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of the Institute of Mathematics and Mechanics (IMM) of the USSR Academy of Sciences. His scientific authority and his management of the Institute secured its the leading role in the field of mathematics and mechanics in the Urals.
Krasovskii represents the scientific school of N. G. Chetayev, going back to A. M. Lyapunov. Through his first studies on the theory of the stability of motion, carried out under the influence of his teachers Ye. A. Barbashin, N. P. Yerugin, I. G. Malkin and N. G. Chetayev, he became well known. The problem of the stability of the motions of non-linear systems under generalized Routh-Hurwitz conditions, where the region of initial disturbances cannot be considered to be small, was solved, as demanded by engineering practice. The Barbashin-Krasovskii theorem of asymptotic stability was published. Here, the derivative of the Lyapunov function, by virtue of the equations of perturbed motion, may be equal to zero in a set not containing whole trajectories. This theorem received wide recognition and was used repeatedly in theoretical and applied research.
second method. Continuing the work of Ye. A. Barbashin, I. G. Malkin, Kh. L. Massera, K. E Persidskii and N. G. Chetayev, Krasovskii developed methods for plotting Lyapunov functions, including the solution of the problem of the inversion of the Lyapunov and Chetayev theorems on instability.
In 1955-1957, he worked for his doctorate under N. G. Chetayev. An invaluable gift of fate was the opportunity to see and hear live the greatest mathematicians and engineers of the time and make use of their advice. Successful work towards his doctorate was also aided by the kind consideration of colleagues at the Institute of Mechanics of the USSR Academy of Sciences: G. K. Pozharitsii, V. V. Rumyantsev, B. S. Razumikhin and V. M. Starzhinskii. In 1957 he defended his Doctorate dissertation on some aspects of the theory of stability of non-linear systems.
By the end of the 1950s, he had constructed an original theory of stability for systems with delay. The incentive to carry out this research was provided by the work of A. D. Myshkis and L. E. El'sgol'ts. Krasovskii suggested that elements of functional space of the histories of motion be selected as the phase states of systems with delay. The evolution of such systems can than be described by an ordinary differential equation, but in functional space. This determined the natural theory of stability of hereditary systems using functionals in the role of Lyapunov functions. The universality of this approach was confirmed theorems on the existence of Lyapunov functionals with the necessary properties. The semigroup property of hereditary systems that was revealed in this case determined the explicit sense of the spectral properties of the corresponding infinitesimal operator and opened the way for the transfer to such systems of the theory of critical cases of Lyapunov stability. This approach earned the recognition of specialists and served as the basis for much research.
The results he obtained during this period were published in the monograph Some Problems of the Theory of Stability of Motion (1959).
In the 1950s, he began research in the field of optimal control. Interest in this field was aroused by the work of Feldbaum, Buschau, Tsian Sue-Sen and Bellman and in particular by the publication by L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and Ye. E Mishchenko of the maximum principle. In 1957, he proposed an approach to problems of optimal control based on methods of functional analysis. A simple and effective theory of linear controlled systems was developed. This approach involved convex programming and focused upon the minimum properties of conjugate designs, including in the treatment of Pontryagin's maximum principle. He then developed a minimax approach to problems of observation under conditions of indeterminate interference. This research was initiated by Kalman.
At the end of the 1950s, Krasovskii had to take upon himself the teaching of courses on the theory of probability in the UrGU and the UPI. This required him to become more thoroughly acquainted with the concepts of Kolmogorov and to study the work of Bernshtein, Khinchin, Feller, Doob Loev, Shannon and Wiener. He became interested in problems of stochastic stability and in problems of the control of random processes, which led to research resulting in the proposal of different approaches to such problems. The combination of classic and new methods made it possible to build a uniform theory of stability and control for ordinary dynamical systems, systems with delay and stochastic systems. The results of Chetayev concerning the stabilization of mechanical systems by forces of a particular nature were extended, and the possibility of constructive improvement in stabilizability based on the gyroscopic effect was substantiated.
