4th International Scientific Conference "Actual problems of the theory of optimal control, dynamical systems and operator equations".
Organizers:
 Ministry of Education and Science of the Kyrgyz Republic
 KyrgyzRussian Slavic University named after the First President of the Russian Federation B.N.Yeltsin.
 Research Center "Mathematical Methods of Optimization (MMO)  OPTIMAL.
The conference is dedicated to the 50th anniversary of scientific and pagegogical and the 75th anniversary of the Doctor of Physical and Mathematical Sciences, Professor Akylbek Kerimbekovich Kerimbekov.

Scientific and methodical work of
Prof. Kerimbekov Akylbek
Kerimbekov Akylbek was born on January 10, 1947 in the AkChii village council, KaraBuura district, Talas region, Kyrgyz Soviet Socialist Republic in the family of a livestock breeder. In 1965, he graduated from the JoonDobo elevenyear school. During his school years he was an activist, in 19601965 he headed the school Komsomol organization and he was a delegate of the Talas regional Komsomol conference three times.

In 1965, he entered the Faculty of Physics and Mathematics of the Kyrgyz State University, which he successfully graduated in 1970.
He began his career in 1970 as a mathematics teacher at the JoonDobo secondary school. In 19711972 he worked as an engineer at the research laboratory of earthquakeresistant constructions (NILSS) of the Frunze Polytechnic Institute. From 1972 to 1992 he worked as a teacher, senior lecturer and associate professor of the Department of Differential Equations of the Kyrgyz State University. Actively engaged in social work. He was the chairman of the trade  union committee of the faculty and a member of the Presidium of the trade  union committee of the Kyrgyz State University.
From 1972 to 1976 he was a postgraduate student at the Automation Institute of the Academy of Sciences of Kyrgyz SSR. Under the scientific guidance of Professor A.I. Egorov he began to study problems of the optimal control theory of systems with distributed parameters. In 1997 he successfully defended master’s thesis on "Approximate solution of problems of optimal control of processes described by a system of telegraph equations" in the Dissertation Council of the Leningrad State University. In 19921998 he worked as the dean of the Faculty of Physics and Mathematics of the Kyrgyz State Pedagogical Institute (since 1996 the Kyrgyz State Pedagogical University named after I. Arabaev, now the Kyrgyz State University named after I. Arabaev). In the period from 1998 to 2006, he worked as the head of the Department of Differential Equations at the Kyrgyz State University named after Zh. Balasagyn (now the Kyrgyz National University named after Zh. Balasagyn). According to the research results, in 2003 he defended his doctoral dissertation on the topic "Nonlinear optimal control of linear systems with distributed parameters" in the Dissertation Council of the Institute of Mathematics of the National Academy of Sciences of the Kyrgyz Republic.
In 2007, the Doctor of Science diploma was nostrified by the Higher Attestation Commission of the Russian Federation. Since 2006, he has been working at the KyrgyzRussian Slavic University as a professor of the Department of Applied Mathematics and Informatics of the NaturalTechnical Faculty. From 2006 to 2019, he worked as the Chief Researcher at the Mathematics Institute of the Kyrgyz Republic National Academy of Sciences.
Scientific work
He has been engaged in scientific research of problems of the optimal control theory of systems with distributed parameters for more than 40 years. The object of study was the technological processes described by partial differential equations and partial integrodifferential equations with a Fredholm or Volterra integral operator. The questions of solvability of nonlinear optimization problems were investigated, i.e. problems where the functions of external influences are nonlinear with respect to the parameter of control. Since the actual processes are usually nonlinear, the solutions of nonlinear optimization problems found by mathematical methods more or less adequately describe the state of the controlled process. Therefore, the research results are of both theoretical and practical interest. Methods for solving nonlinear optimization problems with boundary, distributed and point controls, as well as tracking problems, which are often encountered in applications, have been developed.
