Lev I. Rozonoer

Lev I. Rozonoer


Monday, August 31, 1931

Passed away: 

Tuesday, April 25, 2023

Lev Rozonoer, in full Lev Il’ich Rozonoer, joined the Institute of Automation and Remote Control (IARC), the USSR Academy of Sciences, in 1955, after graduating from Moscow Power Engineering Institute. He had worked at IARC for over 40 years until he left for family reasons for the USA (1996). In 1960, Rozonoer defended his candidate’s dissertation on some aspects of optimal control theory; in 1964, his doctoral dissertation devoted to the theory of systems with compensation of exogenous disturbances. Since 1965, he was Professor of the Department of Theoretical Mechanics at the Moscow Institute of Physics and Technology and also Professor of the Basic Department at IARC.

Rozonoer undoubtedly belongs to those outstanding scientists who have laid the foundations of control theory through their research. Among applied mathematicians, some are famous for their ability to penetrate deeply into the problem core at a substantial level (i.e., to pose the problem); others, for their ability to solve the problem, sometimes overcoming considerable mathematical difficulties. Rozonoer was one of the few with both qualities of equal measure.

Rozonoer became globally recognized for his research on optimal control theory. He gave a simpler and more transparent proof of the maximum principle than in the well-known monograph of L.S. Pontryagin and his students. For some statements, Rozonoer’s proof even has priority over the original counterpart. He also established a series of new fundamental results: sufficient optimality conditions, boundary conditions for some problems, the connection between Pontryagin’s maximum principle and dynamic programming, and a maximum principle for optimal processes in linear discrete systems. Later, Rozonoer showed that the invariance problem of automatic control systems is a variational problem that can be solved using variational methods of optimal systems theory. As a result, he derived necessary and sufficient conditions for invariance in linear systems.

The research of Rozonoer and his students on optimal control of thermodynamic systems is of particular interest. Having treated the classical problem of thermodynamics about the maximum work as a specific problem of optimal control, Rozonoer presented a general statement of the problem of optimal thermodynamic processes and its solution for several application-oriented cases: the problem of a thermodynamic cycle with maximum average power, the problem of a cycle with maximum efficiency (performance) under a given average power, and others.

He significantly contributed to pattern recognition. In 1960—1961, a research group in Aizerman’s Laboratory—Aizerman himself, E.M. Braverman, and L. I. Rozonoer—was formed and began to work intensively. Rozonoer proposed a new idea for constructing recognition training procedures. According to this idea, each point in the space is associated with an “influence function” of this point on all other points: the closer the point is to a given one, the greater its influence will be. Such a function was called a potential function by analogy with the electrostatic potential of interacting electric charges. If such a function is chosen, it is easy to construct some “averaged” influence function over the points presented for training that belong to the same class. Collective theoretical research began on the potential function method as a basis of the general pattern recognition theory. The group’s works on the potential function method have become classic in machine learning and are now included in textbooks on pattern recognition worldwide.

Rozonoer obtained significant results in the theory of algorithms, finite automata, and mathematical logic. Most of them were reflected in the well-known monograph Logika, avtomaty, algoritmy (Logic, Automata, Algorithms), Moscow: Nauka, 1963 (coauthors A.A. Tal’, M.A. Aizerman, L.A. Gusev, L.I. Rozonoer, and I.M. Smirnova). In Rozonoer’s opinion, his most appreciable contribution to this research area was studies on the so-called “paraconsistent logic.” It was an attempt to formalize the human ability to identify the source of contradictions in some theory or its conclusions, to find these contradictions, and eliminate them. In classical logic, it is impossible to formalize operations with contradictory judgments due to the principle “a contradiction implies anything”: a single contradictory judgment completely destroys the whole theory.

In the breadth of scientific interests, Rozonoer was a unique phenomenon, not only at IARC (later, Trapeznikov Institute of Control Sciences). He obtained interesting and nontrivial results in the theory of economic processes with the random interaction of elements, the theory of random logical networks, evolution theory, differential games as well as quantum mechanics and statistical physics.

