Head of Laboratory – Dr.Sc. (Mathematics) Boris Miller

Tel.: (095) 209-47-81; E-mail: bmiller@iitp.ru

The leading researchers of the laboratory include:

Dr.	P. Chochia	Dr.	D. Sushko
Dr.	O. Milukova	Dr.	L. Rubanov
Dr.	A. Prosin		K. Stepanyan

Directions of activity:

· mathematical modeling of images and sequences of images;

· investigation of discrete-continuous and hybrid systems;

· control of stochastic and deterministic discrete-continuous systems;

· application of the theory of generalized optimization to problems of observation control and signal processing;

· methods of regularization for inverse problems;

· image processing, filtering, enhancement, and compression;

· interpretation and scene analysis;

· recognition and identification of video data;

· investigations of man-machine interaction systems for finite object area.

MAIN RESULTS

The investigation of the optimal control existence in nonlinear dynamical systems, described by Ito’s differential equations which are affine with respect to unbounded controls was completed. The method of discontinuous time transformation which gives a possibility to reduce the problem with unbounded controls to a problem with controls from compact set and with controlled stopping time was developed. The concept of generalized solution was introduced and the existence of weak optimal control was proved. In the problem with state independent coefficient at the unbounded controls an equivalence between singular control problem and the optimal control problem within the class of generalized solutions was established. The key point was the problem of the generalized solution approximation by a sequence of progressively measurable or even predictable bounded controls. The basis of such approximation was the discontinuous time transformation method, on the basis of which the sequence of bounded controls and stopping times were constructed in some auxiliary control problem with bounded controls. Thereby, after the inverse time transformation we obtain the sequence of bounded progressively measurable (predictable) controls and the appropriate sequence of ordinary solutions that approximates the generalized (discontinuous) optimal solution at all continuity points and at the terminal point as well. Therefore the basis of the investigation for a wide class of stochastic control problems with ordinary and generalized controls was created.

The new method of the singularities description was suggested for hybrid systems with phase constraints. This method was based on spatial-time transformations in vicinity of the discontinuity points. This method gives the opportunity to describe the singular phase of motion as a solution of an auxiliary (limit) system of differential equations without singularities. Thereby, the optimal control problem can be reduced to a standard one. The method proposed describes the singular solutions in mechanical systems with unilateral constraints, moreover, one can extend this method to a new class of systems with active constraints, where the impulse controls arise during the contact with constraint. The differential equations with a measures were derived for this class of systems and this is a new class of such equations with an impulsive feedback. Till now the only method to describe the uncertainties arising during the impact contacts was a method of differential inclusions,. Meanwhile the method of the discontinuous time transformation gave the possibility to reduce the optimal control problem to a standard one for a system with discontinuous right-hand-side, and by that to replace the phase coordinate singularity with the singularity of the control variable. (B. Miller.)

In the framework of the collaboration agreement between MicroSpec and IITP: «Investigation of Algorithms for the Image Defect Detection» the investigation of the detection algorithms on the images of low resolution was performed. The investigation of modified correlation-extremal algorithms of the images alignment was accomplished, and on their basis the algorithms of defect’s area detection, i.e. the area of significant distinction from the template were created. The algorithms and modeling programs were developed and tested on series of semi-regular objects, the results were approved by MicroSpec. (P. Chochia.)

We complete the development of mathematical model for Radon tomography in 3D and 2D spaces. The model includes the definitions of an object under investigation and a model of measurements (we use the scheme of a tomograph of the 1st generation), data simulation algorithms, reconstruction algorithms, and a methodology for estimation of reconstruction algorithm quality via tomagraphic images. The model is realized as application program. It gives the possibility to carry out mathematical experiments for development of new tomagraphic systems, and for studying and improving of reconstruction algorithms. We study the reconstruction problem in opto-acoustic tomography using Kormak's method. We expand the reconstructing function in series relatively to angle variables (Fourier expansion in 2D or spherical function expansion in 3D). It makes possible to separate the variables and to reduce the problem to the solution of integral equation of Abelian type relatively to space variable for each harmonic. Our investigation shows that this approach does not give the possibility to construct applicable reconstruction algorithms. Thereby we plane to continue the investigations using the alternative approach and try to construct a parametrix for opto-acoustic tomography problem. (D. Sushko.)

In the framework of RFBR Project No. 00-07-90032, development was continue of text-graphic database on the history of russian science. A relational database along with bank of images were developed to represent some personal funds of the Archive in digital form. Specifically, we processed the following funds:

- Fund No. 1916 of the academician A. P. Aleksandrov, RAS President in 1975-1986. The fund comprises 322 storage units regarding years 1932-1986, included in the Archive in 1987. 87 storage units with 517 photographs were digitized and restored and inserted into the database.

- Fund No. 1729 of the academician M. V. Keldysh, RAS President in 1961-1975. The fund comprises 272 storage units regarding years 1937-1986. Above 200 storage units were digitized, their processing and restoration is in progress.

- Portrait gallery of russian scientists of past time selected from Musin-Pushkin collection. The collection is a part of personal fund of the academician N. A. Morozov. The whole collection consists of 2651 storage units which are almost unknown to a wide scientific community. 264 images of scientists were selected from this collection and digitized, their processing and restoration is in progress.]

