December 2016

Head of the department "Optimization of Controlled Processes",

Glushkov Cybernetics Institute, National Academy of Sciences of Ukraine

Doctor of physical and mathematical sciences, professor, corresponding member of NASU Kyiv, Ukraine

E-mail: chik@insyg.kiev.ua

Phone: (380-44) 526-21-58

Fax: (380-44) 526-41-18

Secretary Phone: (380-44) 526-51-58

Address: 40 Glushkov Prsp., 03187 Kyiv, Ukraine

E-mail: g.chikrii@gmail.com

Phone: (380-44) 526-36-67

Address: 119 apt, 32 Glushkov Prsp., 03187 Kyiv, Ukraine

http://www.chikrii.com/aachik.html

Born 1945 July 20 in Ukraine (Khmelnitskyi region, Tarnoruda). Citizen of Ukraine

1952–1960 – I-VIII classes of secondary school (Tarnoruda, Khmelnitskyi region)

1960–1963 – IX-XI classes of secondary school (Satanov, Khmelnitskyi region)

1963–1968 – student of mechanical – mathematical faculty, Lvov University, Ukraine, degree in mathematics

Since 1968 has been working at the Cybernetics Institute of National Academy of Sciences

- Engineer, Cybernetics Institute, Kyiv, 1968-1972
- Junior researcher, Cybernetics Institute, Kyiv, 1972-1975
- Senior researcher, Cybernetics Institute, Kyiv, 1975-1986
- Leading researcher, Cybernetics Institute, Kyiv, 1986-1988
- Head of the laboratory, Cybernetics Institute, Kyiv, 1988-1990
- Head of the department, Cybernetics Institute, Kyiv, 1990

- Candidate of physical and mathematical sciences (PhD), Cybernetics Institute, Kyiv, 1972
- Doctor of physical and mathematical sciences, Cybernetics Institute, Kyiv, 1979

- Head of the department "Optimization of Controlled Processes"

Glushkov Cybernetics Institute of the National Academy of Sciences of Ukraine - Professor of Taras Shevchenko National University (1980-2000, 2011-2016)
- Professor of National Technical University "Kiev Politechnic Institute" (1998-2016)
- Professor of Yurij Fedkovych Chernivtsi National University (2010-2016)

Author of about 450 scientific publications, among them are 5 monographs and 30 international surveys in the journals and books of author collectives, has more than 150 publications abroad.

Supervisor of defended 35 candidate and 3 doctoral theses.

- Grant of Soros professor
**ISSER SPU 041077 (1994-1996)** - Academician of Ukrainian Airspace Academy, 1994
- Corresponding member of International Academy of Computer Science and Systems, 1995
- Corresponding Member of NAS of Ukraine
**(1997)** - State Prize of Ukraine in the field of science and technology
**(1999)** - Grant
**STCU 1746 (2002–2004)**, grant**STCU 5240 (2011–2013)** - V.M.Glushkov prize
**(2003)** - Russian–Ukrainian
**grants FFI (2011-2013, MES)**,**(2013-2015, MES)**,**(2014-2015, NAS)**

- AMS (American Mathematical Society)
- ISDG (International Society of Dynamic Games)
- GAMM (Gesellschaft für Angewandte Mechanik und Mathematik)
- Pacific Optimization Research Activity Group (POP)
- President of Ukrainian Association of Dynamic Games

- Information Technology for Economics and Management (Poland, Gliwice), Editor in Chief around Eastern Europe
- Problems of Control and Information Sciences
- Proceedings of the Steklov Institute of Mathematics (Ekaterinburg branch)
- Theory of Optimal Solutions
- Cybernetics and Computational Technique