Corresponding results of research in the 1950s and 1960s were included in the monograph The Theory Motion of Control (1968).
The requirements of actual practice, and knowledge of the work of Isaacs and Bellman, prompted Krasovskii to investigate problems of guaranteed control under conditions of dynamic and information interference. The construction of the theory of differential games, termed positional games, was begun.
Krasovskii put forward the law of extremal aiming, which constructs a control based on the feedback principle by solving auxiliary problems of expected programmed control. This concept was set out in the monograph The Rendezvous Game Problems (1970).
A more general concept of the positional differential game was then developed, theorems of the existence of the value of a game and of a saddle point were proved and constructive methods were proposed for generating optimal strategies. The key element was the so-called extremal shift of the real controlled object towards the ideal model, abstract or generated on a computer. The concept was extended to control problems under conditions of conflict and uncertainty of hereditary and stochastic systems, and also systems with degenerate higher derivatives.
The results were presented in the monograph Positional Differential Games (1974) (coauthor with A. I. Subbotin).
The properties of irregular equations of the Hamilton-Jacobi type that were revealed in specific problems of positional differential games led to the general concept of the correct solution of such equations. The approach was employed by Subbotin in the form of minimax solutions for a wide class of equations with first-order partial derivatives.
Initially, the constructive solutions were based on auxiliary determinate motions. This limited their effectiveness. By introducing random elements, Krasovskii developed a more effective method which he called stochastic programmed synthesis.
The concept of control under conditions of conflict and uncertainty was a reflection of problems arising in practice and gave these problems an adequate mathematical form. The key concepts were an accessible informational form, the quality index of the process, the minimax-maximin criterion and the control law based on the feedback principle, carrying out a determinate or stochastic strategy. In the latter case, the control realizes outcomes of specially organized random tests. It is fundamental that in this case the ,optimal result according to the minimax-maximin criterion is achieved with a probability as close as desired to unity.
The control methods and procedures developed were oriented towards state-of-the-art computer technology. A comprehensive computing experiment was specified as a cornerstone element of the investigation and was used without fail to clarify the problem, to search for ways of solving it and for systematically checking hypotheses and results of theoretical investigations. The combination of analytical and computing methods resulted in useful applications.
The results of these investigations were presented in the monograph Control of a Dynamical System (1985) and in the monograph Control underLack of Information (1995) (coauthor with A. N. Krasovskii).
Professor Krasovskii is the author of about 300 scientific publications, including six monographs. He promotes the Urals School of Motion Stability Theory and is a founder of the School of the Mathematical Theory of Control. Among his students are engineers and teachers, doctors and masters of science and Corresponding Members and Full Members of the Russian Academy of Sciences.
Working as leader of the IMM of USSR Academy of Sciences, he initiated and encouraged applied studies and the development of the computer section of the Urals Scientific Centre (then the Urals Branch of the USSR Academy of Sciences, and later the Russian Academy of Sciences).
Much of his time and energy is given to reporting on the progress of fundamental science to applied scientists, engineers, teachers, students and schoolchildren. In the 1980s he headed a campaign aiming to computerize schools and colleges in the Sverdlovsk region. This gave impetus to the subsequent raising of standards of schools in Ekaterinburg and the whole region to an adequate level of state-of-the-art information technology.
His authority is high. He has been a member of the Presidium of the Russian Academy of Sciences and a member of the Department of Mechanics and Control Processes of the USSR Academy of Sciences, and he is a member of the Presidium of the National Committee on Theoretical and Applied Mechanics. He is also on the editorial board of leading scientific publications. He has an honorary doctorate from the Urals State Technological University Urals State University, and is a Soros Professor.