Performing a database administrator functions for the State registered database of the RAS history and membership since 1724 – RAS2000. (L. Rubanov.)

The investigation of the image recognition on the basis of the blurring operators classification and the blurring types was performed. The new approach to the identification of the blurring operator and its parameters was suggested. (O. Milukova.)

The new class of the observation control problems in stochastic dynamical systems with noises in observation, depending on the state and the estimate was considered. The existence theorems for optimal generalized solutions were proved. The representation of generalized solution based on the discontinuous time transformation was obtained, the equations in the form of differential equation with measures were derived. (K. Stepanyan.)

A theoretical investigation of the altitude dependence of the electron ionospheric concentration remote measurement method was performed. The method is based on the continuous analysis of nonlinear distortions of modulated signals arising in transmission through the dispersive atmosphere. (A. Prosin.)

GRANTS FROM:

· Russian Foundation for Basic Researches (No. 99-01-01088): "Development of the control theory for nonlinear discrete-continuous systems, described by differential equations with a measures".

· Russian Foundation for Basic Researches (No. 00-07-90032): "Development and creation of text-graphical database on Russian fundamental sciences on the basis of the RAS archives" (jointly with Sector of Digital Optics).

· US National Science Foundation Grant No. (CMS-0000458): "Active Singularity Approach to Control of Nonsmooth Mechanical and Electromechanical Systems Using Wavelet-based and Impulsive Contol Methods".

· Cooperation program CNRS (France) – RAS (Russia). Project CNRS/RAS cooperation № PECO/NET 9570: «Theory of singular control in stochastic systems».

International Project:

Collaboration agreement between IITP and MicroSpec Technologies Ltd., Carl

Zeiss Group (Israel): «Investigation of algorithms for the image defect detection».

PUBLICATIONS IN 2001

1. Miller B. and Bentsman J. Generalized solutions in dynamic systems with unilateral constraints // NOLCOS'01, 5th IFAC Symposium "Nonlinear Control Systems" Saint-Petersbourg, Russia, July 4-6, 2001, Preprints, pp. 625-628.

2. Dufour F. and Miller B. The relation between generalized and singular stochastic control problems // NOLCOS'01, 5th IFAC Symposium "Nonlinear Control Systems" Saint-Petersbourg, Russia, July 4-6, 2001, Preprints, pp. 1147-1153.

3. Miller B. M. and Stepanyan K.V. Discrete-continuous observation control for systems with state dependent noise // NOLCOS'01, 5th IFAC Symposium "Nonlinear Control Systems" Saint-Petersbourg, Russia, July 4-6, 2001, Preprints, pp. 1191-1196.

4. Miller B. Optimal control problems in discrete-continuous (hybrid) systems with phase constraints // International Journal of Hybrid Systems. 2001, v. 1, no. 1, pp. 1-18.

5. Bensman J. and Miller B. Dynamical systems with controlled controlled singularities: Multi-scale and limit representation and optimal control // Proceedings of the 40-th IEEE Conference on Decision and Control, Orlando, Florida, USA, December 2001, pp. 3681-3686.

6. Bentsman J. and Miller B. Mechanical systems with unilateral constraints: Controlled singularity approach // Proceedings of the 40-th IEEE Conference on Decision and Control, Orlando, Florida, USA, December 2001, pp. 3692-3697.

7. Emel’yanov D., Rubinovich E., and Miller B. Advanced guidance law design based in the information-set concept // Proceedings of the 40-th IEEE Conference on Decision and Control, Orlando, Florida, USA, December 2001, pp. 1234-1239.

8. Dufour F. and Miller B. Existence of the optimal generalized solutions in nonlinear stochastic control problems // Proceedings of the European Control Conference, Portugal, Porto, September, 2001, pp. 934-938.

9. Miller B. and Pankov A. Theory of random processes in examples and problems. M.: Moscow aviation institute, 2001, 300 p.

10. Kim S.-K., Lee S.-D., Kim C.-Y., Chochia P., Sushko D., Miller B. Patent 01308622.8-2217: «Method and apparatus for measuring color-texture distance, and method and apparatus for sectioning image into plurality of regions using measured color-texture distance». European Patent Office, 2001.

11. Karnaukhov V.N., Merzlyakov N.S., Osipova N.M., Rubanov L.I. Experience of electronic databases creation in the Archive of the Russian Academy of Sciences // Russian Archives. 2001, № 6.

12. Karnaukhov A., Merzlyakov N., Milyukova O., Karnaukhov V., Wenger E., Aizenberg I., Karnaukhov V. Digital Restoration of Watermark Images // Proceedings of EVA'01, Moscow, Centre PIC of Ministry Culture of Russia, STG, Moscow, 2001, pp. 196-199.

13. Rubanov L.I., Merzlyakov N.S., Karnaukhov V.N., Osipova N.M. Strategy of creation of digital archives accessible through the Internet // IS&T/SPIE’s 14th Annual Symposium «Electronic Imaging 2002: Science and Technology», 20-25 January 2002, San Jose, California, USA (in print).

14. Aizenberg I., Butakov C., Karnaukhov V., Merzlyakov N., and Milyukova O. Blurred Image Restoration Using the Type of Blur and Blur Parameters Identification on the Neural Network // SPIE Proceedings. 2002, vol. 4667 (accepted).