The article is devoted to studying of the object, the mathematical model of which is the vector equation with a distributed delay on a state vector and input signal. It is assumed that the parameters of the mathematical model are unknown, and the limited disturbance influencing the object is unmeasured. The problem of tracing of a reference signal is formulated. In order to ensure qualitative tracking of the reference signal, it is necessary to compensate for the influence of the unmeasured disturbance on the output variable. For solving of this problem the method of the internal model is used. This method proved itself in designing of the robust controls for the discrete systems. In this paper it is used for the continuous systems. The problem of the robust control of the objects with the distributed delay on the state vector and input is being solved. It is assumed that the parameters of the mathematical model of an object are unknown, and only the output variables are available for measurement. As the target conditions the accuracy of tracking of the reference signal is accepted. The control algorithm was obtained allowing to compensate for the aprioristic uncertainty and to reduce essentially the influence of the unmeasured bounded external limited disturbance. The equations of the closed system are a singular system of equations. It was proved, that the received control algorithm ensured implementation of the target conditions. The numerical examples and the results of the computer simulation, which have demonstrated the efficiency of the received algorithm of tracking, are presented.

The article presents efficient computational algorithms for analysis of the stability of the dynamical systems. The algorithms are based on the principle of modal approximation. A numerical algorithm for computing of the poles of the transfer function is proposed, which ensures determination of the poles located in the right half-plane. In order to detect the pole with the positive real part the suggested algorithm exploits the property of the damping factor ς i =- αi αi 2 + βi 2 for the obtained poles λi= αi+i βi . This factor is negative for the poles with positive real parts. The following sequence of the form ς1 α1 , β1 - ς0 < ς2 α2 , β2 - ς0 <...< ςk αk , βk - ς0 is constructed for the computed poles. The sequence is converged to the pole with the positive real part under ς0 <1 . The paper presents an algorithm for computation of the poles of the transfer function with the maximal sensitivity with respect to the circuit parameters. The suggested algorithm allows us to detect the parameters with the maximal impact on the shift of the poles and to determine the critical parameter values corresponding to the boundary of instability.

A nonlinear hybrid mechanical system is studied. It is assumed that on the system homogeneous switched positional forces, linear gyroscopic forces and homogeneous dissipative ones act. Conditions are determined under which the trivial equilibrium position of the considered system is asymptotically stable for any admissible switching law. It is well known that to prove the asymptotic stability uniform with respect to swishing law, it is sufficient to construct a common Lyapunov function for the family of subsystems corresponding to the hybrid system. However, till now there are no general constructive methods for finding of common Lyapunov functions, even for families composed of linear subsystems. The problem is especially difficult for mechanical systems with switched force fields, since such systems are described by differential equations of the second order. This results in the appearance of certain special properties of motions and essentially complicates the analysis of system dynamics. In particular, well known results obtained for switched systems of general form might be inefficient or even inapplicable for mechanical systems. In the present paper, a new approach to the stability analysis is proposed. The approach is based on the decomposition of the original system consisting of differential equations of the second order into two isolated first order subsystems of the same dimension. It should be noted that one of the isolated subsystem is switched, whereas another one is non-switched. Thus, the decomposition method permits us to reduce the problem of a common Lyapunov function constructing for the original family of nonlinear systems of dimension with a special structure to that for an auxiliary family of subsystems of dimension which, generally, do not possess a special structure. The problem of stabilization of the equilibrium position of a system for any switching mode scaling the potential with the aid of small forces of radial correction is considered. For a model of the magnetic bearing of a rotor with nonlinear switched circular forces, the stabilizing feedback control law is constructed by the use of linear gyroscopic and nonlinear dissipative forces.

In recent years the problem of a mobile wheeled robot control has received great attention and lots of solutions have been found. The dynamical model of a mobile wheeled robot includes the mass-inertial parameters, which are customary, as a rule, unknown and time varying. It is difficult to select an exact dynamical model of a wheeled mobile robot for the design of a model-based control. In order to handle such unknown parameters many control strategies were proposed, including sliding-model control and adaptive control. The problem of dynamics of the controlled motion of the mobile robots with omni-directional wheels is of interest to many researches. Such mobile robots are characterized by a full omni-directionality with simultaneous and independently rotational and translation motion capabilities. Therefore, such types of the wheeled robots can implement complicated tasks in a narrow space. An independent control of the rotation of each omni-wheel leads to the inevitable slipping in motion along the motion surface. Therefore, considering slipping between the wheels and the motion surface, a dynamic model of an omnidirectional wheeled mobile robot is of great interest to many researches. The sliding friction occurs both in the direction along the surface of the wheel and transversely to it. It is important to design a motion control, which has no hard performance and allows us to take into account the sliding friction and the inaccuracy of the dynamical model. The aim of this paper is to solve the problem of a non-stationary trajectory tracking control of a mobile robot with four omni-wheels and inaccurately known inertia matrix, taking into account the wheel slip. On the basis of Lyapunov vector functions the discontinuous and continuous control laws were obtained. The results of the numerical simulation are presented.