His scientific achievements and teaching activity are highly valued by the state (he is a Hero of Socialist Labour, a winner of the Lenin and State prizes and a bearer of the Orders of the Soviet Union and Russia) and by the scientific community (he was awarded the M. V. Lomonosov Great Gold Medal of the Russian Academy of Sciences, the A. M. Lyapunov Gold Medal, the Demidov Prize in physics and mathematics and the 'Triumph' Prize; he is also a doctor honoris causa of the Hungarian Academy of Sciences and has received an IEEE award).
The editorial board and staff of Prikladnaya Matematika i Mekhanika and his many disciples, colleagues and friends send him warm greetings on his birthday and wish him good health and further success in his work.
Theorems on the stability of motions governed by a system of two equations. Prikl. Mat. Mekh., t952, 16, 547-554.
The stability of motion as a whole. Dokl. Akad. Nauk SSSR, 1952, 86, 453-456 (coauthor with Ye. A. Barbashin).
The stability of motion under any initial disturbances. M Phys.-Math. Sci. dissertation. Urals State University, Sverdlovsk, 1953.
Calculation of the optimum blank shape in the stamping of articles of the pinion type. Tr. Ural'sk. Politekhn. Inst. 1953, 45, 137-151 (coauthor with O. A. Ganago and I. Ya. Tarnovskii).
The stability under any initial disturbances of solutions of a non-linear system of three equations. Prikl. Mat. Mekh., 1953, 17, 3, 339-350.
The stability of solutions of a system of two differential equations. Prikl. Mat. Mekh., 1953, 17, 6, 651-672.
The stability of motion as a whole under persistent disturbances. Prikl. Mat. Mekh., 1954, 18, 95-102. The behaviour of integral curves as a whole for a system of two differential equations. Prikl. Mat.
of differential equations. Prikl. Mat. Mekh., 1954, 18, 5, 513-532. The stability as a whole of the solution of a non-linear system of differential equations. Prikl. Mat.
Mekh., 1954, 18, 6, 735-737. Adequate conditions of stability of solutions of a system of non-linear differential equations. Dokl.
(coauthor with O. A. Yesin, Yu. R Nikitin and S. I. Popel'). The determination of forces arising in plastic metal working. In Plastic Working of Metals.
Metallurgizdat, Moscow, 1954, No. 3, 5-22 (coauthor with A. A. Pozdeyev and I. Ya. Tarnovskii). Procedure for the graphic calculation of surface and interphase tensions from the shape of a drop.
Tr. Ural'sk. Politekhn. Inst., 1954, 49, 76-81 (coauthor with O. A. Yesin, Yu. P. Nikitin and S. I. Popel').
differential equations. Dokl. Akad. Nauk SSSR, 1955, 101, 1, 17-20. The stability of motion in the critical case of a single zero root. Mat Sbornik, 1955, 37, 1, 83-88.
The inversion of the theorems of A. M. Lyapunov's second method for investigating the stability of motion. Uspekhi Mat. Nauk, 1956, 11, 3, 159-164.
The theory of A. M. Lyapunov's second method for investigating stability. Mat. Sbornik, 1956, 40, 1, 57-64.
The theory of A. M. Lyapunov's second method for investigating the stability of motion. Dokl. Akad. Nauk SSSR, 1956, 109, 3, 460-463.
Inversion of the theorems of Lyapunov's second method and problems of the stability of motion to a first approximation. PriM. Mat. Mekh., 1956, 20, 2, 255-265.
The application of A. M. Lyapunov's second method for equations with time lags. PriM. Mat. Mekh., 1956, 20, 3, 315-327.
Mechanics of the USSR Acad. Sci., Moscow, 1956.
The stability of quasi-linear systems with delay. Dokl. Akad. Nauk SSSR, 1958, 119, 3, 435-438.
126, 2, 267-270. Optimal control in non-linear systems. Izv. VUZ Matematika, 1959, 5, 122-130. The problem of the existence of optimum trajectories. Izv. VUZ Mathematika, 1959, 6, 81-87. Some Problems of the Theory of Stability of Motion. Fizmatgiz, Moscow, 1959. Stability of Motion.
