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:

Using the new approach to the description of dynamic for nonlinear controllable discrete-continuous systems with unilateral constraints it was obtained the description of controllable mechanical systems with inilateral constraints. This new method gives the opportunity to derive the optimal control for systems with so-called active constraints, having the controls arising during the singular phase of motion at the instant of contacts with obstacles.

The suboptimal filter, for the estimation of state in hybrid systems driven by hidden Markov process was obtained on the basis of truncation procedure in optimal infinite dimentional filter, suggested by B. Miller and W. Runggaldier. It was shown that in the case of rare change of state the performance of the suboptimal filtering is almost the same as for optimal one.

The new approach to image segmentation problem, basing on united color-texture image analysis in appropriated feature space, was proposed. The set of algorithms for extracting color and texture features and for combining them into united feature space was developed. For the analysis in obtained color-texture feature space the modifications of color, texture metrics, and united metric were proposed.

Segmentation algorithm is based on primary transition from usual pixel-wise image representation to cluster-based image description, where an image is represented as a map of disjoint areas, and contains the series of iterative procedures for simplification the obtained map.

The research of reconstruction problem for unbounded operators was prolonged. We studied the problem of numerical solution of convolution equation in case when the kernel spectrum is the entire function of the exponential growth and may have zeros at some real points. We are looking for the solution in the class of finite functions. Under some additional assumptions we constructed the exact solution of the correspondent continuous problem. It was shown that in this case the construction of numerical solution (via discrete data) could be reduced to numerical integration, differentiation, and computation of singular convolution.

In the course of activity according to the grant of Russian Foundation for Basic Research and Federal Program "Informatization of Russia", a dedicated database was developed and registered in the State Registry. The database comprises a history and personal information about the Russian Academy of Sciences since 1724. A CD-ROM based on those data was created and issued. The database is also accessible through the newly developed Web site of RAS Digital Image Archive at http://hp.iitp.ru.

New class of stochastic dynamic systems, namely, systems with noises in observations, depending on state and estimation, is investigated. The solution of linear estimation problem in class of linear filters was found. The separation theorem for uncomplete data process control problem was proved on base of this solution.

Investigations of the noise stability for multi-channel FDM-FM systems, containing radio-channels with scattering and reflections in atmosphere, were performed.