Heavy vehicles are an important class of the multi-purpose mobile ground vehicles. According to an expert opinion, development of the heavy mobile robots (mobots) based on HTVs will boost the efficiency of different purpose HTVs. It should be underlined that most of the domestic and foreign mobot solutions are usually based on a remote control, when a specially trained expert uses a cable or wireless liaison to control a mobot's spatial motion and other functionalities from a control station. Thus, the individual control method, in which certain functions of a Control station operator can be delegated to the onboard control system, is nowadays of huge interest worldwide. For this reason, within a mobot, besides the remote control modes, the individual control modes can be implemented, which are carried out by the onboard control system only, without any direct involvement of a control station operator. That means formalization of the expert knowledge acquired by human crew members in the form of a set of time diagrams of the operating members' configuration. There are many works dedicated to development of the executive level control actions of small and medium autonomous mobots. However, the achieved results are almost inapplicable for development of the executive level controls for the heavy autonomous mobots. To a great extent this is due to the fact that there are many uncertainties concerning the movement process of the mobots of the aforesaid class. Such uncertainties include imperfect dynamics model of the mobot, complexity of interaction between the robot's running gear and the movement surface, etc. This article is dedicated to the software of the mobot execution level control actions in the standalone mode. Employment of the methods of the situation control and formalization of the expert knowledge made it possible to implement the software for the execution level control actions in the form of a set of coherent time diagrams showing variation of the operating members' configuration in the conditions of uncertainties.

The topic of the article is a three-dimensional model of the exoskeleton with the links of variable length. The idea is based on the analysis of the equations for a truss of the mechanical systems with a different number of links, and on generalization of the equations of motion of the exoskeleton in the vector-matrix form. Formulas are derived for the elements in each matrix, which is a part of the equation. The proposed matrix form of the equations of motion of the exoskeleton is universal and can be applied to the motion of the rod of a mechanical system with any number of links, which change their length. The structure of the matrix will remain the same, the change will concern the dimensionality, number of masses, lengths of the links of each matrix element. In practice, the proposed model can be used to create manipulators, anthropomorphic robots, exoskeletons and artificial limbs, artificial yielding links, which imitate the properties of the biological tissues of the human musculoskeletal system, so that movement of the artificial mechanism could be as close as possible to the movement of a person. The result allows us to automate writing of equations of motion for the rod of n-tier systems, of the three-dimensional model of the exoskeleton type, bypassing the stage of their preparation, which is a novelty of the research.

The traditional forecasting of events is based on a preliminary design of their models. Employment of such models as a part of the intelligent robots cannot take into account the whole variety of the situations, which may arise. It is desirable that an adequate model of events is formed by a robot itself. In the interests of intellectualization of the autonomous robots the task of predicting events without setting models of their development is considered. Objective is to increase the functionalities of fore-casting of the events with the changing laws of their development. In order to address this problem a new method for predicting is proposed. The method involves the use of a recurrent neural network with controlled synapses and with a layer structure in the form of a double spiral. The method is based on associative memorizing of the current and delayed signals, and extraction of the future events from the memory of the neural network. According to the method is not necessary to know in advance, in accordance with which law the observed events will develop. The development model of such events is formed by the dynamic neural network itself in the process of accumulation of its experience. The method makes it possible to predict the parallel events at various depths with a gradual improvement of the results. These results are the sliding multistep forecasts. Due to this the intelligent robots can qualitatively predict events and plan their responses. The simulation results, reflecting the peculiarities of such prediction, are presented. The recommendations for the use of the proposed method have been formulated.