The nonlinear optimization problems with programmatic process control were investigated using the concept of a generalized solution, the maximum principle for systems with distributed parameters. It was found that the desired optimal control is defined as a solution of a nonlinear integral equation that contains the desired function both under the integral and outside the integral. For such nonstandard nonlinear integral equations, a solution construction methodology was developed, which made it possible to develop an algorithm for constructing a complete solution to the nonlinear optimization problem and its approximations under program control of the process. The influence of the integral operator on the solvability of the nonlinear optimization problem is noted. On the example of the study of the solvability of individual problems of nonlinear optimization, it was established that the "nonstandard equation" has the property of universality, i.e. it takes place regardless of the nature of the controlled process. Thus, new results have been obtained in the optimal control theory of systems with distributed parameters. The main content of the method was reported in 2014 in Seoul (South Korea) at the World Congress of Mathematicians.
The study of nonlinear synthesis problems in the of optimal control was carried out using the concepts of a generalized solution and the Fréchet differential according to the BellmanEgorov scheme. It is established that the synthesis of the optimal control is carried out according to the formula, where the desired optimal control is defined as a nonlinear function of the gradient of the Bellman functional. For the Bellman functional in the case when the controlled process is described by an integrodifferential equation, a nonlinear integrodifferential equation is obtained, which contains the gradient of the Bellman functional nonlinearly. Such an equation of a nonstandard form was obtained for the first time and it became necessary to develop methods for solving it. He found the structure of the solution, according to which this equation splits into two equations, one of which is a purely differential equation and is solved independently of the second. This approach allows us to develop an algorithm for constructing the desired optimal control depending on the state of the controlled process, i.e. solve the synthesis problem. The theoretical results were tested on the example of solving the problem with point controls. The main results were reported in 2018 in Rio de Janeiro (Brazil) at the regular World Congress of Mathematicians.
Studies of nonlinear spectral theory were carried out using Lagrange's Theorem “On finite increments”. He developed a methodology that allows finding a certain class of solutions to nonlinear algebraic, integral and differential equations with parameters. These results are new and can be useful in solving nonlinear optimization problems and the theory of nonlinear spectral problems. The main results were reported at the ISAAC International Conference, which was held in Vaxjö (Sweden) in 2017.
The developed methods are constructive and can be useful in developing new methods for studying nonlinear optimal control problems described by functional equations of a more complex nature.
The results formed the basis of three new scientific directions:
 Research methods of nonlinear operator equations with a parameter;
 Synthesis of optimal control in the nonlinear optimization problems;
 Methods of program control in the nonlinear optimization problems.
Monographs:
 Mathematical methods of optimal control of electromagnetic oscillations. – Bishkek Publisher: Arabaev KSPU, 1997, 112 p
 Nonlinear optimal control of oscillations in transmission lines.– Bishkek, Publisher: KRSU, 2009, 132 p
 Approximate solution of the nonlinear optimization problem for the thermal processes.– Saarbrucken, Publisher: LAP LAMBERT Academic Publishing, 2011, 132 p
 Investigation of the Hill equation by the polarization method. – Bishkek, Publisher: Maxprint, 2013, 126 p
 Nonlinear movable point control for the heat transfer process. – Bishkek, Publisher: Maxprint, 2013, 116 p
 Nonlinear optimal boundary control for the thermal processes. – Bishkek, Publisher: KRSU, 2020, 194 p
Selected scientific articles of recent years:
 Kerimbekov A., Abdyldaeva E. Optimal distributed control for the processes of oscillation described by fredholm integrodifferential equations. // Eurasian mathematical journal, 2015, Vol. 6, №2. – P. 2840.
 Kerimbekov A., Nametkulova, Kadirimbetova A. Optimality Conditions in the Problem of Controlling Thermal Processes with an IntegroDifferential Equation // Izvestiya IGU, –2016, V.16, ser. "Mathematics"  S. 2427.
 Kerimbekov A., Nametkulova, Kadirimbetova A. Approximate solution of the problem of distributed and boundary control of the thermal process // Izvestiya IGU,  2016, vol. 16. ser. "Mathematics"  S. 7188.
 Kerimbekov A., Abdyldaeva E. On equal relations in the problem of boundary vector control of elastic oscillations described by Fredholm integrodifferential equations // Journal "Proceedings of the Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences", 2016, V.22, No. 2.  S. 163176.
