Analysis of probability distribution of a random variable of an execution time of the program in the presence of random failures

The mathematical model of an estimation of an execution time of the program in the presence of random failures is studied. For decreasing of influence of failures on a program execution time the known method of checkpoints is considered. The main objective consists in reception of the formula for a distribution function of a random variable of an execution time of the program and an estimation of a quantile of the received distribution. Properties of a mean value of a random variable of an execution time of the program are studied.     

Method for segregation of suspected logical malfunctions in combinatorial discrete devices

Consideration was given to the direct problem of technical diagnosis which lies in determining the technical state of a combinatorial discrete device from the results of testing. The graph and analytical models of behavior of the combinatorial discrete device allowing for the technical state of its elements were presented. A method of segregation of the suspected logical malfunctions under which observable behavior of the combinatorial discrete device is possible was proposed.     

Universal software packages to model the distributed-parameter systems

Consideration was given to the universal software packages for modeling objects and distributed-parameter systems obeying the partial differential equations. The packages may serve as important tools for industrial automation because the majority of industrial objects have distributed parameters. The review presented the results of comparing a number of commercial packages against a set of user-defined criteria. Its final part was devoted to some freeware packages. Conclusions were drawn, and recommendations for using the considered packages were given.     

On calculation of the power indices with allowance for the agent preferences

In the general case, complexity of the algorithm to calculate the power indices grows exponentially with the number of voting agents. Yet the volume of calculations may be reduced dramatically if many coalitions have equal numbers of votes. The well-known algorithm for calculation of the Banzhaf and Shapley-Shubik indices was generalized, which enables fast calculation of the power indices where entry of the voting agent into a coalition depends on its preferences over the set of the rest of agents.     

Parametric synthesis method of integral systems on the basis of root locus curves of Kharitonov polynomials

The method is developed for the synthesis of a stable set of characteristic polynomials of an interval dynamic system on the basis of the initial unstable set with the use of the system model in the form of a free root portrait. The synthesis is carried out by changing the boundaries (adjustment) of the interval of uncertainty of a free polynomial term, which enables affording the stability without a change of the configuration of the root portrait of the system. As a criterion of the adjustment, the distance is assigned that is measured along trajectories of the root portrait; in particular, a new polynomial can be defined by the nearest polynomial to the prescribed one with due regard for requirements of the quality of the system.     

Substantial and formal deductions in logics with vector semantics

The problem of logic deduction for one class of logics with a vector semantics is discussed. In the given logics the trustiness is represented by a vector with components 〈Truth; Lie〉, which do not depend on each other. The problem of organization of “substantial” and “formal” deductions is considered. In the first case the meaning of truth (semantics) of judgements is taken into account, whereas in the second case only the structure of judgements (syntax) is considered.     

To the optimal identification of multivariate systems under perturbations of unknown covariances

We consider the problem of parameter and covariance estimation for multivariate stochastic systems described by regression models with special structure perturbations of unknown covariance. Sufficient conditions of uniformly optimal estimations are obtained for system parameters and covariances. The observation vector distribution family is factorized, and the full sufficient statistics is found under those conditions. Equations for uniformely optimal unbiased estimates of covariance parameters are obtained.     

Two-level orientation control system of flexible spacecraft with active stabilization of structural elastic oscillations

Active stabilization of the elastic oscillations of the flexible objects belonging to the class of flexible spacecraft (FSC) was shown to be required for stable orientation control in addition to the main goal of control. An algorithm of Kalman estimation of the FSC coordinates and parameters was constructed, and a principle was proposed for two-level orientation control based on realtime estimates of the controlled coordinates. At that, the first level of control orients the FSC by the estimated “rigid” component of the total motion, and the second level stabilizes its structural elastic oscillations using the estimated elastic modes as controls. A number of algorithms was proposed to actively damp the elastic oscillations, and the methods of mathematical modeling were used to prove that in the case of two-level control the combined FSC motion is a stable manifold closed in a bounded domain where the requirements on the desired dynamics of FSC orientation processes are satisfied.     

Partial orders and Jordan normal form

Consideration is given to the relation between the structure of the acyclic binary relation and the adjacency matrix of its corresponding graph. In this case, the existing methods for studying the binary relations and their corresponding graphs in terms of the spectrum, that is, the set of eigenvalues, of the adjacency matrix are inapplicable because for the acyclic relations this matrix is nilpotent and its spectrum is identically zero. Therefore, a more refined characteristic of the matrix is required. The present paper considers the Jordan normal form (JNF) as such.     

Tracking in linear MIMO systems under external perturbations

Consideration was given to tracking the given trajectories of the output variables of the linear multiple-input multiple-output dynamic systems under uncontrollable external perturbations. A procedure to rearrange the mathematical model of a control plant in a consistent block form of controllability and observability of the output (measurable) variables with regard for the external perturbations was developed within the framework of the block approach. This form underlies the decomposition procedures of feedback design enabling one to track the given trajectories invariantly to the external perturbations.     

Problems of boundary observability of elastic vibrations described by the system of telegrapher equations

Problems are solved for the observability of elastic vibrations described by various boundary problems for the system of telegrapher equations. The initial conditions that generate observable vibrations are found in the explicit form. The necessary time period of an observation is defined. The solutions of observation problems are given in the case of the classical and generalized solutions of the class L ₂ of appropriate boundary problems.     