number of titles taken into account – 124

number of references – 270

**h–index** (Hirsch index) – **10**

number of titles taken into account – 264

number of references – 1492

**h-index** – **16**

- Convex and applied nonlinear analysis, theory of set-valued mappings, Aumann’s integral, measurable structures
- Mathematical theory of optimal control, differential inclusions, complete conflict controllability
- Game problems for discrete systems, Pontryagin’s direct methods, semigroup operators of Pshenichnyi
- Theory of search for moving objects, stochastic dynamic games
- Differential games of pursuit and evasion, nonlinear problems on moving objects collision avoidance
- Evolutionary game problems
- Game problems for systems of integral, integral-differential and differential-difference equations
- Dynamic games with groups of participants. Group pursuit, pursuit in turn (dynamic "commercial traveler" problem), game problems under state constraints
- Systems with impulse control, integral and mixed constraints on control
- Game problems for systems with fractional derivatives of Riemann – Liouville, Dzharbashyan – Nersesyan – Caputo, Miller – Ross, Hilfer, Gryunvald – Letnikov
- Investigation of the method of resolving functions, upper and lower resolving functions, matrix resolving functions, choice of extremal selections
- Positional methods in game problems, generalization of the Krasovskii extremal targeting rule, Pontryagin’s maximum principle
- Dynamic systems of variable structure, hybrid systems
- Game problems for systems with distributed parameters
- Methods of the theory of making decision, artificial intelligence and system analysis
- Systems of control by spacecrafts and systems of search for sea objects
- Modeling of sport single combating, competition of firms
- Aircraft control systems, soft landing

General method to study differential games is developed –
**method of resolving functions (MRF)**, based on using the inverse
Minkovski functionals and special set-valued mappings constructed in
accordance to the parameters of conflict-controlled process. MRF makes
it feasible from the unified position to study a wide range of problems
in condition of conflict and uncertainty. These are the problems with
many participants and under state constraints, problems of the pursuit
in turn (dynamic "commercial traveller" problems) in condition
of conflict, control of various inertia objects and various types of
constraints on objects dynamics. Note that this method justifies the
classic rule of parallel pursuit, well known to engineers engaged in
design of rocket and airspace technology. Also note that MRF makes it
possible to study game problems for the processes evolving according to
relationships more complicated than ordinary differential equations.
In particular, also studied are differential-difference,
integral-differential games, as well as game problems for the Volterra
and Fredholm integral equations and systems with fractional derivatives.
The method is extended to the case of matrix resolving functions and
the resolving functionals, connected to the case of the equations with
distributed parameters. Upper and lower resolving functions of various
types are introduced, with their help sufficient condition of the game
termination in class of quasi and stroboscopic strategies are obtained.

**The positional method of pursuit**, associated with the time of first
absorption, is developed which justifies pursuit along the "line of sight".
The Krasovskii rule of extremal targeting is extended to the case of the
group pursuit, the cases with exchange and without exchange of information
in the group are examined, leading to different kinds of regularity conditions.
The cases of integral and mixed constraints on controls, delay of information,
systems of variable structure, impulse controls are explored, with account
of possibility for state constraints.

It is laid a foundation of **the nonlinear theory of collision avoidance**.
The analog of the Taylor formula for a solution of the nonlinear dynamic
system is established that plays a key role in elaborating the methods.
The methods of evasion along a direction and of variable directions,
method of invariant subspaces and recursive method are suggested. The
conditions of first and higher order are studied. The μ-problem of
L.S. Pontryagin is solved. Sufficient conditions for escape a group of
pursuers as well as conditions of evasion under the moving objects groups’
counteraction are derived. Also obtained are sufficient conditions of
collision avoidance in the class of ε-strategies and
ε-counter-strategies in the minmax or maxmin form. Comparison with
the workaround method of L.S. Pontryagin is made.

A cell markovian model is proposed to analyze game problems with
incomplete information (so called **search problems**) in which
the probability of detection or the mean time of detection plays the
role of performance criterion. The process of search is described by
bilinear system with a stochastic matrix standing for the control block.
Solving the problem is reduced to evaluating minmax or multiple minmax
of certain polynomial function of many variables. The discrete Pontryagin
maximum principle and the Bellman method of dynamic programming are
used as tools for optimization. The search on a line, in the region and
search on summon, group search with exchange and without exchange of
information and secret search by homogeneous and heterogeneous forces
are studied.

A number of the problem-oriented computer systems, modeling complexes and simulators were worked out related with control of various nature moving objects in conditions of conflict and uncertainty. In particular:

**Search for moving objects**. To solve game problems with incomplete information (when only probabilistic distribution of the initial position is known) the computer system of search and tracking for moving objects for need of navy was developed on the basis of the cell model of search. The work refers to special subject-matter and is implemented in corresponding institutions. Search for submarines is performed by heterogeneous forces (aircrafts, helicopters, airborne ships). Note that the game cell model of search is connected with the discretization of the process both in state and time. Search on a finite set of possible states is defined by the transition law of probability distribution of the players with the transition stochastic matrix depending on their controls. Such process appears as bilinear and markovian. To study it the technique of finite markovian chains is used. The discrete maximum principle and the method of dynamic programming are applied for optimization of detection probability of the target and the mean detection time.

