Taras Shevchenko National University of Kyiv|Faculty of Cybernetics

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Scientific school of mathematical modeling and optimal control

Scientific school was formed on the basis of the studies of professors Bublik B.M., Bejko I.V., Garashchenko F.G., Kirichenko M.F., Nakonechniy O.H., Khusainov D.Ya. and their followers.

Summary of research: optimal control, mathematical modeling, special numerical methods; stability, sensitivity, controllability, observability, adequacy and feasibility analysis, parameters, functionals and solutions estimation, systems with variable dimension of phase space; pseudoinversion of matrices, optimization of distributed systems with generalized effect and incomplete data. A modern scientific direction - constructive theory of mathematical modeling and optimal control was created. Technical contribution consists of more than 700 publications including 20 monographs and textbooks. 27 doctoral and more than 100 PhD theses were defended.

On the basis of theoretical results the informational and mathematical technology of space flight and hydroacoustics, optimal design of accelerating-focusing systems and manipulation robots were implemented.

Main research fields

  • Development of mathematical theory of practical stability, structural and parametric optimization.
  • Investigation of stability of differential equations by Lyapunov functions method. Stabilization of control systems.
  • Development of algorithms of dynamical systems identification.
  • Simulation and optimization of complex control systems.
  • Mathematical modeling of distributed space-time processes.
  • Development of mathematical methods and programs of data processing with incomplete information.
  • Optimal system design of charged particles acceleration.
  • Optimization and control of mechanical systems.
  • Methods of recognition.
  • Computer thematic cartography.

Involvement in themes and projects

2001-2003 years - International STCU Project "Software and hardware simulation and optimization of control systems of microsatellites orientation".

2001-2003 years - Theme "Modeling of spatial visual images of human faces for the computer speech synthesis" within the scientific and technical program "shaped computer" (three projects).

2003-2005 years - Theme "Creation of the computer system of 3D human head imaging for operational portrait identification" for the Service for Minors of Kyiv City State Administration. Funding - from the budget of Kyiv City State Administration.

2005-2006 years - Theme "Development of an information retrieval system "Expert " in order to combat criminal offenses for Head Department of Ministry of Home Affairs of Ukraine in Kiev.

2006 - won a grant for the applied research project.

2007-2011 years - Theme "Development of advanced technologies for processing audio information for electronic screen readers in the education of children with visual impairments". Funding - from the budget of the Kyiv City State Administration.

2007 - Grant of the President of Ukraine to support research of young scientists "Investigation of problems of practical stability of dynamic systems with multivalued right-hand side", granted by Ministry of Education and Science of Ukraine.

2008-2009 years - Theme "Modeling and analysis of alternative dynamic systems in transport".

2008-2009 years - Theme "Developing geospatial applications for NAP SNS".

2009-2010 years - Theme in the form of "Service" - "Development of software for converter of S-57 electronic card".

2010-2011 years - Theme in the form of "Service" - "Development of software for converter of S-57 electronic card and settings on a PC using the viewer." 

Themes of practical developments

Dynamic simulation of charged particle beams and parameter optimization of the accelerators structure of different kinds

A unique method for solving optimization problems of trajectory optimization for mathematical models of real charged particle accelerator is created. Problem solutions of undifferential optimisation are received on the basis of structural and parametric optimization methods. The research results were implemented in the leading scientific centers of the former USSR and in the academic institutes of NASU. On the subject of researches was defended 1 doctoral dissertation and more than 15 candidate's dissertations.

Automation system for solving problems of kinetic control systems identification

The automation system of flight test processing is developed. More than 15 years the CSM Department performed research works together with Aviation Research Institute (Zhukovsky) and the construction department of O.K. Antonov. Original methods of flight tests data processing are created. The system presented more than 15 parameters and conditions estimation methods that allow solving both linear and nonlinear identification problem in conditions of "noisiness" and incomplete field of measurements, including the data processing potential in real-time mode.  The package allows solving the problem of identification for the dynamic systems, which mathematical model is described by the systems of the ordinary differential equations or functional relationships.