Applications of Lyapunov's Second Method to Differential ~ystems and Equations with Delay. Stanford University Press, Stanford, California, 1963.
Analytical development of controllers in stochastic systems with limitations on the rate of change of the control action. PriM. Mat. Mekh., 1961, 25, 3, 420-432 (coauthor with E. Ao Lidskii).
Uniform asymptotic stability of systems of differential equations with a small parameter at the derivatives. PriM. Mat. Mekh., 1961, 25, 4, 680-690 (coauthor with A. I. Klimushev).
Root mean square optimum stabilization under random attenuating disturbances. PriM. Mat. Mekh., 1961, 25, 5, 806-817.
Selection of the parameters of optimum stable systems. In Proceedings of the Ist International IFAC Congress. Vol. 2. Theory of Discrete, Optimum and Self-Adjusting Systems. Izd. Akad. Nauk SSSR, Moscow, 1961, 482-489.
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Analytical development of controllers in systems with random properties. II. Equations for optimal control. Approximate method of solution.Avtomatika i Telemekhanika, 1961, 22, 10, 1273-1278 (coauthor with E. A. Lidskii).
Analytical development of controllers in systems with random properties. III. Optimal control in linear systems. Minimum root mean square error. Avtomatika i Telemekhanika, 1961, 22, 11. 1425-1431 (coauthor with E. A. Lidskii).
The analytical development of an optimal controller in a system with time lags. Prikl. Mat. Mekh., 1962, 26, 1, 39-51.
Theoretical and Applied Mechanics. Moscow, 1960. Review of Papers. Izd. Akad. Nauk SSSR, Moscow-Leningrad, 1962, 36-47.
SSSR. Tekhn. Kibernetika, 1963, 6, 3-15 (coauthor with Yu. S. Osipov).
The theory of controllability and observability of linear dynamical systems. Prikl. Mat. Mekh., 1964, 28, 1, 3-14.
The approximation of a certain problem of analytical development of controllers in a system with delay. Prikl. Mat. Mekh., 1964, 28, 4, 716-724.
The problem of the stabilization of a mechanical system. Prikl. Mat. Mekh., 1964, 28, 5, 801-811 (coauthor with M. S. Gabrielyan).
The observation of a non-linear controlled system in the vicinity of prescribed motion. Avtomatika i Telemekhanika, 1964, 25, 7, 1047-1057 (coauthor with E. G. Al'brekht).
A certain property of the gyroscopic stabilizability of a controlled conservative mechanical system. Izv. Akad. Nauk SSSR. Tekhn. Kibernetika, 1964, 5, 156-164.
Optimal processes in systems with time age. InAutomat. and Remote Control Theory. Butterworths, Oldenbourg, 1964, 327-332.
The problem of the quality of stability of processes in systems with random parameters. In Proceedings of 4th All-Union Mathematical Congress. 1961. Nauka, Leningrad, 1964, Vol. 2, 451-456.
The problem of the damping of a linear system with minimum control intensity. Prikl. Mat. Mekh., 1965, 29, 2, 218-225.
Correction of the motion of a two-degree-of-freedom system with one cyclic coordinate. Prikl. Mat. Mekh., 1965, 29, 3, 401--407 (coauthor with G. S. Shelement'yev).
The problem of the damping of a linear system. Prikl. Mat. Mekh., 1965, 29, 5, 828-834 (coauthor with V. I. Bondarenko and Yu. M. Filimonov).
The stabilization of non-stationary systems. Prikl. Mat. Mekh., 1965, 29, 6, 1081-1083 (coauthor with N. G. Bulgakov).
argument. Differents. Uravneniya, 1965, 1, 12, 1551-1556. The stabilization of systems in which interference depends on the magnitude of the control action.
of 2nd All- Union Congress on Theoretical and Applied Mechanics 1964. Review of Papers. Nauka, Moscow, No. 1, 77-93.