Any aircraft mission includes a land movement phase. Such phases are carried out under control of a pilot. At this time the aircraft crew experiences high psychological stresses. Stressful conditions create prerequisites for improper or erroneous actions. Therefore, the human factor plays a decisive role in ensuring safety and accident free flights of the air transport. In order to improve the crews' situational awareness, the algorithmic methods for assessing of the current and predicting of the future movement of the aircraft were developed. The methods are based on the energy approach to the flight control. The well-known energy balance equation is generalized to the runway modes by adding a member, reflecting the absorption of energy to overcome the drag of the mechanical forces. The new member is presented in the following form: ∆ HE b= t1 t2 V kb dt , where k_b is the normalized braking coefficient equal to the ratio of the total resistance forces from the chassis to the weight of an aircraft. Here H_E (*) = E (*)/ mg is the specific energy. The extended equation ∆ HE =∆ HE eng+∆ HE D+ HE b+∆ HE w describes how to change the total energy of an aircraft throughout its trajectory, including the ahead segment. The length of this segment is calculated from the conditions of achievement of the required final energy state. In the braking mode the final state is determined by a known speed taxiing. The target braking distance is described by the following equation: Db =0,5 V t 2- Vtaksiin t 2 / gnx t . However, this forecast does not take into account the change in the braking forces on the ahead lying trajectory. Therefore, in order to improve the reliability of forecasting the method of algorithms' correction was offered. The correction coefficients are the functions of the mass, velocity and braking coefficient. These functions are approximated by the polynomials up to degree-4. The computer research stand was developed, including the mathematical model of Tupolev Tu-204. The deterministic and statistical tests within the range of the aircraft mass of 70-105 tons, approach speed of 200-220 km/h and friction coefficient of 0,3-0,75 were performed. The estimates of the accuracy of the forecast on the basis of the tests are presented.

Problem statement: The task of real time cargo traffic scheduling for the International Space Station (ISS) is considered. The problem of strategic and tactical scheduling of the flights, delivery, return, disposal and allocation of ISS cargo traffic, including more than 3500 entities, is very complex and time-consuming. In order to solve this problem it is important to take into consideration numerous factors, constraints and preferences, such as changing fuel, water and supplies demand, ballistics and solar activity, particular types of spaceships and docking modules. Changes in dates of launch, landing, docking and undocking, crew size and other parameters affect the flight program and cargo traffic. These changes cause dynamic rescheduling in the chain of changes of the interconnected parameters, which would be specified, recalculated and coordinated. The problem is formalized as a dynamical balance of interests (consensus) between the orders and resources. Methods: The method of real-time adaptive cargo traffic rescheduling is proposed. The method is based on a multi-agent technology for identification and solving of conflicts by negotiations of agents. ISS cargo traffic scheduling method develops the suggested method of conjugate interactions in the Demand-Resource Networks (DRN) by using cargo priorities. The advantages of the suggested solution for the adaptive events processing without stopping and restarting of the system are shown. Benefits of the method include high flexibility and efficiency for the event-driven adaptation of the cargo schedules in real time. Results: The developed method was implemented in the multi-agent system for ISS cargo scheduling with the use of a multi-agent platform for real time scheduling. Practical relevance: The developed system is based on the multi-agent technologies and is now in commercial operation. It is applied in the cargo traffic scheduling for the Russian Segment of ISS. The system ensures such advantages as ISS cargo traffic scheduling similar to the schedules created by experienced operators; flexible and quick reaction to the events which cause cargo traffic rescheduling; double or triple reduction of the manual labor and increase of the decision-making efficiency; real-time monitoring and control of the schedule implementation.

The topic of the article is the computational fluid dynamics method for investigation of the contour stability in the rogue waves. Sampling of the Reynolds-averaged Navier-Stokes (RANS) equations was done by the method of the control volumes. In order to solve the linear system of the scalar equations, an implicit Gauss-Seidel method was used. Pressure-velocity coupling was achieved by using the Pressure-Implicit with Splitting of Operators (PISO) algorithm. The volume of the fluid (VOF) model was used to solve a single set of the momentum equations and tracking of the volume fraction of each of the fluids throughout the domain. A geometric reconstruction scheme was implemented to represent the interface between the fluids using a piecewise-linear approach. In order to compute the translational and angular motion of the center of gravity of the vessel contour, the three degrees of freedom (3DOF) solver was used. Variable sampling in the time domain was used to ensure stability of the solution. A rogue wave with a single high central peak and two small side elevations was used in a numerical wave tank, which met most of the marine observations. The wavelength of the 30-meter high rogue waves, which can capsize marine vessels of a big displacement, was calculated. On the basis of the spatial spectrum of the rogue wave, equations of the velocity of the fluid flowing into the numerical wave tank were obtained. Due to the non-linear processes the rogue wave height reached its maximum and then collapsed to form a plunging breaker. The contour was positioned at a predetermined distance from the initial position of the rogue wave and when the contour met with the rogue wave, the heeling angle of the contour was calculated. On the basis of a series of numerical experiments, the distances and the wavelengths of the rogue waves capsizing the contours of the fishing vessels were calculated. It was discovered that the rogue waves with the length of 120-140 meters and high steepness capsize the contours of the fishing vessels with displacement up to 9260 tons.