Anatoly Butkovskii, in full Anatoly Grigor’evich Butkovskii (also transliterated as Butkovskiy or Butkovsky), was an outstanding scientist, pioneer, and founder of a new research and applications-oriented line of cybernetics, known as control of distributed parameter systems. From 1975 to 2011, he was Head of the Laboratory for Control Theory and Principles of Distributed Parameter Systems at Trapeznikov Institute of Control Sciences, the Russian Academy of Sciences.

Butkovskii graduated from the Moscow Institute of Steel and Alloys and the Department of Mechanics and Mathematics of Moscow State University. He received his diploma in mathematics while working in Academician Pontryagin’s group at Steklov Mathematical Institute, the USSR Academy of Sciences.

At the age of 27, Butkovskii was conferred a candidate’s degree in engineering. One year later, he defended his doctoral dissertation and became the youngest Dr. Sci. (Eng.) in the USSR.

He authored or coauthored 350 scientific papers and more than a dozen monographs published in Russia, the USA, the UK, and the Netherlands. Under his supervision, 30 postgraduates became Cand. Sci. (Eng.) and Cand. Sci. (Phys.—Math.); several postgraduates, doctors of sciences. Butkovskii was a member of the editorial boards of the RAS journals Automation and Remote Control and Control Theory and Systems. He was Member of several Academies in Russia and abroad. Also, he was a member of the editorial board of Systems Sciences and the Advisory Board of Advances in Computing Sciences published by Springer.

In 1996, Butkovskii was named among the five most prominent experts in control theory from Russia; see the report History of Control Since 1960 presented at the 13th IFAC World Congress in the USA.

For his pioneering research and achievements in the control theory of distributed parameter systems, Butkovskii was awarded the Andronov Prize by the USSR Academy of Sciences. He summarized the corresponding results in the monograph Teoriya optimal’nogo upravleniya sistemami s raspredelenymi parametrami (Theory of Optimal Control of Distributed Parameter Systems), Moscow: Nauka, 1965. In 1969, the monograph was published in the USA under the title Distributed Control Systems by Elsevier.

Butkovskii’s theoretical and applied research was significant due to its close connection with real production. Butkovskii had many officially registered inventions and patents. For the first time, he strictly formulated control problems for distributed parameter systems, particularly in the case of control actions applied on the boundaries to control distributions inside the domains.

Butkovskii was the first to pose optimal control problems for distributed parameter systems, formulated and proved the maximum principle for control systems described by integral equations (the Butkovskii maximum principle). On this basis, he derived integral equations for the optimal control function. These equations are known as the Butkovskii integral equations.

He introduced the concept of finite control and posed the finite control problem (the Butkovskii problem). This problem is determining exact and constructive descriptions for the set of all admissible trajectories of a controlled plant on a finite horizon. The Butkovskii problem can be considered a realization of the controllability problem formulated in 1960 by Professor R. Kalman.

In the 1970s, Butkovskii proposed to use number theory methods in control, a non-traditional approach at that time. The corresponding results were reflected in his monographs Metody upravleniya raspredelennymi sistemami (Control Methods for Distributed Systems), Moscow: Nauka, 1975, and Strukturnaya teoriya raspredelennykh system (Structural Theory of Distributed Systems), Moscow: Nauka, 1977. The second book was published in English under the title Structural Theory of Distributed Systems, Ellis Horwood Publishers, 1983.

Professor Butkovskii also formulated and considered a new topical problem, the so-called problem of optimal mobile control. Such problems arise in technological processes with mobile sources of energy, force, or other physical quantities. As an approximate tool for solving this problem, he proposed the so-called method of substitution and implementation, which follows from the nonlinear moment problem. Note that this problem was pioneered by Butkovskii as well.

In 1993, Professor Butkovskii proposed the unified geometrical control theory (UGCT), also known as the theory of control structures (TCS). This approach emerged from the need for a more powerful control theory for distributed parameter systems to describe very complex objects and processes (hot and cold plasma, composite materials, electromagnetic fields in lasers, micro-objects at the quantum level, etc.). Hopefully, within the geometrical approach, many disciplines in cybernetics (control science) can be considered from a unified structural point of view.

UGCT—TCS is based on a powerful and modern mathematical apparatus: Bourbaki’s theory of structures, fiber bundle theory, symmetry theory, and other mathematical concepts. Butkovskii established that the concept of control can be identified with the concept of connectivity in a bundle. From a physical point of view, control can be identified with gage fields, which are currently considered in theoretical physics as the main technique to describe interactions in nature (gravitation, electromagnetism, and strong and weak interactions of elementary particles).

Within the UGCT-TCS framework, Butkovskii formulated necessary and, separately, sufficient optimality conditions for multidimensional distributed differential control systems in invariant geometrical terms.