The ]problem of the changing of a linear system. Prikl. Mat. Mekh., 1967, 31, 3, 460-467 (coauthor with Yu. M. Repin).
The rendezvous problem. Dokl. Akad. Nauk SSSR, 1967, 173, 2, 285-287 (coauthor with V. Ye. Tret'yakov).
(coauthor with N. E Yerugin).
Lectures on Control Theory. No. 2. Generalized Programmed Control of Linear Systems. Ural'sk. Gos. Univ. Sverdlovsk, 1968.
Applied Mechanics. Nauka, Moscow, 1968, 179-244.
A. I. Subbotin). Regularization of a certain differential game. Izv. Akad. Nauk SSSR. Tekhn. Kibernetika, 1969, 1, 3-8. A differential game of approach I. Rough case. Differents. Uravneniya, 1969, 5, 3, 407-423. Game problems of dynamics. I. Izv. Akad. Nauk SSSR. Tekhn. Kibernetika, 1969, 3-12.
A. I. Subbotin). The pursuit problem. Dokl. Akad. Nauk SSSR, 1970, 191, 270-272. A differential game of approach. Dokl. Akad. Nauk SSSR, 1970, 193, 2, 284-287. Lectures on Control Theory. No. 3. General Scheme of a Differential Game. Examples. Ural'sk. Gos.
Univ., Sverdlovsk, 1970. Lectures on Control Theory. No. 4. The Principal Game Problem of Guidance. Absorption of the Target.
1970, 8, 10-25 (coauthor with M. A. Gavrilov, A. M. Letov and V. S. Pugachev).
The structure of game problems of dynamics. Prikl. Mat. Mekh., 1971, 35, 1, 110-122 (coauthor with A. I. Subbotin).
Paris, 1971, Vol. 3, 177-181. Rendezvous Game Problems. Nat. Tech. Inf. Serv., Springfield, VA, 1971.
of Soviet Mathematicians. Nauka, Moscow, 1972, 118-124.
Approximation in a differential game. Prikl. Mat. Mekh., 1973, 37, 2, 197-204 (coauthor with A. I. Subbotin). A differential game of approach-evasion. I. Izv. Akad. Nauk SSSR. Tekhn. Kibernetika, 1973, 2, 3-18. A differential game of approach-evasion. II. Izv. Akad. Nauk SSSR. Tekhn. Kibemetika, 1973, 3, 22-42. Extremal control in a non-linear positional differential game. Izv. Akad. Nauk SSSR. Tekhn.
1stAll-Union Conference on the Game Theory (Yerevan, 1968). Izd. Akad. Nauk Arm. SSSR, Yerevan, 1973, 206-207.
Position Differential Games. Nauka, Moscow, 1974, = JeuxDiffdrentiels. Mir, Moscow, 1977 (coauthor with A. I. Subbotin).
Games. Inst. Matem. Mekh. Ural'sk, Nauch, Tsentra Akad. Nauk SSSR, Sverdlovsk, 1974, 26-76 (coauthor with V. D. Batukhtin).
Minimax aiming in a differential game. In Extremal Strategies in Positional Differential Games. Inst. Mat. Mekh. Ural'sk, Nauch, Tsentra Akad. Nauk SSSR, Sverdlovsk, 1974, 121--137.
Stochastic strategies in differential games. Dokl. Akad. Nauk SSSR, 1975, 220, 5, 1023-1026 (coauthor with A. I. Subbotin and V. E Rossokhin).
Extremal control in a non-linear positional differential game. In Differential Games Control Problems: Collection of Scientific Proceedings of the Institute of Mathematics and Mechanics, Urals Scientific Centre, USSR Acad. Sci., 1975, 15, 34-63 (coauthor with V. D. Batukhtin).
Differential games in mixed strategies. In Problems of Analytical Mechanics and Theories of Stability and Control. Nauka, Moscow, 1975, 11-18 (coauthor with A. I. Subbotin).