The cases of search in the region, on summon, on the line, by a group of objects, and interaction of objects’ groups are encompassed in the computer system; dependence of detection radius on the motion velocity is taken into account. The technique can be applied for the search of crashed objects in difficult of access regions, for search of fish shoals and sunk ships.**Cosmic Research**. The method of resolving functions and the positional methods are especially efficient in the analysis and modeling of moving objects groups’ interaction. On their basis, in cooperation with the airspace institutions, the modeling complex for the "star wars" program was created for optimization of interaction of controlled cosmos based objects groups, moving along circular or elliptic orbits. The method of decomposition is used that makes it possible to reduce the process of optimization to several simpler problems of group and in turn pursuit. First of them is based on situation of encirclement by Pshenychnyi and efficiency of its solving crucially depends on the players’ disposition and control resources. Pursuit in turn is a combination of the "commercial traveller" type problem and the control problem which should be solved together. Computer realization on specific examples allows reducing the time of variants’ rundown. In so doing, control is constructed on the basis of parallel pursuit, substantiated by the method of resolving functions.

Certain ideas of groups’ interaction are used in modeling of aerial battle of groups of aircrafts.**Aviation**. Safe aircraft take off and landing is a problem of paramount importance, especially in extreme conditions (lateral wind, rain, covering with ice of the take-off and landing strip etc.) The algorithms are created and on their basis simulators are developed for training pilots in order to minimize risk. The work is performed in cooperation with the Institute of Aviation of the Defense Ministry of Ukraine.

By suggestion of American colleagues, the game problem on**soft landing**(coincidence of geometric coordinates and velocities) is solved. It is realized on computer for the dynamic systems of second order under friction and simulates the process of aircraft landing on aircraft carrier. The ocean surface stays for the state constraint (aircraft can not dive) that essentially complicates the problem.

Several ways of soft landing are proposed, on the basis of combination of classic methods of the dynamic games and mathematical methods of optimal control. Simulation package, realizing the soft landing is developed. The work is performed in cooperation with NIST (National Institute of Standards and Technology, Gaithersburg, USA). Joint book is published. Chinese institutes – the 28-th Institute (Nankin) and the Politechnical Institute (Harbin) take an interest in this elaboration.**Collision avoidance**. The original problem of Pontryagin – Mishchenko on avoidance of moving objects collision from arbitrary initial positions on semi-infinite interval of time is taken up in planning safe movement in airports and seaports by dispatcher offices. Methods of collision avoidance for nonlinear controlled systems are elaborated. The counteraction of groups of controlled objects is studied. In airports the flights schedules are making up with account of the airliners dynamics and the dispatcher should be ready to interfere in precarious situation, which threatens to become an accident. Analogous circumstances arise in the places of great amount of floating fund. Knowledge of the potentials of controlled crafts and water area, on the basis of preliminary computations, makes it possible to avoid collisions.**Control of particle beams**. One of the applications of mathematical theory of control of the systems with distributed parameters is control of charged particles on the basis of the Vlasov and Fokker –Planck –Kolmogorov equations. It is realized in the frames of the project STCU with Kharkiv and Kiev physicists in cooperation with the Brookhaven National Laboratory (USA). The related software is presented in the report materials and mathematical part is published in the joint papers in international journals.**Interception of targets**. Rules of pursuit along the line of sight, parallel pursuit and pursuit along a ray are traditional engineer methods of mobile targets interception in conflict condition. They are theoretically substantiated on the basis of ideology of the method of resolving functions and extremal targeting. In so doing, the situations of group approach and state constraints are encompassed that makes it feasible to solve a number of model examples from the classic book of R. Isaacs. Because the guaranteed controls in examples are found in explicit form, the computer realization allows the process visualization.

Software package is created for interception of mobile targets in various situation of conflict counteraction, which are applied in performing the tasks dealing with special subject-matter.

