The aim of the research is to develop a practically implementable formalized method for synthesis of conrollers for the general form systems based on the common isomorphism principle formerly offered in the theory of the systems. The research results are rigorous substantiation of the new type controllers structure - isomorphic controllers - and the formalized procedure of their synthesis. It was demonstrated that a feedback in the form of isomorphic controller is necessary and sufficient for controllability of the system in contrast to the well-known methods, first postulated the necessity of a feedback and then offered application of the procedure for controller synthesis. The feasibility of presenting a model (transfer function) of an object as a combination of an isomorphic controller and a reference model was proved, which allowed to localize the ensuring of controllability in the controller, which represents a controlling mean, and the required quality of the transient processes - in the reference model realizing a control objective. Such a localiztion provides a possibility to obtain extremely high quality of the transient processes in the control loop. The use of a mathematical apparatus of the modern algebra based on morphisms has provided significantly high level of generality of the proven statements about the general form systems and linear systems controllability. The advantages of isomorphic controllers, reference models and the high gains method combination for the linear systems were shown. Such a combination ensures a high control quality as well as increase of the loop robustness in respect of the parametric disturbances and noise impact. Application examples of the isomorphic controller synthesis for the linear systems, which demonstrated their features, are provided. The advantages of the isomorphic controllers were substantiated and generalized.

As is known, the problem of the inverted pendulum plays the central role in the control theory. In particular, the problem of the inverted pendulum (as a test model) presents many challenging problems to the control designs. Because of their nonlinear nature, the pendulums have preserved their usefulness and now they are used to illustrate many of the ideas emerging in the field of a nonlinear control. Typical examples of that are the feedback stabilization, variable structure control, passivitybased control, back-stepping and forwarding, nonlinear observers, friction compensation, and nonlinear model reduction. The challenges of the control made the inverted pendulum systems a classic tool for the control laboratories. It should also be pointed out that the problem of stabilization of such a system is a classical problem of the dynamics and control theory. Moreover, the model of the inverted pendulum is widely used as a standard for testing of the control algorithms (for PID controllers, neural networks, fuzzy control, etc.). In this paper, the authors investigate the elastic inverted pendulum with a hysteretic nonlinearity (a backlash) in the suspension point. Namely, the problems of stabilization and optimization of such a system are considered. The algorithm, which ensures an effective procedure for finding of the optimal parameters, is presented and applied to the considered system. The results of the numerical simulations, namely the phase portraits and the dynamics of Lyapunov function, are also presented and discussed.

The game task of confrontation of the attacked hardware-redundant dynamic system with an attacking enemy operating in conditions of incomplete information about the behavior of the attacked enemy in a conflict was posed and solved numerically and analytically. The attacking party aspires to increase the intensity of failures of the components of the attacked system due to its attack resources, up to its total failure. The attacked party, due to the corresponding strategy of redistribution of the reserve units of the hardware-redundant dynamic system between the failed main units at the appropriate instants of time, strives to maximize the probability of a failure-free operation of the attacked system by the end of the confrontation (game) with the attacking enemy. Behavior of the system under attack in the process of a conflict is approximated by the Markov process, while the number of the operable states is equal to the number of the failed functional units, not exceeding the number of the standby units. As a function of the board in the considered game the probability of a failure-free operation of the attacked system is used by the time the game ends. The solution to the game is the vector of the system setup moments after the corresponding failures of the functional units and a set of the reservation vectors corresponding to the instantaneous settings of the attacked system, which maximize the probability of a system failure during a conflict. The differential game model is reduced to a multi-step matrix model with the given probabilities of the states of the attacking enemy. Numerical algorithms for calculation of the reservation vector for the attacked system are presented, which maximize the probability of its trouble-free operation by the end of the game and for solving of the game problem in a form convenient for its implementation on a personal computer.