Closed-loop differential games. In Optimization Techniques. IFIP Technical Conference (Novosibirsk). Lecture Notes in Computer Sciences. Springer, Berlin, 1975, Vol. 27, 422-424.
Optimal control under conditions of conflict or uncertainty. Proc. IFAC 6th World Congress (Boston and Cambridge, Massachusetts). Dtisseldorf, 1975, Part 4, 28.5/1-28.5/8.
3,567-570 (coauthor with L. N. Bol'shev, V. A. II'in, V. A. Prokhorov, B. S. Sotskov and A. N. Tikhonov).
(coauthor with A. G. Chentsov).
Programmed designs for positional game control. Prikl. Mat. Mekh., 1978, 42, 1, 3-14. The synthesis of control in a differential game, Dokl. Akad. Nauk SSSR, 1978, 239, 5, 1041-1043. Differential games. Approximation and formal models. Mat. Sbornik, 1978, 107, 4, 541-571.
On designing differential games. II. Probl. Control and Inform. Theory, 1979, 8, 1, 3-11 (coauthor with A. G. Chentsov).
Differential games: actual problems and their formalization. A Link between Sci. andAppl. Automat. Contr.: Proc. 7th Trienn. World Con~ IFAC, Helsinki, 1978. Pergamon Press, Oxford, 1979, Vol. 2, 975-982.
Helsinki, 1980, Vol. 1,151-163. Game-theoretical optimization of differential systems. In Optimization Techniques: Proc. 9th IFIP Conf.
(Lect. Notes Control and Inform. Sci.). Springer, Berlin, 1980, Vol. 22, Part 1, 37-53.
Stochastic programmed synthesis for a determinate positional differential game. Prikl. Mat. Mekh., 1981, 45, 4, 579-586 (coauthor with A. N. Krasovskii and V. Ye. Tret'yakov).
Stochastic programmed synthesis for a positional differential game. Dokl. Akad. Nauk SSSR, 1981, 259, 1, 24-27 (coauthor with V. Ye. Tret'yakov).
Valentin Vital,yevich Rumyantsev (60th birthday tribute). Differents. Uravneniya, 1981, 17, 8, 1522-1525 (coauthor with N. R Yerugin and N. N. Moiseyev).
The stochastic programmed synthesis of strategies in a differential game. Prikl. Mat. Mekh., 1982, 46, 6, 885-892.
(coauthor with V. Ye. Tret'yakov).
A certain problem of optimal control for a minimum ensured result. Izv. Akad. Nauk SSSR. Tekhn. Kibernetika, 1983, 2, 6-23 (coauthor with V. Ye. Tret'yakov).
Stochastic programmed synthesis of a certain guaranteeing control. Control and Inform. Theory, 1983, 12, 2, 79-95 (coauthor with V. Ye. Tret'yakov).
The problem of Control with Incomplete Information. Inst. Matem. Mekh. Ural'sk. Nauch. Tsentra Akad. Nauk SSSR, Sverdlovsk, 1984 (coauthor with S. I. Tarasova, V. Ye. Tret'yakov and G. I. Shishkin).
The problem of control under conditions of incomplete information. Prikl. Mat. Mekh., 1984, 48, 4, 533--539.
Minimax control and stochastic maximin. Differents. Uravneniya, 1984, 20, 9, 1523-1529. Extremal aiming and extremal displacement in a game-theoretical control. Probl. Control and Inform.
Theory, 1984, 13, 5, 28%302.
Sverdlovsk, 1985 (coauthor with A. N. Krasovskii and V. Ye. Tret'yakov). Determinate strategy and stochastic programs. Prikl. Mat. Mekh., 1985, 49, 2, 179-190. A positional differential game. Tr. Mat. Inst. Akad. Nauk SSSR, 1985, 169, 159-179. Control with an information deficit. Dokl. Akad. Nauk SSSR, 1985, 280, 3, 536-540.
