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A theoretical basis and algorithms for accelerating the method of non-uniform coverings have been developed. The developed approaches are based on the use of additional conditions of extremum of the first and second order.

The methods of solving multicriteria problems based on the non-uniform coverings concept have been studied. Approaches based on local search, which improve the quality of the approximations obtained and accelerate the search, have been developed. The proposed approach has been implemented within the object-oriented C ++ library. In particular, classes for reductions, reduction plants, classes for reductions application and Base-Solver, that use these classes, have been developed. Series of computing experiments showing high performance of the offered methodology and computer program have been performed. A new approach based on the prior estimation of improper integrals along the system solution has been proposed. It differs from the known methods of studying the absolute stability of the equilibrium position.

Implementation program of nonlinear system's equilibrium position absolute stability problems has been developed. Nonlinear system's equilibrium position absolute stability theorems have been proved. Additional correlation connecting the phase variables have been obtained in order to study the absolute stability of nonlinear controlled systems, which makes it possible to obtain more effective conditions for the absolute stability of nonlinear systems.

Mathematical and information models of controlled dynamic systems have been developed.

Models of controlled dynamical systems have been studied.

The question of solving optimal control of ordinary differential equations' nonlinear system have been considered in two different cases.

An information system has been developed to study the stability and optimal control of complex electrical power systems on the basis of mathematical models. The system is designed for quick identification of the damaged elements in emergency situations in order to ensure the normal operation of the entire system. The system has been implemented within the object-oriented C # programming language.

Dynamic study of the precise electrical power system

Управление системы "синхронный генератор-паровая турбина"

Control system "synchronous generator-steam turbine"

Устойчивость движения синхронного генератора

                                                      Dynamic stability of the synchronous generator


Software control of the electrical power system

макетThe model of the electrical power system consists of three thermal power plants (TPP), a residential houses and a control center. Synchronous functioning of the system is ensured by the  program complex located in the control center. The software analyzes the synchronous operation state of the system at every instant.

If an accident or malfunction occurs in the system, as a result of which the system loses its synchronization, then this software product determines it by sensors. And if one of the power plants fails, power of the remaining stations will automatically increase to ensure the required power consumption. Using the characteristics of the failed generator, the software chooses the optimal control algorithm for it, and acting on this algorithm, leads the failed generator to the operational state.

Obtained intellectual property certificates:

Kospanova K. K., Kalimoldayev M. N., Dzhusupov A. A., Grechko S. M. Certificate of state registration of rights to the object of copyright entitled "Mathematical modeling and dynamics of specific controllable systems in oil and gas industry" (the scientific work) No 543, April 26, 2010.  

Biyashev R. G., Kalimoldayev M. N., Nysanbayeva C.E., Kapalova N. A., Amirgaliyeva Zh. E. Certificate of state registration of rights to the object of copyright entitled «GentestCrypt» (computer program), No 1877, December 22, 2010.   

Koybagarov K.Ch., Musabayev R.R., Kalimoldayev M.N. Certificate of state registration of rights to the object of copyright entitled “Morphological analyser of Kazakh language” (program complex for computers), No 1605, December 5, 2013.   

Sharshenaliyev Zh.Sh., Kalimoldayev M.N., Zamay V.I., Dobrovolsky N.S., Kalashnikov A.L., Patent No 1731 registered in state invention register of the Kyrgyz Republic, 31.03.2015 entitled “Method of liquid level measurement and device for its implementation” Institute of Automatics and Information Technologies of the National Academy of Sciences of the Kyrgyz Republic.



Kalimoldayev M.N., Aisagaliev S.A.  Certain problems of synchronization theory // Journal of Inverse and III-posed Problems. – De Gruyter, 2013 – V. 21, Issue 1. – p. 159-175.

Kalimoldayev M. N., Jenaliyev M. T., Abdildayeva  A. A. On the optimality one power system // 2nd International Conference on Analysis and Applied Mathematics (ICAAM-2014). - Shymkent, Kazakhstan. – 2014. – Vol. 1611. – P. 194-198.

Ahmetzhanov  M. A., Jenaliyev  M. T., Kalimoldayev  M. N. On the controllability of the multidimensional phase system // 2nd International Conference on Analysis and Applied Mathematics (ICAAM-2014). - Shymkent, Kazakhstan. – 2014. – Vol. 1611. – P. 190-193.

Alimhan  Keylan, Otsuka Naohisa, Adamov A. A., Kalimoldayev  M. N. Global Practical Output Tracking of Inherently Nonlinear Systems Using Continuously Differentiable Controllers // Mathematical problems in engineering. – 2015.

M.N.Kalimoldayev, L.S.Kopbosyn, A.A.Abdildayeva, T.Duzbayev, M.Akhmetzhanov. Stability of motion “In the large” of some class of phase system // Journal of Mathematics and System Science. – 2015. - №5. – Р. 118-121.

G.A. Amirkhanova, A.I. Golikov, Yu.G. Yevtushenko. On an Inverse Problem of Linear Programming // Proceedings of the Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences. - 2015. - Vol. 20, No 2. - p. 7.

Kalimoldayev M.N., Jenaliyev M.T., Kopbosyn L.S., Abdildayeva A.A. The optimal control problems of nonlinear systems // ICINCO - 12th International Conference on Informatics in Control, Automation and Robotics. – Colmar, Alsace, France, 2015. – Р. 54.

M.N. Kalimoldayev, L.S. Kopbosyn, A.A. Abdildayeva, T.Duzbayev,      M.Akhmetzhanov. “Stability of motion “In the large” of some class of phase system” // Journal of Mathematics and System Science 5 (2015) 118-121.

M.N. Kalimoldayev, A.V. Alexeyeva, G.A. Amirkhanova. Economic soliton of spatially two-dimensional nonlinear mathematical model A1.  International Conference “Computational and Informational Technologies in Science, Engineering and Education” (CITech-2015) Almaty, Kazakhstan, 24-27 September 2015.

A.V. Alekseeva, G. A. Amirkhanova (2 + 1) -dimensional nonlinear equation A5 and its (2 + 1) -dimensional bilinear H1 form // European Journal of Scientific Research, "Paris University Press", 2015, No 1 (11). - p. 636-642.

 M. Kalimoldayev, M. Jenaliyev, A. Abdildayeva, Leila Kopbosyn.  Optimal Control of the Complex Power System Model // IJET: International Journal of Engineering & Technology. Vol: 14, Issue: 04.

 Kalimoldayev M.N., Abdildayeva A.A., Kopbosyn L.S. Problems of optimal control of phase systems // International Congress of Mathematicians, Seoul, 2014, P.291.

Keylan Alimhan, Naohisa Otsuka, Maksat N. Kalimoldayev, Orken J. Mamyrbayev An Expanded Method to Robustly Practically Output Tracking Control for Uncertain Nonlinear Systems // Int. Journal of Math. Analysis, Vol. 8, 2014, no. 18, 865 - 879 HIKARI Ltd.