The theory of the kinematic control of the rotational (angular) motion of a rigid body and the spatial motion of a free rigid body used in the article is based on the quaternion and biquaternion kinematic models of the rigid body motion. In this theory, the kinematic equations of the rotational and (or) translational motion of a body are considered as the mathematical models of a rigid body motion, and the vectors of the angular and (or) translational velocities of a body or kinematic screws are used as the controls. The goal of the kinematic control is transfer of a rigid body from its assigned initial position to the desired final position by applying the required (program) angular and (or) linear velocities to the body. Also, the goal of the kinematic control can transfer a rigid body from its given initial position to any selected program path and, further, to an asymptotically stable motion along the program path with the required program angular and linear velocities by applying the required stabilizing angular and linear velocities to the body. In the article the authors present a review of the papers dedicated to the following applications of the theory of the kinematic control of a rigid body motion in the mechanics of a space flight, inertial navigation and mechanics of the robot manipulators: two-circuit control of the rotational motion of a rigid body (spacecraft) using a strapdown inertial navigation system; adjustable strapdown systems for orientation and navigation of the moving objects; TSP-Argus motion control platform complex for Mars-94 space project; optimal reorientation of the orbit, of the orbital plane and correction of the angular elements of the orbit of the spacecraft by means of a reactive acceleration, orthogonal to the plane of the orbit of the spacecraft; solving of the inverse problems of the kinematics of the robot manipulators using the biquaternion theory of the kinematic control; kinematic control for the mechanics of the robotic manipulators (independent program motion speed control).

This paper presents the questions of development and research of the new synthesis method of a control system for the autonomous and remotely controlled underwater robots equipped with underwater multilink manipulators. This system was designed for implementation of the widely used underwater research manipulative operations in an automatic mode. Some of them are: taking soil samples and geological rocks, determination of the composition and density of the soil with special probes and drills, taking precipitation samples with the hermetically sealed soil tubes, measurements by means of the thermistor sensors in different layers of the sedimentary soil. A control system based on the proposed method was developed. In an automatic mode, this system determines location of the bottom surface in relation to the underwater robot by means of the onboard multi-beam hydroacoustic sonar. During a robot's immersion, the developed system evaluates the complexity of the bottom relief in the working area and takes decisions on the suitability of the said relief for a trouble-free implementation of the specified manipulative tasks. Also, the proposed system determines a robot's spatial orientation and the position for the most efficient and safe manipulation operations. The algorithm for formation of the spatial trajectories of the multilink underwater manipulator's working tools was proposed. These trajectories are formed with account of the borders of the manipulator's workspace, where a sampling device can be oriented perpendicular to the bottom surface. This algorithm uses information about the continuously updated model of the bottom surface. The experimental tests of the synthesized control system were done in a deep-sea expedition for research of its operability and functioning features. The experiment results proved the efficiency and simplicity of a practical realization of the proposed system.

In the modern world there are strict requirements to the unmanned aerial vehicles (UAV) in terms of the range of their taslis and the operating conditions. In order to solve this Mnd of taslis, it is necessary to produce technical resources for obtaining and processing of the information about the environment. One of these technical means for obtaining and processing of information about the environment is the machine vision system (MVS). The input information in the MVS is a current halftone image (CI) of the stationary ground multi-object scenes produced in an air flight. Quality estimation is one of the first operations done with this image. This operation allows one to tal

This paper presents MIMO fuzzy logic system for control of the parameters of an autonomous system for cooling of the cutting tool on three axis milling machine with CNC, which controls voltage of the FET gate, thereby changing the temperature of the Peltier element, and the voltage on the fan used to cool the warm side of the Peltier element. Accordingly, the fuzzy logic control system has two input and two output variables. The input ones are the temperature in the cutting zone and the temperature of the warm side of the Peltier element, and the output voltage at the gate of a field effect transistor and the voltage at the fan. Simulation of the fuzzy logic system was carried out by numerical methods using soft and hard arithmetic operations, as well as different operators of fuzzy implications for hard arithmetic operations. In modeling of the fuzzy logic of MIMO system for control of the parameters of an autonomous system for cooling of the cutting tool in the task of operation of CNC equipment, different operators of the fuzzy implications were obtained and graphs were compared of the voltage on the fan and of the temperature on the warm side of the Peltier element. Their strong and weak points were identified. The best results were obtained employing the soft arithmetic operations, the use of which for the fuzzy logic of MIMO system generates the necessary voltage value for the gate of the MOSFET and the fan depending on the temperature in the cutting zone and on the warm side of the Peltier element.