These and other results were presented in his monograph K edinoi geometricheskoi teorii upravleniya (Toward a Unified Geometrical Control Theory), Moscow: Nauka, 2001 (coauthors A.V. Babichev and S. Pohjolainen).

Butkovskii’s main books are as follows:

1. K metodologii i filosofii kibernetiki. Kratkie tezisy (To the Methodology and Philosophy of Cybernetics. Short Abstracts), Moscow: Institute of Control Sciences RAS, 2010. — 80 p.;
2. New Stand Point on Growing Role of Mathematics and Cybernetics in Science and Technology (Theory and Application), Tampere: Tampere University of Technology, 2006. — 173 p.;
3. K edinoi geometricheskoi teorii upravleniya (Toward a Unified Geometrical Control Theory), Moscow: Nauka, 2001. — 352 p. (coauthors A.V. Babichev and S. Pohjolainen);
4. Characteristics of Distributed-Parameter Systems, Handbook of Equations of Mathematical Physics and Distributed-Parameter Systems (Mathematics and Its Applications), Springer, 1993. — 412 p. (coauthor A.V. Pustyl’nikov);
5. Control of Quantum-Mechanical Processes and Systems (Mathematics and Its Applications), Springer, 1990. — 232 p. (coauthor Yu.I. Samoilenko);
6. Phase Portraits of Control Dynamical Systems (Mathematics and Its Applications), Springer, 1990. — 170 p.;
7. Mobile Control of Distributed Parameter Systems (Series in Mechanical Engineering), Chichester: Ellis Horwood, 1987. — 310 p. (coauthor A.V. Pustyl’nikov);
8. Fazovye portrety upravlyaemykh dinamicheskikh sistem (Phase Portraits of Controlled Dynamic Systems), Moscow: Nauka, 1985. — 136 p.;
9. Upravlenie kvantovo-mekhanicheskimi protsessami (Control of Quantum-Mechanical Processes), Moscow: Nauka, 1984. — 256 p. (coauthor Yu.I. Samoilenko);
10. Structural Theory of Distributed Systems, Chichester: Ellis Horwood, 1984. — 315 p.;
11. Green’s Functions and Transfer Functions Handbook (Mathematics and Its Applications), Chichester: Ellis Horwood, 1982. — 238 p.;
12. Teoriya podvizhnogo upravleniya sistemami s raspredelennymi parametrami (Mobile Control Theory for Distributed Parameter Systems), Moscow: Nauka, 1980. — 384 p. (coauthor A.V. Pustyl’nikov);
13. Upravlenie nagrevom metalla (Control of Metal Heating), Moscow: Metallurgiya, 1981. — 272 p. (coauthors S.A. Malyi and Yu.N. Andreev);
14. Kharakteristiki sistem s raspredelennymi parametrami (Characteristics of Distributed Parameter Systems), Moscow: Nauka, 1979. — 224 p.;
15. Strukturnaya teoriya raspredelennykh sistem (Structural Theory of Distributed Systems), Moscow: Nauka, 1977. — 320 p.;
16. Metody upravleniya sistemami s raspredelennymi parametrami (Control Methods for Distributed Parameter Systems), Moscow: Nauka, 1975. — 568 p.;
17. Optimal’noe upravlenie nagrevom metalla (Optimal Control of Metal Heating), Moscow: Metallurgiya, 1972. — 440 p. (coauthors S.A. Malyi and Yu.N. Andreev);
18. Optimal’noe upravlenie elektromekhanicheskimi ustroistvami postoyannogo toka (Optimal Control of Electromechanical DC Devices), Moscow: Energiya, 1972. — 112 p. (coauthor A.Yu. Cherkashin);
19. Metody teorii avtomaticheskogo upravleniya (Methods of Automatic Control Theory), Moscow: Nauka, 1971. — 744 p. (coauthor A.A. Feldbaum);
20. Distributed Control Systems, Elsevier, 1970. — 446 p.;
21. Teoriya optimal’nogo upravleniya sistemami s raspredelennymi parametrami (Optimal Control Theory for Distributed Parameter Systems), Moscow: Nauka, 1965. — 475 p.

Many of them are presented in the Institute’s database:
https://www.ipu.ru/d7ipu/books_library_grid?combine=Бутковский

The list of journal papers by Butkovskii is available at Math-Net.Ru:
https://www.mathnet.ru/php/person.phtml?option_lang=eng&personid=58222

His publications, including inventions, can be also found at:
https://elibrary.ru/author_items.asp?authorid=4309&pubrole=100&show_refs=1&show_option=0

Articles about A.G. Butkovskii

In addition, see the Wikipedia page devoted to Butkovskii:
https://ru.wikipedia.org/wiki/Бутковский,_Анатолий_Григорьевич

Scopus Author ID: 6603905587