Algorithmical and control software of microsatellite orientation

The specialized software package for the problems solving of control system synthesis of microsatellite orientation with restrictions to phase variables with optimal and close to optimal on processing speed exponents of the transition process is created. The package contains a kernel, the evaluation unit of control modes, the block of parameters initialization and a renderer. It allows carrying out the computing experiments connected with calculations of reorientation modes and microsatellite stabilization, to change input parameters and to add plug-ins to implement new mathematical models.


The "Modelling of dynamic systems" package (MDS)

The universal multiplatform software tools are developed for the preparation and carrying out of computing experiments with mathematical models. The MDS allows you to set both one (holistic) model, and to draw up complexes of such models in which each component functions under its own laws. Means for dynamic analysis of the assumed models (or complexes of models) are given. There is an opportunity to work with arbitrary data type, which allows making calculations with extra accuracy. In a debugging mode the automatic control of the admissibility of operations is carried out.

The package of automatic processing of complex experiment results

The program for automatic processing of empirical data in material science, chemistry and medicine without construction of studied processes mathematical model. The reproducing of a response function surface according to results of experiment by way of multidimensional spline function on a chaotic grid and finding the point of optimum response function is carried out. It makes it possible to find optimum of operating factors in the experiment according to given criteria. In a dialogue it is further processing of disturbing function values on the basis of minimax criterion.

Information Retrieval System "Expert"

An information retrieval system "Expert " in order to combat criminal offenses for Head Department of Ministry of Home Affairs of Ukraine in Kiev was developed.

Informational and analytical system for the analysis and optimization of transport movements

A system for making an optimal decisions regarding to transport movements at the "silo-ports" stage was developed.

Recognition of handwritten and printed math texts

A software package for recognition of handwritten mathematical text was developed. The result of recognition is presented as a LaTeX file.

Generation of three-dimensional images (surfaces) by two-dimensional paintings.

Проведено експерименти з формування базису двовимірних зображень просторового об’єкта з властивістю повноти для відтворення його тривимірного образу. Розроблено методи відтворення координат точок на поверхні об’єкту в тривимірному просторі за їхніми двовимірними проекціями. Створено програмні засобів просторового огляду об’єкту.

Compression of graphical information and scanned texts

The algorithms for lossless data compression were developed. The dictionaries of characters were created. The frequency filtering and cluster analysis theory were used for characters partition into classes of equivalence. The minimum weight trees for each class were constructed using various metrics.

OCR of scanned data tables

A method of scanned data tables recognition which are presented as a graphic file was developed.

Digital processing of banknotes images

The methods of digital processing of banknotes images which are used for solving the tasks of denomination recognition and checking banknotes validity were developed.

Classification of spatial objects

An algorithms for recognition and classification of spatial objects, namely the allocation and classification of aircraft, based on satellite data and recognition of fields, based on satellite images, were created.

Development of changes detection algorithms for aerial photography.

Changes detection methods in the new graphical representation (raster) within a border of selected vector object by information about old, new raster and shape-file (file which contains an information about region vectorization) were developed.

Mathematical modeling of distributed space-time processes in direct and inverse statements

The method of mathematical modeling of dynamic processes, distributed in limited and unlimited space-time regions was developed. This method allows to construct the state function of such processes in incompletely specified initial boundary conditions, to restore the function and the unknown initial boundary conditions in the presence of partial observations of the system state, to solve the  problems of studied processes control through the functions of distributed space-time perturbations, through the boundary and initial perturbation. Methods were tested by the solving  of the ecology problems. The software package that allows you to set and solve the problem of modeling of space-time processes of arbitrary nature was developed.

Manipulation robots guidance and associative neurocomputer memory synthesis for movements planning in the environment with restrictions

Dynamic real-time manipulation guidance methods and approaches to the synthesis of associative memory with recursively non-linear regressive structure were developed.