 Kerimbekov A., Abdyldaeva E. On the Solvability of a Nonlinear Tracking Problem Under Boundary Control for the Elastic Oscillations Described by Fredholm IntegroDifferential Equations // System Modellıng and Optımızatıon Dergisi. 27th IFIP TC 7 Conference, CSMO 2015. Sophia Antipolis, France, June 29–July 3, 2015. Revised Selected Papers. Sprınger  2017, P. 312322
 Kerimbekov A., Abdyldaeva E., Duyshenalieva U. Generalized solution of a boundary value problem under point exposure of external forces // International Journal of Pure and Applied Mathematics Dergisi. 113(4). 2017 . 609623.
 Kerimbekov A., Abdyldaeva E., Duishenalieva U., Seidakmat kyzy E. On solvability of optimization problem for elastic oscillations with multipoint sources of control // International Conference «Functional analysis in interdisciplinary applications» (FAIA2017), AIP Conference Proceedings 1880, edited by Tynysbek Kal'menov and Makhmud Sadybekov (American Institute of Physics, Melville, NY, 2017), 060009 (2017)
 Kerimbekov A., Abdyldaeva E. The Optimal Vector Control for the Elastic Oscillations Described by Fredholm IntegralDifferential Equations // Analysis and Partial Differential Equations: Perspectives from Developing Countries. Imperial College London, UK, 2016, –pp. 1430
 Kerimbekov A. On a Class of Solutions of the Nonlinear Integral Fredholm Equation //Trends in Mathematics Research Perspectives (Analysis, Probability, Applications, and Computation. Proceedings of the 11^{th} ISAAC Congress, Vaxjo (Sweden) 2017). Switzerland, Birkhauser.  2019, P. 191197
 Kerimbekov A., Seidakmat kyzy E. On Solvability of Tracking Problem Under Nonlinear Boundary Control //Trends in Mathematics Research Perspectives (Analysis, Probability, Applications, and Computation. Proceeding97s of the 11^{th} ISAAC Congress, Vaxjo (Sweden) 2017). Switzerland, Birkhauser.  2019, P. 207218
 Kerimbekov A., Tairova O. Building Bellman Egorov Equation for a Task of Optimal Control Ubiquitous Computing and the Internet of Things: Prerequisites for the development of ICT, // Studies in Computational Intelligence, Volume 826. Springer Nature Switzerland AG. – 2019. P. 12031212.
 Kerimbekov A., Synthesis of Distributed Optimal Control in the Tracking Problem in Optimizing Thermal Processes Described by IntegroDifferential Equations //Itogi Nauki i Tekhniki. Modern mathematics and its applications. Subject reviews. Volume 183 (2020). DOL:10/36535/0233672320202838597. 8597
 Kerimbekov А., Abdyldaeva Е., Asanova Zh., Uraliev А. On the Solvability of Nonlinear Integral Equations //AIP Conference Proceedings 2325, 020033 (2021)pp. 02002410200244.
 Kerimbekov А., Doulbekova S. On solvability of the nonlinear optimization problem with the limitations on the control //AIP Conference Proceedinds 2325, 020043 (2021) pp.02004310200434.
 Kerimbekov A., Baetov A., Krasnichenko L. On the solvability of a semilinear hyperbolic equation with a parameter //Journal of Physics: Conference Series 1847 (2021) 012018 IOP Publishing doi:10.1088/17426596/1847/1/012018
 Kerimbekov A., Ermekbaeva E., Seidakmat kyzy E. On the solvability of the tracking problem in the optimization of the thermal process by moving point controls Vestnik Karagandinskogo Universiteta //Mat Series No. 2(101)/2021 P.124131
 Kerimbekov A., On the solvability of the problem of synthesis of distributed and boundary controls in the optimization of oscillatory processes // Proceedings of the Institute of Mathematics and Mechanics. Ural Branch of the Russian Academy of Sciences 2021 С128140
Textbooks and educationalmethodical manuals:
 The concept of norm and its application (Bishkek, 1991)
 Algebra and Mathematical Analysis (Bishkek, 1995)
 Optimization methods (Bishkek, 2016)
 Differential equations . Bishkek; Maxprint, 2017. –320 p. (2nd edition, Bishkek: 2019. p. 336)
 Encyclopedic edition "Story of KaraBuura"  Bishkek; Uchkun, 2008. –336 p.
 Popular scientific publication "A brief report on the history of Kyrgyzstan" . Bishkek; Maxprint, 2017. –238 p.