The authors consider a descent of a spacecraft capsule with small controlled aerodynamic and constant mass asymmetries in the Martian atmosphere. The aerodynamic asymmetries of the capsule are due to two controlled surfaces, which have two positions: closed and open ones. As is faown, small mass and aerodynamic asymmetries of the capsule can lead to various types of resonance phenomena and effects. It should be noted that the cause of the accidents during an atmospheric descent of a spacecraft may be a resonance capture, which leads to a significant increase of the angle of attach. The purpose of this wo^ is to provide analysis and estimation of the probability of a principal resonance capture of a capsule with small variable mass and aerodynamic asymmetries resulting in arbitrary angles of attacL The theoretical significance of this wo^ is an approximate analytical estimation of the probability of a principal resonance capture. This estimation of the probability of a resonance capture is expressed in the terms of the elementary functions. Of practical interest is implementation of a controllable transition to the coplanar combination of the asymmetries for the capsules having an orthogonal combination of the asymmetries during a reentry. This transition may be implemented according to the introduced control law. Calculation of the probability of a resonance capture is considered on the example of the problem of the atmospheric descent of a capsule with the mass-inertial characteristics similar to the Mars Polar Lander spacecraft. The authors demonstrate that a transition from the orthogonal to the coplanar combination of the asymmetries contributes to a significant reduction of the probability of a resonance capture. The presented estimates can be used for calculation of the probability of capture or passage through a principal resonance during a descent of a spacecraft in the atmosphere of any planet.

The sea waves cause the effect of a rotational motion (i.e., pitch, roll and heading angle) of ships. The ship rotational motions result in beam pointing error of the phased array radar aboard the ship. The antenna stabilization aimed to achieve a beam pointing accuracy over a long dwell time is an important problem for the shipborne phased array radars. Due to the dynamic and stochastic nature of the sea environment, the shipborne phased array radar must be able to compensate for the ship's motion adaptively. In this paper, the linear discrete Kalman filter is proposed as a predictor for the shipborne phased array radar, which can compensate for the beam pointing error and track the air and sea surface targets. The pitch, roll and heading angles and the its velocities data are measured on-line from a gyroscope of the sea vehicle and used from the ship motion mathematical models for their prediction. It is proved, that the pitch, roll, and heading motion models may be considered as independent. All these models are presented as the same second order linear differential equations with different parameters. Besides, equivalent linear discrete state space models for the angles' changes are constructed in the paper. The estimation accuracy of the Kalman filter (predictor) depends on the values of different parameters, such as the parameters of the ship's motion mathematical model, measurement error covariance matrices, etc. The sea environments are very dynamic, hence, there is a need for an adaptive system for the controlling and compensating devices, operating regardless of the ship's motion. Continuous monitoring of the environment and adapting filter ensure parameters with less computational burden needed for a real time application. The paper describes a technique for identification of such parameters by the measured correlation functions of the pitch, roll, and heading angles. Finally, it is proved by the computer simulations that the proposed compensations technique is a real time applicable algorithm for a shipborne phased array radar. The computer simulation was performed with the following parameters: the measurement frequency for the gyroscopes was 100 Hz, the prediction times of the Kalman filter were 0.01 s and 0.1 s. The following two cases were considered. In the first case, only the predicted angles were measured with gyroscopes. In the second case, the angles and the rates of their change were measured. The simulations demonstrated that the presented prediction algorithm ensured higher accuracy (less root mean square errors of the predicted angles) than the initial accuracy of the gyroscopes measurements.