The development of adaptive, algorithmic and software technologies for solving an analysis, classification and recognition of voice and images problems

An algorithms for solving an analysis, classification and recognition of voice and images problems were created

Modeling and processing of voice information. Ukrainian language synthesizer

A mathematical, algorithmic and software for computer sounding of textual information were developed. Voice technology will facilitate a communication of computer with user, save human resources, make the computer accessible for people with visual impairments. Ukrainian language synthesizer was created.

The creation of virtual images and animations of the human face

A new mathematical methods, algorithms and software for 3D image of human head creation with possibilities to emotional state animation and speech process visualization were developed. 

The computer system of 3D human head image creation for efficient portrait identification. 

The technology of 3D human head image creation according to eyewitnesses information from different points of view was proposed. Real time parametric model fitting for the maximum agreed with the description of witnesses was performed. Such system is needed to combat international terrorism and to create a highly efficient access control security systems.

Technology of audio and video information transfer for telecommunication systems.

Methods of face modeling and recognition and creation of it 3D animated model were developed. This methods can significantly reduce the information volume and the load on transmission lines and achieve data transmission in real time.

Radar information display system for digital locator "Petrel-1"

A closed system for displaying primary and secondary information for the digital locator "Petrel-1" was created. The system is based on algorithms of rapid radar data conversion from polar to Cartesian coordinate system and is the technical element of a radar prototype "Petrel-1."

Innovative technologies Complex System Modelling Department (CSM)

1. Micro-satellite orientation management system. Algorithms and software

The software package for micro-satellite orientation management system problem solving has some phase parameters. The package includes a calculation mode control block, initialization parameter block and a visualization subsystem. It allows to change the input parameters and modules to create new mathematical models using the reorientation and stabilization modes.

2. MDS package ("Modeling of dynamic systems")

MDS allows creating a big model and model complexes (submodels act in their own way). The calculations can be done with high accuracy and we can check all the operations. You can find the additional information on www.soft.unicyb.kiev.ua.

3. The automation system for identification problem solving of dynamic control systems

The laboratory of complex system modeling is engaged in developing of estimation methods for flying vehicle parameters and the mathematical models of their motion using the results of measuring. There are some original methods and data processing automation systems. The laboratory of complex system modeling has had the joint scientific work with the aircraft scientific research institute (c. Zhukovskiy) and KB by O.K. Antonov for more than 15 years by now. The flight processing system was designed and accepted by MAP committee (USSR).

At the moment the advanced version of the system was designed for PC in Windows environment. It includes more than 15 estimation methods of the parameters and conditions that allow solving the linear and nonlinear identification problems under of "noise" conditions and parameter incomplete in real time. The system can solve the identification problems for dynamic systems of mathematical model described by differential equation or functional correlation system. The system has the easy interface.

4. The package of the result automatic processing for multi-factor experiment with the support of mono and dialogue modes

The package supports the result automatic processing in science of materials, chemistry and medicine without mathematical model creation of the processes. The package can reconstruct the functions using experiment results, multi-dimention spline-functions on the chaotic net.

5. Mathematical modeling portioned space-time processes in direct and inverse setting

The mathematical modeling method of the dynamic processes conditions was constructed. The methods allows creating of the process function with incomplete initial-marginal conditions, restoring this function and an unknown initial-marginal conditions at presence of the partial observations on condition of the system, solving of the process control using functions of portioned space-time disturbances and marginal and initial disturbances.The method was used for ecologic problem solving. The created program complex  allows putting and solving the modeling space-time process  problems of different nature.

6.   Modeling and processing technologies for voice information.  Ukrainian language synthesizer

Mathematical, algorithmic and software supports were designed to insonify the computer text information. The technologies make easier PC usage, allow saving time and human resources and let the people with vision problems use computer. The synthesizer was created for Ukrainian language.

7.  The system creation of three-dementional computer image of  human head for operative portrait identification

The technology creation for human head space image from a witness memory in real time. Such a system is vital to fight against international terrorism and to make the high-performance safe access control systems.

8.  The development of perspective information technology for audio and video information transmissions in telecommunication

The purpose of the work was virtual video creation. The process of modeling, identification of a person’s lineaments and animation of their three-dimensional model. It reduces the amount of the information and decreases the overload on the transmission lines. 

