*Stochastic Systems*

Reachability and
Attraction Domains for Linear Systems with Bounded Control: A Characterization
via Invariant Ellipsoids

*B.
T. Polyak, P. S. Shcherbakov *

*Institute
of Control Science, RAS, Moscow *

*Key words:*
attraction domain, invariant ellipsoid, linear matrix inequalities, absolute
stability.

This paper is aimed at
efficiently characterizing reachability and attraction
domains of linear systems specified in the state space description. We
consider bounded controls in the form of the linear static state feedback and saturated control. A
description of reachability and attraction domains for such systems is given
in terms of invariant ellipsoids using the
apparatus of linear matrix inequalities and semidefi-nite programming formulation. Design of saturated
control is based on the ideas of the theory of absolute stability.

Bibliogr.: 17 refs.

Analysis of a Dynamic
Plant with Constraints on the Output Coordinates Using the Invariant Plunging
Method

*V. M. Ponyatskiy*

*KBP, Tula*

__kbkedr@tula.net__, __pwmru@rambler.ru__

*Key words:*
identification, dynamic plant, estimate, parameter, restrictions.

The
approach for the analysis of the dynamic plant with constraints on the output
coordinates based on the invariant plunging method is considered. The synthesis of algorithms for the estimation of a transfer
ratio, time constant and a damping ratio for non-stationary dynamic
plant with constraints on output coordinates is given. Simulation of the
algorithms derived is performed and recommendations on their adjustment are
presented. The estimation of a transfer ratio and time constant of the servodrive of the twirled pilotless aircraft is done
using the agorithms proposed.

Bibliogr.: 8 refs.

*Randomized Algorithms*

Pseuogradient
Method with Input Perturbations for Non-Stationary Unconstrained Optimization Problem

*A. T.
Vakhitov, L. S. Gurevich, *

*St.
Petersburg State University*

__av38@yandex.ru__, __gurevich.lev@gmail.com__

*Key words:* stochastic optimization, randomization,
tracking, pseudo-gradient.

Applications
of methods of stochastic optimization with simultaneous perturbations of input
with two measurements on each step (SPSA type)
to problem of global convex optimization of non-stationary functional are
considered. Upper bound for estimation error of the algorithm is proven for almost arbitrary noise and one time
differentiable functional.

Bibliogr.: 11 refs.

Randomized Algorithms for Computing the Invariant
Zeros of Large-Scale Dynamic Systems

*M. Sh. Misrikhanov, V. N.
Ryabchenko,*

*Main
electricity transmission company “Center”, Moskow*

mms@mes-centra.ru rvn@mes-centra.ru

*Key words:* MIMO-system, invariant zeros, squaring
up, eigenvalue problem, large electric power system.

An algorithm for the
large dynamic MIMO-system invariant zeros determining
problem is described. The problem of invariant zeros determining with the help of randomized squaring up of
initial MIMO-system is reduced to the standard eigenvalues problem of numerical
matrices. Practical applications of the algorithm proposed lie at the area of
large electric power systems.

Bibliogr.: 10 refs.

*Queuing Systems*

Analysis of Some Implementation
Methods for Priority Queues

*E. A. Aksenova, A. V.
Sokolov *

*IAMR
KarSC RAS, Petrozavodsk *

aksenova@krc.karelia.ru avs@krc.karelia.ru

*Key words:* priority queue, random walk,
Markov’s chains.

The
paper presents the analysis of some priority queue realization methods. It is possible
to produce operations: to insert, to delete the maximum, to find the maximum.
Suppose that probabilities of operations
are known. The priority queue is realized using array or k consecutive
FIFO-queues. Mathematical models of this methods are developed. The task is to
choose the method that maximizes the average time until memory overflow.

Bibliogr.: 9 refs.

Optimal Allocation of n Stacks and/or Queues in
Single-Level Memory

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

*Petrozavodsk
University, IAMR KarSC RAS, Petrozavodsk*

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

*Key words:* LIFO-stacks, FIFO-queues, linked
list, Markov’s chains, dynamical data structures.

This
paper concerns issues related to building mathematical models and
optimal algorithms of stacks and queues in single-level memory. These
models are constructed as n-dimensional random walks.

Bibliogr.: 6 refs.

Evaluation of Lyapunov Exponent for Stochastic Dynamic
Models of Queueing Systems

*N. K. Krivulin*

*St.
Petersburg State University*

*Key words:*
stochastic dynamical system, Lyapunov exponent, idempotent algebra, queuing
systems, mean service cycle time.

The
problem of evaluation of Lyapunov exponent in queuing system analysis
based on models and methods of idempotent algebra is considered.
General existence conditions for the limit that determines Lyapunov exponent
are given, and examples of evaluation of the limit for systems with matrices of
particular types are presented. A method of evaluation of Lyapunov
exponent is proposed based on some appropriate decomposition of the
system matrix. A general approach to modeling of a wide class
of queuing networks is considered, and examples of the models are given. It is shown
how to find the value of mean growth rate of the
system state vector through the evaluation of Lyapunov exponent. Results
of evaluation of the mean growth rate for the models under consideration are
presented.

Bibliogr.: 24 refs.

Optimal Control for Interdependent Periodically
Nonstationary Stochastic Automata System in the Fuzzy Set Conditions

*E. N. Mosyagina, M. K.
Tchirkov *

*St.
Petersburg State University *

*Key words:*
periodically nonstationary stochastic automaton, automata system,
fuzzy surroundings, fuzzy conditions, optimal strategy.

