Granichin O.N. (SPbSU) Close loops, averaging and randomization in control and data mining .... 3

Krivokon D.S., Vakhitov A.T. (SPbSU) Randomization in single camera depth estimation problem using the idea of asymptotic observer .... 49

Vidyaeva K.O. (SPbSU) Generalization of the Krylov method for queuing problems 60

Drac A.V., Sokolov A.V. (PetrSU, IAMR KarSC RAS, Petrozavodsk) Mathematical analysis of processing M FIFO-queues .... 75

Fidelman D. A. , Khristinich V. B.. (SPbSU) Statistical analysis of errors in numerical solution of quasilinear equation systems .... 83

Pavlenko D.V. (SPbSU) Matching and merging algorithms for abstract syntax trees .... 95

Ponyatskiy V.M. (GUP "KBP", Tula) Use of linear matrix inequalities in the determination of the set of feasible values of the Kalman filter .... 121

Ponyatskiy V.M. (GUP "KBP", Tula) Analysis of dynamical plants via finite-frequency identification method and test results .... 129

Benderskaya E.N. (SPbSPU) Nonlinear dynamical systems as a basis of new intelligent systems .... 136







Randomized Algorithms

Close Loops, Averaging and Randomization in Control and Data Mining

O. N. Granichin

Saint Petersburg State University

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 State University,

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. . Vidyaeva

Saint Petersburg State University

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 Monte Carlo approach. The results of numerical experiments with problems in queuing theory are given.

Bibliogr.: 3 refs.


Mathematical Analysis of Processing M FIFO-Queues

A. V. Drac, A. V. Sokolov

Petrozavodsk State University, IAMR KarSC RAS, Petrozavodsk,

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 State University

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 State University

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, Tula,

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, Tula,

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.