from the same microphone array. Developed VAD showed a high sustainability to external noise. It ignored the noise from not-target directions during 100 % of the testing time. And the VAD from the WebRTC had 88 % of false positive activations.

High computational efficiency of spacecraft docking dynamic simulation is needed for analysis based on a great number of random initial conditions, and sometimes for real time simulation. From the point of view of this dynamical process, a docking mechanism with many kinematical loops, in spite of its low mass, is more complex than a spacecraft. Some efficient simulation algorithms for such a class of mechanical systems are considered in this paper. For efficiency purposes, they are realized using a specialized symbolic manipulation system. Before simulation, a multi-loop mechanical system is transformed to a tree structure using constrain equations instead of individual joints. This paper states that a possibility of partitioning kinematical loops to controlled and dependent kinematical chains, and a limited number of structure types of the latter are typical for docking mechanisms. This paper proposes a modification to the Composite Rigid Body Algorithm (CRBA) for a transformed tree structure mechanical system with a moving base, and an additional recursive algorithm for the calculation of the force and moment acting on this base. Both of these supplements to CRBA allow linking of separate dynamic equations of a spacecraft and a mechanism. The Articulated Body Algorithm (АВА) is applied to partially open kinematical chains without kinematical loops, which occur in some central type docking mechanisms (the probe-cone type). The АВА calculates by itself the force and moment acting on the mechanism base and the spacecraft.

The problem of improvement of maneuverability of a spacecraft which is controlled by inertial actuators (system of powered gyroscopes, by gyrodynes) is considered. We suggest to increase speed of implementation of rotary maneuvers by optimization of control algorithms of spacecraft motion. The task of construction of optimal laws of variation in the angular momentum vector of a spacecraft as control function so as to ensure the transition of the spacecraft from an arbitrary initial attitude to the required final angular position at minimal time has been solved completely. Main difference is the necessity of determining during optimization the maximum admissible magnitude of the angular momentum since it is unknown a priori. The problem is solved by using Pontryagin’s maximum principle, and solution is based on the quaternion differential equation relating the vector of spacecraft angular momentum to the quaternion of orientation of the body-fixed coordinate system. The optimality conditions of reorientation regime without "unloading" of the gyro-system are written in analytical form, and the properties of optimal motion are studied. Key relations and the equations for construction of the optimal control program are given. The condition for determination of the moment of the beginning of the braking which uses current parameters of motion (information on angular position of a spacecraft and measurements of angular velocity) was given, it considerably improves accuracy of spacecraft transfer into a required position. The aspects of determination of optimal modulus of angular momentum between acceleration and braking if spacecraft rotates under disturbances are discussed in detail. The formalized equations are derived, and computational expressions for calculating the optimal value of the key parameter of control law are obtained. Results of the mathematical simulation of the spacecraft motion under the designed control method are presented.