The Problem of Control with an Ensured Result. Sredne-Ural'sk. Knizh. Izd., Sverdlovsk, 1986 (coauthor with V. Ye. Tret'yakov).
Differential Equations: Proceedings of the International Conference (Novosibirsk, 1983). Nauka, Novosibirsk, 1986, 93-102 (coauthor with V. Ye. Tret'yakov).
Nikolai Terent'yevich Tynyanskii. Uspekhi Mat. Nauk, 1986, 41, 4, 143-144 (coauthor with A. G. Vitushkin, M. I. Zelikin, et al.).
Yu. L. Yershov, Yu. A. Mitropol'skii, D. K. Faddeyev, et al.).
V. G. Zhitomirskii (1934-1988). Informatika i Obrazovaniye, 1989, 5, 13-16 (coauthor with B. Sutyrin and L. N. Shevrin).
Control and stabilization under lack of information. Izv. Ross. Akad. Nauk. Tekhn. Kibernetika, 1993, 1, 148-151.
A differential game for the minimax of a positional functional. In Advances in Nonlinear Dynamics and Control (Ed. A. B. Kurzhanski). Birkh~iuser, Boston, 1993, 41-73 (Progress in Systems and Control Theory, Vol. 17) (coauthor with A. N. Krasovskii).
Valentin Konstantinovich Ivanov. UspekhiMat. Nauk, 1993, 48, 5,147-152 (coauthor with V. V. Vasin, M. M. Lavrent'yev, Yu. S. Osipov, A. N. Tikhonov, et al.).
Control under Lack of Information. BirkNiuser, Boston 1995. (Systems and Control: Foundat. and Appl.) (coauthor with A. N. Krasovskii).
Mathematical modelling in school. Izv Ural'sk. Gos. Univ., 1995, 4, 12-24.
Problem of conflict control with hereditary information. Prikl. Mat. Mekh., 1996, 60, 6, 885-900 (coauthor with N. Yu. Lukoyanov).
Modelling - mathematics, information science, logic - in school. Informatika i Obrazovaniye, 1997, 2, 65-71; 3, 3-7; 6, 5-12; 7, 3-7 (coauthor with T. N. Reshetova).
Nikolai Pavlovich Yerugin: 90th birthday tribute. Differents. Uravneniya, 1997, 33, 5,579-582 (coauthor with A. E Andreyev, I. V. Gaishun, V. I. Gromak, et aL).
Ivan Vasil'yevick Gaishun: 50th birthday tribute. Different. Uravneniya, 1997, 33, 6, 723-729 (coauthor with N. A. Izobov, V. A. Ii'in. V. M. Matrosov, A. A. Samarskii and A. M. Samoilenko).
In memory of Andrei I. Subbotin. In Proc. 8th International Symposium on Dynamic Games and Applications, Maastricht, The Netherlands, 1998, XIII-XXIII (coauthor with E. G. Al'brekht, A. G. Chentsov, et al.).
Ser. Modern Mathematics and its Applications, 1999, Vol. 60, 24-41 (Proceedings of the International Conference dedicated to the 90th Birthday of L. S. Pontryagin, Moscow, 1998, Vol. 1, Optimal Control).
Equations of the Hamilton-Jacobi type in hereditary systems: minimax solutions. Tr. IMM UrO Ross. Akad. Nauk, 1999, 6, 1-2, 110-130 = Equations of the Hamilton-Jacobi type in hereditary systems: minimax solutions. Proc. Steklov Inst. Math.: Control in Dynamic System, 2000, Suppl. Issue 1, S136-$153 (coauthor with N. Yu. Lukoyanov).
The work of S. N. Chernikov on Linear inequalities. Inf. Byull. AMP, 2001, 9, 11-26 (coauthor with I. I. Yeremin).
A school problem as an element for the teaching of experimental mathematics. Vestnik Chelyab. Univ. Ser. 3. Mathematika. Mekhanika. Informatika, 2003, 2, 50-132 (coauthor with A. N. Kotel'nikova).

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