Dynamic features of flexible spacecraft control in process of its transformation into a large space structure

Consideration was given to dynamics of angular motion control of the flexible spacecraft reconstructed into a large space structure. In formal terms, this transformation lies in gradual reduction of the constructive rigidity to small values giving rise to low-frequency ( $ \tilde f Consideration was given to dynamics of angular motion control of the flexible spacecraft reconstructed into a large space structure. In formal terms, this transformation lies in gradual reduction of the constructive rigidity to small values giving rise to low-frequency ( ≤ 0.05 Hz) oscillations which represent one of the attributes of the class of large space structures. The existing quantitative definition of the large space structure was specified. It was demonstrated that as the frequencies of structure’s elastic oscillations approach those of the control of object “rigid” motion, a new kind of interrelations between the motions of both types, the so-called “capture” of the controller frequency by that of the elastic oscillations, arises which impairs control efficiency to the point of losing system stability. Analytical (for the linear control systems) and computer-aided (for the discrete systems) methods for determination of the boundaries separating the two qualitatively different forms of existence of the transformed elastic object were proposed. Some results of computer simulation of the orientation control of variable objects such as flexible spacecraft and large space structure were presented. Original Russian Text ? I.N. Krutova, V.M. Sukhanov, 2008, published in Avtomatika i Telemekhanika, 2008, No. 5, pp. 41–56. This work was supported by the Russian Foundation for Basic Research, project no. 05-08-18175.     

On one extremal problem of adaptive machine learning for detection of anomalies

An adaptive algorithm to solve a wide range of problems of unsupervised learning by constructing a sequence of interrelated extremal principles was proposed. The least squares method with a priori defined weights used as a starting point enabled determination of the “center” of learning sample. Next, a natural passage from the least squares method to more flexible extremal principle enabling adaptive determination of both the “center” and weights of the learning sample events was performed. Finally, a universal extremal principle enabling determination of the scaling coefficient of the membership function in addition to the “center” and weights was constructed.     

Non-smooth guiding potentials in problems on forced oscillations

New classes of non-smooth guiding potentials are determined. The introduced concepts are used for solving the problem on periodic oscillations of controlled objects described by the system of differential equations and by the system of differential inclusions.     

Design of discrete control system of flexible spacecraft maintaining robust stability of elastic oscillations

For the flexible spacecraft with a nonlinear orientation control system using flywheel engines, an approach to making its elastic oscillations robust stable was considered. It relies on a purposeful variation of the boundaries of the stability domains in the parameter space of the spacecraft and controller with the aim of maximizing the number of robust stable elastic modes of the flexible spacecraft. To make its control stable in the large, consideration was given to the possibility of expanding the basic algorithm by adding the sum of the components using the estimated coordinates of the remaining series of low-frequency unstable modes. Presented was an example of mathematical modeling of the proposed spacecraft orientation system which corroborated operability of the approach making the multifrequency spacecraft stable to the elastic oscillations.     

Design of modified PD algorithm to control angular motion of large space structure

Consideration was given to the design of an algorithm to control orientation of the large space structure (LSS) in the presence of infralow (less than 0.01Hz) frequencies of elastic oscillations exerting considerable influence on the quality of transients due to closeness of the LSS eigenfrequencies to the frequency of control of the object’s “rigid” motion. Procedure for designing a modified PD-algorithm for orientation of the LSS with infralow frequencies of elastic structural oscillations was described. Methods were proposed for calculation of the coefficients of additional components of the modified algorithm and determination of the LSS eigenfrequency boundary to the right of which the orientation control system is robust to the deviations of the object frequencies or inaccuracy of their definition. Some examples of mathematical modeling of the processes of the relay gyroforce control of LSS orientation using the proposed algorithm were given.     

Robust control of composite beams

The structure uncertainty effect is considered on actively controllable composite beam that is a part of the structure of a civil building in a seismodangerous zone. The solution of the problem for active control of vibrations of the composite beam is based on the introduction of a simplified model of sensors and an actuator, which are implemented in the form of piezoelectric plates pasted on two opposite planes of the beam. A suggestion is made of the practical approach that affords the robust control of the composite beam and is founded on the modern H ₂- and H _∞-methods of the theory of control. The effectiveness of the suggested approach for the suppression of vibrations of the composite beam under consideration is illustrated by the examples of numerical modeling.     

Control of incompletely controllable differential-difference systems with delay

A problem of control of linear autonomous differential-difference systems for violation of the condition of complete controllability and uncontrolled initial state is studied. A problem of system trajectory nullification and its delay there within any specified time period is posed. A new condition for solvability of this problem is proved and a constructive solution is proposed.     

Signal restoration in linear systems with trends

For the unique solution of the problem of calculation of the inputs and outputs of a linear system from observations comprising additive quasipolynomial additives (trends) with unknown parameters, the existence conditions were established. Formulas to calculate the system signals and trends from the observations of the total signal were presented.     

Linear systems with multiple singular values

Properties of linear dynamical systems are studied in the case of Hankel singular values of high multiplicity for monosingular and bisingular systems. Singular values of the Hankel operator take only one or two values for such systems. Properties of transfer functions are analysed. Algorithms of transfer function analysis and design are developed. Relations between frequency characteristics and Hankel singular values are established.