- SCIENCE AND TECHNOLOGY CENTER IN UKRAINE, Project #1746 (2002 - 2004)

**"ANALYSIS OF DYNAMICS AND DEVELOPMENT OF OPTIMAL ALGORITHMS FOR CHARGED PARTICLE TRANSPORT IN PLASMA MEDIA"**

Participating Institutions: Institute of Cybernetics, National Academy of Sciences of Ukraine (leading), National Scientific Center “Kharkiv Institute of Physics and Technology”, Brookhaven National Laboratory (USA) - SCIENCE AND TECHNOLOGY CENTER IN UKRAINE, Project #5240 (2011 - 2013)

**"NEW METHODS FOR ROMOTELY SOUNDING OF CHEMICAL AND BIOLOGICAL COMPONENTS USING OPTICAL INSTRUMENTS"**

Participating Institutions: Space Research Institute under NAS and National Space Agency, Center for Applied Optimization ISE Department, University of Florida, Gainesville, USA

- Project # Φ40.1/021 (2011–2012)

**"GAME PROBLEMS OF CONTROL, ROUTING AND TASKS ALLOCATION IN GROUP OF OBJECTS"**

Participating Institutions: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine, Institute of Mathematics and Mechanics Ural Branch of RAS (Ekaterinburg, Russia) - Project # Φ53.1/006 (2013–2014)

**"PROBLEMS OF GROUP CONTROL UNDER UNCERTAINTY, WITH ELEMENTS OF ROUTING"**

Participating Institutions: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine, N.N. Krasovskii Institute of Mathematics and Mechanics Ural Branch of RAS (Ekaterinburg, Russia) - Project # 03-01-14 (2014-2015)

**"GAME PROBLEMS OF DYNAMICS UNDER INFORMATION UNCERTAINTY"**

Participating Institutions: Glushkov Institute of Cybernetics of NAS of Ukraine, M.V. Lomonosov State University Faculty of Computational Mathematics and Cybernetics Chair of L.S. Pontryagin (Moscow, Russia)

- Conflict-controlled processes, Naukova Dumka, 1992, 384 p. (in Russian)
- Linear quadratic differential games, Naukova Dumka, 1994, 320 p. (in Russian, in co-authorship with V.J. Zhukovskij)
- Conflict-Controlled Processes, Kluwer, Boston-London–Dordrecht, 1997, 424 p., republished in 2007, 2010, 2013, by Springer Science and Business Media
- Soft Landing of Moving Objects, Gaithersburg, NIST, USA, 1998, 137 p.
- Dynamic games with discontinuous trajectories, Naukova Dumka, 2005, 220p.
(in Russian).

(in coauthorship with Yu.G. Krivonos and I.I. Matychyn).

