**ABSTRACTS**

*Randomized
Algorithms*

Close Loops, Averaging and Randomization in Control
and Data Mining

*O. N. Granichin*

*Saint Petersburg** *

*Key words: *information, signals, data, knowledge, control, feedback, averaging,
randomization.

This article is based on
the materials prepared for the workshop “Randomization and Averaging in
Estimation, Optimization and Control” which was proposed by the author together
with A.L. Fradkov at the international conference IEEE MSC-2012. The purpose of
the workshop was to explain the key results and applications of the two
important tools for system analysis and design, namely, randomization and
averaging. These tools can largely facilitate the numerical solutions of
various estimation, optimization and adaptive control problems, which are
typically formulated under limited resources and insufficient data.

Bibliogr.: 99 refs.

Randomization in Single Camera Depth Estimation
Problem Using the Idea of Asymptotic Observer

*D. S. Krivokon,*

*A. T Vakhitov*

*Saint Petersburg** *

__dmitry00@gmail.com__, __alexander.vakhitov@gmail.com__

*Key words: *randomization, depth
estimation, dynamical systems.

We introduce a random perturbation-based
algorithm for estimating the depth of a
moving or stationary point using an optical flow observed by a single camera.
Incorporation of random perturbations facilitates the removal of the ambiguity
in the case of the moving point observed by a single camera and to attenuate
the noise and discretization error. We demonstrate the performance of the
proposed algorithm over simulations with different types of noise including
non-zero mean and different motion models.

Bibliogr.: 12 refs.

*Discreet
Systems*

Generalization of the Krylov Method for Queuing
Problems

*K. Î**. Vidyaeva*

*Saint Petersburg** *

*Key words: *k-minimal polynomial of an operator, spectrum of a linear operator,
Monte-Carlo method, stationary mode.

The concept of a k-minimal
polynomial of an operator is introduced together with an approximate method for
finding this polynomial. The method is based on computing the iterates of
certain functionals of the operator. The properties of the algorithm are
discussed when using the

Bibliogr.: 3 refs.

Mathematical Analysis of Processing *M *FIFO-Queues

*A. V. Drac, A. V. Sokolov*

*Petrozavodsk** *

__adeon88@mail.ru__, __avs@krc.karelia.ru__

*Key words: *FIFO-queues, dynamic data structures, mathematical modeling.

This paper presents a
mathematical model of a behavior of *M *FIFO-queues in a single-level
memory which admits the insertion into one of the queues at odd steps and the
deletion from one of the queues at an even step. The probability of deletion
from an empty queue and the average size of queues after *N *steps are
calculated.

Bibliogr.: 7 refs.

Statistical Analysis of Errors in Numerical Solution
of Quasilinear Equation Systems

*D. A. Fidelman*

*V. B. Khristinich*

*Sankt-Petersburg** *

*Key words: *systems of quasilinear
equations, statistical analysis.

This work is devoted to
statistical analysis of errors that occur during the numerical solution of
systems of linear and quasilinear equations depending on the stability
parameters. The behavior of statistical characteristics of solutions are
studied for initial and boundary perturbations with certain probability distributions.
The considered approaches are illustrated via solving of acoustics equations.

Bibliogr.: 4 refs.

*Information
Systems*

Matching and
Merging Algorithms for Abstract Syntax Trees

*D. V. Pavlenko*

*Saint Petersburg** *

*Key words: *version control system,
merge, diff3, abstract syntax tree.

Matching and merging are
the most important problems in the version control field. Use of matching files
semantics allows to better display their difference visually and to merge
different versions of the same file by automatically resolving the conflicts.
As a rule, merging algorithms are based on matching algorithm. The paper
proposes a matching algorithm for abstract syntax trees.

Bibliogr.: 17 refs.

Use of Linear Matrix Inequalities in the Determination
of the Set of Feasible Values of the Kalman Filter

*V. M. Ponyatskiy*

*KBP, *

__kbkedr@tula.net__, __pwmru@rambler.ru__

*Key words: *dynamic plant,
parameters.

The paper discussed the
design of the Kalman filter using linear matrix inequalities (LMIs). With the
proposed approach, a set of feasible transmission coefficients of the filter
can be characterized. The choice of specific values of the filter parameters is
carried out in accordance with the additional conditions, e.g., based on the
required bandwidth of the filter and its dynamical properties. An example of the
design of the Kalman filter using LMI techniques is given.

Bibliogr.: 6 refs.

Analysis of Dynamical Plants via Finite--Frequency
Identification Method and Test Results

*V. M. Ponyatskiy*

*KBP, *

__kbkedr@tula.net__, __pwmru@rambler.ru__

*Key words: *identification, dynamic
plant, model, estimates, parameters.

We consider estimation
of the coefficients of linear dynamical plants in passive experiment using the
finite-frequency identification method.
Simulation results show that, in order to obtain the estimates, the frequency
range of the input signal should be close to the value of the adjust frequency
of the plant.

Bibliogr.: 3 refs.

*Hybrid
Computers*

Nonlinear Dynamical
Systems as a Basis of New Intelligent Systems

*E. N. Benderskaya*

*St. Petersburg** State Politechnical University*

*Key words: *nonlinear dynamic system, chaotic dynamics, pattern recognition,
intellectual tasks, artificial intelligence.

The article examines the
nonlinear dynamic formation of the intelligent system structure by an input image.
The main components of this new approach to pattern recognition problems are
considered as well as its advantages and limitations. An example of using the
chaotic dynamics for the clustering problems is given.

Bibliogr.: 20 refs.