9. The dynamic modeling of charged particles and parameter structure optimization of boosters of different types

The unique method for optimization problem solving for  trajectories optimization of booster mathematical models of charged particles was created. On the base of the optimization structured-parametric methods were obtained some problem solutions of undifferentiated optimization. The results were applied at the leading scientific centre of the former Soviet Union and at the academic institute NAN Ukraine. A doctoral thesis and 15 Ph.D. thesises were defenced.

10. Informational-search system "Expert"

At the moment we are working out  the informational-search systems to fight against the criminal breaches in Kiev. GU MVD Ukraine in Kiev is our customer.

11. Informational-analytical system for analysis and optimization for transport transportation

The informational-analytical system for taking the optimum decisions deal with transportation as "elevators-ports" was created.

12. Mathematical and printed texts identification obtained from portable camera

The identification problem is solved for texts scanned by a portable camera. The camera scans a text fragment afterwards images gets into the processing module. The identification result displays as a ASCII file.

13. The creation of display in system of radio-locating information for digital locator "Burevesnik-1"

Closed display system of source and secondary information for digital locator "Burevesnik-1" was created. The system is based on new effective algorithms of fast information translation from a polar to a Cartesian co-ordinates. At the moment we are developing the methods for autoseizure and accompaniment objects.

14. Modeling, analysis and syntheses untraditional dynamic systems

The Analysis and building estimation features of the hybrid dynamic systems.  The Study of the tasks to stability and control in dynamic system, which are described function-differential equations with delay and neutral type. Optimum control in system function-differential equations. The Analysis and syntheses in system differential-difference of the equations. The Study to stability and stabilization in system with aftereffect with portioned parameter parameter. The Study to vagary in nonlinear dynamic system of the special type. The Estimation of dimensionality attractors.         The Building and study of the mathematical models of the dynamic systems to superconductivity, building and study of the models "Magnetic potential pit". The Estimation of the areas to stability in phase and parametric space.

15.  Digital processing of the banknote images

Digital processing of the banknotes images is used to solve the problems deal with the nominal value banknote identification and checking its validity. This process is divided into several stages, which are connected with the optical equipment quality and of the scan conditions of the banknotes images.

16.  Change detection algorithm development for aerial photos using the new raster images and the old vector presentations of the region

Let’s consider the region. We have already had some graphic images (new rasters) obtained using air-photography. Besides, we have some information about the region as a Shape-file (old vector) in the past. Having done the synchronizing of the vector and raster layers we analyzed the differences between them.

Problem A. The operator chooses the middle point of vector object (on the old vector). We have also some information about the type of the object obtained from the shape-file (e.g. buildings, roads, plants, etc). It is necessary to pay attention to the changes identified on the new raster within the vector object and outside the object as well. It is necessary to take into account the presence of shaded area.

Problem B.  Having had the information about the new raster, the old vector and the shape-file with information about internal points we could find the changes, the same ones as in Problem A.

17. Adaptive, algorithmic and program (software) technologies creation to solve the problems related to analysis, classification, voice and image identification

The main purpose of the work is the creation of theoretical base for programmatic and program-algorithmic technologies to solve the problems related to analysis, classification, voice and image identification. First of all, the work relate to the modern telecommunicational problems connected with analysis, clarification , voice and image identification. The main results of the work are the demonstrative materials. We have participated in some projects and we have already had some different partners – institutions from Ukraine, England, Germany, Israel, USA, Czech Republic, members of the main directorate Ministry of Internal Affairs in Kyiv, the main directorate education and science in Kyiv.

18. Recognition of handwritten mathematical text

         The developed software converts a scanned image containing handwritten mathematical text and formulas into its textual representation in LaTeX format.

These are requirements for the input data:
         1)      symbols in words are written separately;
         2)      formulas in text are marked with ‘#’ symbol.

         Most of one-lined formulas containing indexes, subscripts, integral or sum ranges, fractions and complex symbols are recognized.


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