- Wissenschaftliche zeitschrift, Leipzig Techn. High.School, 1982 (B.N. Pshenichnyi, J.S. Rappoport)
- Mathematical Control Theory,
**Int. Math.Banach Center Publ.**, vol.14, PWN, Warsaw, 1985 - J. "Facta Universitatis", Univ. of Nis, Jugoslavia, 1994, vol. 1, No.4 (Klimenko He. V.)
- New Trends in Dynamic Games and Applications,
**Birkhauser**, Boston–Basel–Berlin, 1995, (J.S.Rappoport, P.V. Prokopovich) - J. of Math. Science, Dynamical Systems, 2,
**Springer**, 80 (1996) - Game Theory and Appl. III, Nova Science Publ., Inc., New York, 1997
- J. of Math., Game Theory and Algebra, Nova Science. Publ., Inc. vol.7, #2/3, 1998
- Game Theory and Appl. VI, Nova Science Publ., Huntington, New York, 2001. (S.D. Eidelman)
- Computer and Mathematics with Applications,
**Pergamon**, Washington, USA, vol. 44, 2002 (S.D. Eidelman) - Nonlinear Analysis: Real World Applications,
**Elsevier**, 2005 (V.F. Zadorozhnii and others) - Advances in Dynamic Games,
**Birkhauser**, Boston, vol.8, part II, 2006 - J. of Math. Science,
**Springer**, New York, vol. 139, #5, 2006 (A.A. Belousov) - Advances in Dynamic Game Theory,
**Birkhauser**, Boston, vol. 9, 2007 (I.I. Matychyn) **Springer**Book "Pareto-Optimality, Game Theory and Equilibria", 2008- Optimization Method and Software, Spec. issue ded. to the memory
of Prof. N. Shor,
**Taylor and Francis**, Oxfordshire, UK, vol. 23, No. 1 , 2008 - Annals of the Int. Society of Dynamic Games,
**Birkhauser**, 2009 (I.I.Matychyn) - Proceedings of the
**Steklov Institute of Mathematics**, Moscow, 2010, Suppl.1 (I.I. Matychyn) - Proceedings of the
**Steklov Institute of Mathematics**, Moscow, 2010, Suppl.2 (A.A. Belousov) - New Trends in Nanotechnology and Fractional Calculus Applications,
**Springer**, Dordrecht, Heidelberg, London, New York, 2010 (I.I.Matychyn) - Proceedings of the
**Steklov Institute of Mathematics**, Moscow, 2010, vol. 271 - Annals of the Int. Society of Dynamic Games, Boston,
**Birkhauser**, 2011, vol.11 (I.I. Matychyn) - Book "Modeling and Optimization", Lublin Univ. Technology, Poland, 2011 (I.I. Matychyn, K. Gromaszek, A. Smolarz)
- Annals of the Int. Society of Dynamic Games, Boston,
**Birkhauser**, 2012, vol.12 (A.A. Belousov, A.G. Chentsov) - Mathematika Balkanica, New Seriea, vol.26, 2012, Fasc. 1-2 (I.I. Matychyn, V.V. Onyshchenko)
- Set-Valued Mapping in Game Problems of Dynamics, Proceedings of
ISAAC, Progress in analysis,
**Steklov Institute of Mathematics**, Moscow, 2012 - Dynamic Games Involving Impulses, Poland, Lublin Univ. Technology, 2013 (I.I. Matychyn, K. Gromaszek)
- Bilinear Markovian Processes of Search for Stationary and Moving Objects, NATO Science for Peace and Security, Series D: Information and Communication Security, IOS Press, 2014, vol. 37 (P. Pardalos, V. Jatsenko, M. Fenn)
- Proceedings of the
**Steklov Institute of Mathematics**, Moscow, 2015, vol. 291 (G.Ts. Chikrii) - Proceedings of the
**Steklov Institute of Mathematics**, Moscow, 2016, vol. 292 (L.A. Vlasenko) - Proceedings of the
**Steklov Institute of Mathematics**, Moscow, 2016, vol. 293 (L.A. Vlasenko, A.G. Rutkas)