Synthesis procedure of
complex optimal control for a periodically nonstationary
stochastic àutomatà finite set, joined in an interdependent system,
under condition of the fuzzy given goals representation in a complex’
particular tact and in view of non-stationary interdependent fuzzy conditions
for controlling actions on automata, included in a system, are considered.

Bibliogr.: 5 refs.

*Learning and Adaptation*

Adaptive Parameter
Estimation in the Multi-user Parallel Computing Systems

*A. T. Vakhitov*

*St.
Petersburg State University*

*Key words:* scheduling, parallel computations,
linear estimation, stochastic optimization.

The task of parallel
computing system parameters estimation is described.
The problem settings for the estimation of computing node performance,
network bandwidth, task execution time are given. It is taken into
consideration that the parameters can change in time. The estimates can be used by the scheduling algorithm. In the SPRInt laboratory of the SPbSU the scheduling
service-broker for the modeling of the adron therapy experiments.

Bibliogr.: 14 refs.

Stereovision Algorithms: A Survey

*A. T. Vakhitov, L. S. Gurevich, D.
V. Pavlenko*

*St.
Petersburg State University*

__av38@yandex.ru__, __gurevich.lev@gmail.com__, __dmit10@gmail.com__

*Key words:* stereovision.

The
stereovision problem is to obtain the distance based on inputs from two or more
cameras. The input data may be a single image or
video series. We consider the particular case when two images are compared.

Bibliogr.: 16 refs.

Statistical Methods of Automatic Word Extraction in
Vietnamese Documents

*Le Trung Hieu*

*St.
Petersburg State University*

*Le Anh Vu University ELTE,
Budapest, Hungary*

*Le Trung Kien Hue University,
Vietnam*

__vkhhieukien@yahoo.com__, __leanhvu@inf.elte.hu__, __hieukien@hotmail.com__

*Key words:* words localization in Vietnamese
documents, statistical methods, adaptation.

In this paper, we implemented
application of statistics on creating a
Vietnamese list words and phrases. The aim of our projects is thus to build a common linguistic database that is freely
and easily exploitable for the automatic processing of Vietnamese.

Bibliogr.: 15 refs.

Adaptive Adjustment Method for
Control Flow of Individual Tasks in Parallel Environment^{}

*M.
A. Panshenskov*

*St.
Petersburg State University*

*Key words:* distributed
computing, task scheduling, adaptive methods, communication.

The model of isolated
task execution is formulated in extended control
flow terminology. The two main classes of possible bottlenecks in the control flow are identified: data transfer
through communication channels and
task execution on the computing nodes. For each case the scheduling algorithm is proposed. The
execution time upper bound depending on the size of the heterogeneous computing
network is proposed.

Bibliogr.: 10 refs.

Analysis of Implementation Methods for Adaptive
Control Systems with Kalman Filter^{}

*V. M. Ponyatskiy*

*KBP, Tula*

__kbkedr@tula.net__, __pwmru@rambler.ru__

*Key words:* control
system, adaptation, dynamic errors, Kalman filter, pass band.

Design
of the control system with Kalman filter adapting to operating and revolting
affecting in real interfering conditions is considered. The algorithm of
adaptation implements functions of detection and decision making. The pass band of Kalman filter and parameters of the of control law are changed according to the
magnitude of the dynamic control errors.

Bibliogr.: 14 refs.

Adaptive Audio-Visual Clustering for Multiple Object
Localization

*V. Khalidov, F. Forbes, M. Hansard,
E. Arnaud, R. Horaud*

*Inria, Grenoble, France*

*Keywords:* multimodal
systems, mixture models, expectation maximization.

This
paper addresses the issue of identifying and localizing those objects
in a scene that are both seen and heard. In particular, the task of
localizing human speakers is emphasized. We explain the benefits of a human-like
configuration of sensors (binaural and binocular) for gathering both auditory
and visual observations. It is shown that the identification and localization
problem can be recast as the task of adaptive
clustering the audio-visual observations into coherent groups. We propose a probabilistic generative model that
captures the relations between audio and visual observations. This model
maps the data to a representation of the
common 3D scene-space via a pair of mixture models. Inference is performed by a
Generalized Expectation Maximization (GEM) algorithm, which provides
cooperative estimates of both the auditory activity and the 3D position
of each object. Different versions of GEM
are described and compared, their performance on the tasks of multiple
and single speaker detection and localization is demonstrated.

Bibliogr.: 27 refs.

Cluster Stability Algorithms Based on Index or
Stability Functions

*D. S. Shalymov*

*St. Petersburg State University*

*Key words:* clustering, cluster validation.

Clustering
is the subject of active research in several fields such as statistics,
pattern recognition, machine learning etc. Review of several algorithms
for assessing cluster stability is performed. The first group of
described algorithms uses indexes, based on multivariate statistics, which
compare dispersions within and between the clusters. The second group
uses stability functions that measure the consistency of labels assignments
to sample elements. Notion of clustering and cluster stability
is introduced. Basic principles of clustering algorithms are discovered.

Bibliogr.: 11 refs.

*Information Systems*

Design of a Quality Monitoring
Information System for the Education Process at the University Level

*O. N. Granichin, O. A. Granichina,*

*St.
Petersburg State University,*

*Herzen
Russian State Pedagogical University*

Oleg_granichin@mail.ru Olga_granichina@mail.ru

*Key words:*
quality monitoring, educational process, information system, randomized balanced
scorecard method.

The
original approach to the designing of the information monitoring system of the university
educational process’s quality is described. The randomized
balanced scorecard method is used for the convolution of versatile estimates.

Bibliogr.: 9 refs.