Participation in scientific conferences:
Professor Kerimbekov A.K. participated at international congresses and conferences:
 International Congresses of Engineers  2011 London
 International Congresses of Mathematicians  2014, Seoul, South Korea / 2018, Rio de Janeiro, Brazil
 Congress of the Turkic World Mathematical Society (1999  Elazyg, Turkey; 2007  Sakaria, Turkey; 2009  Almaty, Kazakhstan; 2014  IssykKul "Aurora", Kyrgyzstan; 2017  Astana, Kazakhstan)
 ISAAC World Congresses (2013  Krakow, Poland; 2017  Vaxjo, Sweden; 2021 Brussels, Belgium)
 International conferences that were held at different times in the cities of Almaty, Astana, Tashkent, Istanbul, on the island of Cyprus, Ulaanbaatar, Yekaterinburg, Irkutsk, etc.
Scientific and public work
 20042015  Member, ViceChairman and Chairman (20132015) of the Expert Council of the National Attestation Commission for the award of candidate and doctoral dissertations in physical and mathematical sciences
 20082013  Chairman of the Dissertation Council in the specialty 01.01.02  differential equations, dynamical systems and optimal control, organized by him at the Higher Attestation Commission of the Russian Federation in the KyrgyzRussian Slavic University
 Since 2010 – Member of the International Mathematical Society (ISAAC International Society for Analysis, its Applications and Computation)
 Since 2013 Chairman of the Expert Council on Scientific Projects of the Kyrgyz Republic Ministry of Education and Science
 2015 (December 2, 2015) Member of the Council for Science, Innovation and New Technologies under the Prime Minister of the Kyrgyz Republic
 2016 Member of the interdepartmental working group on the development of priority areas for the development of science in the Kyrgyz Republic
 Since 2017  Member of the Board of the World Mathematical Society of TurkicSpeaking Countries
 Since 2017  Member of the Editorial Board of the scientific journal "Proceedings of Institute of Applied Mathematics" of the Institute of Applied Mathematics, Baku State University
 Since 2019, Member, Chairman of the Expert Council on Scientific Projects of the Ministry of Education and Science of the Kyrgyz Republic
 Since 2021, member of the Dissertation Council D 05.21.631 at the Institute of Mechanical Engineering and Automation of the National Academy of Sciences of the Kyrgyz Republic and the KyrgyzRussian Slavic University
Scientific and organizational activities
In addition to research work, Professor Kerimbekov A.K. promotes scientific achievements in mathematics and optimal control theory among students (bachelors, masters), graduate students and young teachers.
He organized:
 Scientific seminar "Optimal control theory for systems with distributed parameters", which has been regularly operating since 2010
 Scientific Research Center at the KyrgyzRussian Slavic University "Mathematical Methods of Optimization (MMO)  OPTIMAL" and the classroom named after.Professor Ya.V. Bykov (corresponding member of the Academy of Sciences of the Kyrgyz SSR), where events are regularly held to popularize the scientific heritage of Professor Ya.V. Bykov, domestic and foreign mathematicians;
 2008 1International scientific conference "Actual problems of control theory, topology and operator equations", dedicated to the 15th anniversary of the KyrgyzRussian Slavic University.Under his general editorship, a onevolume scientific collection was published;
 20132International conference "Actual problems of control theory, topology and operator equations", dedicated to the 20th anniversary of the KyrgyzRussian Slavic University and the 100th anniversary of Professor Yakov Vasilyevich Bykov.Under his general editorship, a twovolume scientific collection was published;
 20173Internationalconference "Actualproblemsofcontroltheory, topologyandoperatorequations", dedicatedtothe 25thanniversaryoftheKyrgyzRussianSlavicUniversityandthe 70thanniversaryofProfessorA.Kerimbekov.Thematerialsoftheconferencewerepublishedin 2 issuesofthejournal “Science, newtechnologiesandinnovationsofKyrgyzstan”
Akylbek Kerimbekovich is currently working as a professor at the Department of Applied Mathematics and Informatics of the NaturalTechnical Faculty of the KyrgyzRussian Slavic University and director of the Research Center "Mathematical Optimization Methods (MMO)  OPTIMAL" in the KyrgyzRussian Slavic University.