- O.M. Patlandzoglu, A.A. Chikrii. On one class of quasi-linear differential games of pursuit //Differential Equations, 1997, vol.33, No 6. – P. 786-794 (in Russian)
- A.A. Chikriy, K. G. Dzyubenko. Bilinear Markov Processes of Searching for Moving Targets // J. of Automation and Information Sciences, 1997, vol. 33, No 5, p 92-107
- A.A. Chikrii, O.Ì. Patlandzoglu. About conjugate differential games of pursuit // J. of Automation and Information Sciences, 1998, No 4, p. 40-50
- S.D. Eidelman, A.A. Chikrii. Dynamic game problems of approach for the equations of fractional order // Ukrainian Mathematical Journal, 2000, No11. – P. 1566-1583 (in Russian)
- A.A. Chikrii, S.D. Eidelman. Generalized Mittag-Leffler matrix functions in game problems for evolutionary equations of fractional order //Cybernetics and Systems Analysis, 2000, Vol. 36, No 3, p. 315–338
- A.A. Chikrii, S.D. Eidelman. Control Game Problems for Quasilinear Systems with Riemann-Liouville Fractional Derivatives//Cybernetics and Systems Analysis, 2001, Vol. 37, No 6, p. 836–864
- J. Albus, A. Meystel, A. Chikrii, A. Belousov, A. Kozlov. Analytical Method for Solution of the Game Problem of Soft Landing for Moving Objects//Cybernetics and Systems Analysis, 2001, Vol. 37, No 1, p. 75–91
- J. Albus, A. Meystel, A. Chikrii, A. Belousov, A. Kozlov. Analytic Method for Solving the Game Problem of Soft Landing for Moving Objects // Dopovidi of NAS of Ukraine, 2001, No 8. – P. 61-65 (in Russian)
- A.A. Chikriy, G.Ts. Chikrii, K.Yu. Volyanskiy. Quasilinear Positional Integral Games of Approach // J. of Automation and Information Sciences, 2001, vol.33, No10, p.5-28
- I.V. Serhienko, A.A. Chikrii. The Scientific Heritage of B. N. Pshenichnyi //Cybernetics and Systems Analysis, 2002, Vol. 38, No 2, p. 153–174
- A.P. Ignatenko, A.A. Chikriy. A Problem of Evasion of Two Controlled Objects from a Group of Pursuers in the Three-Dimensional Space // J. of Automation and Information Sciences, 2002, vol. 34, No 1, p. 3-32
- S.D. Eidelman, A.A. Chikrii. Interpolation polynomials of Lagrange-Sylvestre in the game fractional problems. Fractional problem of boy and crocodile // Dopovidi of NAS of Ukraine, 2002, No5. – P. 65-71 (in Russian)
- A.A. Chikrii, S.D. Eidelman. Asymptotic representations of the generalized functions of Mittag – Leffler in fractional games of second order // Dopovidi of NAS of Ukraine, 2002, No 6. – P. 69-74 (in Russian)
- V.M. Kuncevich, A.A. Chikrii. Controlled Processes: Methods of Investigation and Applications //Cybernetics and Systems Analysis, 2003, Vol. 39, No 4, p. 477–487
- A.A. Chikriy, I.I. Matichin. Resolving Functions in Parallel and Pure Pursuit // J. of Automation and Information Sciences, 2003, vol. 35, No 11, p. 5-11
- A.A. Chikriy, A.P. Ignatenko. On Substantiation of the Proportional Navigation Method in the Simple Pursuit Problem // J. of Automation and Information Sciences, 2004, vol. 36, No 1, p. 19-27
- A.A. Chikrii, I.I. Matychyn. On one class of game problems with impulse control // Dopovidi of NAS of Ukraine, 2004, No 6. – P. 73 – 77 (in Russian)
- A.A. Chikrii, G.Ts. Chikrii, S.D.Eidelman. Linear fractional games of approach // Prikladnaya Matematika I Mekhanika, 2004, vol. 68.- No 5, P.746-757 (in Russian)
- A.A. Chikrii, I.I. Matychyn. Linear differential games with impulse control of the evader // Dopovidi of NAS of Ukraine, 2004, No 10. – P.80-85 (in Russian)
- A.A. Chikrii, I.I. Matychyn, G.Ts. Chikrii. Conflict controlled processes with discontinuous trajectories//Cybernetics and Systems Analysis, 2004, Vol. 40, No 6, pp.800–811
- A.A. Chikrii, I.I. Matychyn. Motion Camouflage in Differential Games of Pursuit // J. of Automation and Information Sciences, 2005, vol.37, No 3, p. 1-5
- A.A. Chikrii, J.S. Rappoport, K.A. Chikrii. Sufficient conditions for solvability of game problems of approach in the class of stroboscopic strategies // Dopovidi of NAS of Ukraine, 2005, No 9. – P. 71-76 (in Russian)
- A.A. Chikriy, I.S. Rappoport. Measurable Many-Valued Maps and Their Selectors in Dynamic Pursuit Games //J. of Automation and Information Sciences, 2006, vol. 38, No 1, p. 57-67
- A.A. Chikrii, J.S. Rappoport, K.A. Chikrii. On the theory of pursuit in the class of stroboscopic strategies // Dopovidi of NAS of Ukraine, 2006, No 6. – P. 72-77 (in Russian)
- K.G. Dzyubenko, A.A. Chikriy. On the Game Problem of Searching Moving Objects for a Model of Semi-Markovian Type // J. of Automation and Information Sciences, 2006, vol. 38, No 9, p.1-11
- A.A. Chikrii, I.I. Matychyn. An analog of Cauchy formula for the linear systems of fractional order // Dopovidi of NAS of Ukraine, 2007, No 1. – P. 50-55 (in Russian)
- A.A. Chikrii, J.S. Rappoport, K.A. Chikrii. Multivalued mappings and their selectors in the theory of conflict-controlled processes //Cybernetics and Systems Analysis, 2007, Vol. 43, No 5, p.719–730
- A.A. Chikrii, I.I. Matychyn. Presentation of Solutions of Linear Systems with Fractional Derivatives in the Sense of Riemann-Liouville, Caputo and Miller-Ross // J. of Automation and Information Sciences, 2008, vol. 40, No 6, p. 1-11
- A.A. Chikrii, J.S. Rappoport, K.A. Chikrii. Comparison of guaranteed times in conflict-controlled motion //Cybernetics and Systems Analysis, 2008, Vol. 44, No 4, p.537–546
- A.A. Chikriy, A.G. Chentsov, I. I. Matychyn. Differential Games of the Fractional Order with Separated Dynamics // J. of Automation and Information Sciences, 2009, vol. 41, No 11, p. 17-27
- A.A. Chikrii, I.I. Matychyn. Game problems for linear systems of fractional order // Proceedings of the Institute of Mathematics and Mechanics, Ural Branch of RAS, Ekaterinburg, 2009, vol. 15, No 3 – pp.262–278 (in Russian)
- A.A. Chikrii, A.A.Belousov. Linear differential games with integral constraints // Proceedings of the Institute of Mathematics and Mechanics, Ural Branch of RAS, Ekaterinburg 2009, vol. 15, No 4 – pp.290–301 (in Russian)
- A.A. Chikrii. Guaranteed results in game problems of the motion control // Proceedings of the Institute of Mathematics and Mechanics, Ural Branch of RAS, Ekaterinburg, 2010, vol. 16, No 5 – pp.223–232 (in Russian)
- A.A. Belousov, Ju.I. Berdyshev, A.G. Chentsov, A.A. Chikrii. Solving the dynamic traveling salesman game problem //Cybernetics and Systems Analysis, 2010, Vol. 46, No 5, p. 718–723
- A.A. Chikrii, I.I. Matychyn. On the linear conflict-controlled processes with fractional derivatives // Proceedings of the Institute of Mathematics and Mechanics, Ural Branch of RAS, Ekaterinburg, 2011, vol. 17, No 2. – pp.256–270 (in Russian)
- A.A. Chikrii, J.S. Rappoport. On the theorem of inverse image for
*L*x*B*- measurable set-valued mappings // Dopovidi of NAS of Ukraine, 2011, No 11. – pp.54–58 (in Russian) - I.V. Serhienko, A.A. Chikrii. Talent multiplied by diligence. To 75 birthday of the president of RAS, academician Yu.S.Osipov. // Visnyk of Academy of Sciences of Ukraine, 2011, No 5. –– pp.55–60 (in Ukraine)
- I.V. Serhienko, A.A. Chikrii. Developing B.N. Pshenichnyi’s scientific ideas in optimization and mathematical control theory //Cybernetics and Systems Analysis, 2012, Vol. 48, No 2, p. 157–179
- A.A. Chikrii, J.S. Rappoport. Method of resolving functions in the theory of conflict-controlled processes //Cybernetics and Systems Analysis, 2012, Vol. 48, No 4, p.512–531
- A.A. Chikrii, A.A. Belousov. Linear differential games with convex integral constraints // Proceedings of the Institute of Mathematics and Mechanics, Ural Branch of RAS, Ekaterinburg, 2013, vol.19, No 4. – P. 308-319 (in Russian)
- A.A. Chikrii, G.Ts. Chikrii. Matrix Resolving Functions in Dynamic Games problems //Kibernetika i Systemnyj Analiz, 2014, Vol. 50, No 2, p. 44-63 (in Russian)
- A.A. Chikrii, G.Ts. Chikrii. Matrix Resolving Functions in Dynamic Games of Approach //Cybernetics and Systems Analysis, 2014, Vol. 50, No 2, p. 201–217
- A.A. Chikriy, L.A. Vlasenko. The Method of Resolving Functionals for a Dynamic Game in a Sobolev System // J. of Automation and Information Sciences, 2014, vol.46, No 7, p. 1-11
- V.J. Zhukovskiy, A.A. Chikriy. On Discrete Conflict-Controlled Processes Described by Grunvald-Letnikov Fractional Systems // J. of Automation and Information Sciences, 2015, vol.47, No1, p. 24-34
- A.A. Chikrii, L.A. Vlasenko. One differential game with distributed parameters // Proceedings of the Institute of Mathematics and Mechanics, Ural Branch of RAS, Ekaterinburg, 2014, No 4. – P. 5-14 (in Russian)
- L.A. Vlasenko, A.G. Rutkas, A.A. Chikrii. One differential game in abstract parabolic system // Proceedings of the Institute of Mathematics and Mechanics, Ural Branch of RAS, Ekaterinburg, 2015, No 2. – P.26-40 (in Russian)
- V.J. Zhukovskij, A.A. Chikrii, N.G. Soldatova. Existence of Berge equilibrium in conflicts under uncertainty // Avtomatika i Telemekhanika, 2016, No 4. – P. 114-133 (in Russian)
- A.A. Chikriy, V.K. Chikrii. Image Structure of Multivalued Mappings in Game Problems of Motion Control // J. of Automation and Information Sciences, 2016, vol. 48, No 3, p. 20-35
- A.A. Chikriy. Set-valued mapping and its selections in dynamic game problems //Kibernetika i vychislitelnaya technika, 2016, p. 5-22 (in Russian)
- A.A. Chikrii, G.Ts. Chikrii, V.J. Zhukovskij. Game problems of control for functional – differential systems, Poland, Lublin, 2016, 55 p

The results of studies were presented at the International Congress of
Mathematicians (Berlin 1998), International Congresses of Artificial
Intelligence (Geithersberg 1996, 1997), International Symposiums on
Dynamic Games and Applications (Monreal 1994, Kanagawa 1996,
Maastricht 1998), European (Brussels 1997) and Asian (Seoul 1997)
Conferences on Control, International Congress on Optimization
(Victoria 1996), International Conference Dedicated to Ninetieth
Anniversary of L.S. Pontryagin (Moscow 1998), International Conference
on the Theory of Hybrid Dynamic Systems ADPM 2000 (Dortmund 2000),
the Third International Congress of Nonlinear Analytics (Sicilia 2000),
the Eighth European Conference on Particle Acceleration (Paris 2002),
International Conference on Applied Mathematics Dedicated to the 65
Anniversary of B.N. Pshenichnyi (Kiev 2002), International Symposium
on Dynamic Games and Applications (Saint-Petersburg 2002), International
Conference "Automatics" (1998-2007), International Conference
Dedicated to 80-th Anniversary of N.N. Krasovskii (Ekaterinburg 2004),
International Conference to the Memory of A.I. Subbotin (Ekaterinburg 2005),
11–th International Congress on Theory of Dynamic Games (USA-2004),
12-th International Congress on the Theory of Dynamic Games (France,
Sophia Antipolis 2006), International Conference "Modeling and
Investigation of Dynamic Systems Stability" (Kiev 2007),
International Autumn Crimean Mathematical School (Crimea 2007),
International Conference *"Nonlinear Dynamical Analysis"*
(Saint-Petersburg 2007), International Conference *"Analysis and
Singularities"* (Moscow 2007), International Conference "Knowledge–
Dialogue–Decision" (Bulgaria, Varna 2007), International Conference
"Concurrent Systems & Programming" (Poland, Warsaw 2007),
International Conference "Issues of Computation Optimization"
(Crimea 2007), International Conference Dedicated to Centennial
Anniversary of L.S. Pontryagin (Moscow 2008), International Conference
"Actual Problems of the Theory of Stability and Control"
(Ekaterinburg 2009), International Conference Dedicated to 95-th
Anniversary of E.A. Barbashin (Minsk 2013), at the International Forums:
"Dynamic Games and Applications" (Canada, Bannf 2010), 8-th
International Congress of the ISAAC (Moscow 2011), 6-th International
Conference "Transform Methods and Special Functions" (Sofia 2011),
DSMCI – 2013 (Kiev 2013). International Conference "Dynamic Systems:
Stability, Control, Optimization" (Minsk 2013), XII All-Russian
Meeting on Control Problems (Moscow 2014), International Conference
"System Dynamics and Control Processes" (Ekaterinburg 2014),
International Seminar Dedicated to 70–th Anniversary of A.I. Subbotin
"Control Theory and the Theory of Generalized Solutions of
Hamilton – Jakobi Equations" (Ekaterinburg 2015), International
Conference "Automatics - 2015" (Odessa), International
Conference "Differential – Functional Equations and Their Applications"
(Chernivtsi 2016), International Conference “Automatics - 2016” (Sumy 2016).

- Theory of differential games
- Introduction to general games theory
- Elements of convex analysis
- Theory of set-valued mappings and its application
- Search for moving objects
- Method of pursuit and evasion
- Conflict–controlled process for functional-differential systems
- Optimal control
- Applications for dynamic games
- Fractional calculus and its application