Rozonoer’s main books are as follows:

  1. Poslednie teksty. Teoriya sistem. Fizika. Chelovek, nauka, sotsium (Recent Writings. Systems Theory. Physics. Man, Science and Socium), Moscow: Fizmatlit, 2018. — 720 p.;
  2. 70 let teorii invariantnosti (70 Years of Invariance Theory), Moscow: LKI, 2008. — 254 p. (coauthors S.N. Vassilyev, Z.M. Lezina, V.Yu. Rutkovskii, V.M. Kuntsevich, A.G, Butkovskii, A.V. Proskurnikov, V.A. Yakubovich, E.M. Solnechnyi, S.F. Konovalov, and M.Sh. Misrikhanov);
  3. Mark Aronovich Aizerman (1913—1992), Moscow: Fizmatlit, 2003. — 318 p. (coauthors F.T. Aleskerov, A.A. Dorofeyuk, I.B. Muchnik, E.S. Pyatnitskii, L.I. Rozonoer, A.L. Chernyavskii, and A.N. Shubin);
  4. Metod potentsialnykh funktsii v teorii obucheniya mashin (The Method of Potential Functions in the Theory of Machine Learning), Moscow: Nauka, 1970. — 384 p. (coauthors M.A. Aizerman, E.M. Braverman, and L.I. Rozonoer);
  5. Logik-Automaten-Algorithmen, Munchen: Oldenbourg, 1967. — 431 p. (coauthors M.A. Aizerman, L.A. Gusev, L.I., Rozonoer, I.M. Smirnova, and A.A. Tal’);
  6. Logika. Avtomaty. Algoritmy (Logic, Automata, Algorithms), Moscow: Fizmatlit, 1963. — 556 p. (coauthors M.A. Aizerman, L.A. Gusev, L.I., Rozonoer, I.M. Smirnova, and A.A. Tal’).

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

The list of journal papers by Rozonoer is available at Math-Net.Ru:

1. L. I. Rozonoer, Certain Hypotheses in Optimal Control Theory and the Relationship of the Maximum Principle with the Dynamic Programming Method, Avtomat. i Telemekh., 2003, 8,  40—43      Autom. Remote Control64:8 (2003), 1237—1240.    
2. L. I. Rozonoer, On Linear-Quadratic Optimization and Linear-Quadratic Differential Games, Avtomat. i Telemekh., 1999, 5,  170—186    Autom. Remote Control60:5 (1999), 744—757.  
3. L. I. Rozonoer, Determination of a State of a Quantum System from Results of Measurements, Probl. Peredachi Inf.35:4 (1999),  84—94      Problems Inform. Transmission35:4 (1999), 359—368.
4. L. I. Rozonoer, On the Dissipation of Energy upon Classical Measurement and on the Relation between Information and Entropy, Probl. Peredachi Inf.34:2 (1998),  62—64    Problems Inform. Transmission34:2 (1998), 147—149.
5. M. E. Braverman, L. I. Rozonoer, Robustness of Linear Dynamical Systems. II, Avtomat. i Telemekh., 1992, 1,  41—52      Autom. Remote Control53:1 (1992), 34—43.
6. M. E. Braverman, L. I. Rozonoer, Robustness of Linear Dynamical Systems. I, Avtomat. i Telemekh., 1991, 11,  17—23      Autom. Remote Control52:11 (1991), 1493—1498.
7. L. I. Rozonoer, Supplement to the Paper: “Proving Contradictions in Formal Theories. I”, Avtomat. i Telemekh., 1985, 4,  172.    
8. L. I. Rozonoer, On Identification of Inconsistencies in Formal Theories. II, Avtomat. i Telemekh., 1983, 7,  97—104      Autom. Remote Control44:7 (1983), 908—914.
9. L. I. Rozonoer, On Identification of Inconsistencies in Formal Theories. I, Avtomat. i Telemekh., 1983, 6,  113—124      Autom. Remote Control44:6 (1983), 781—790.
10. L. I. Rozonoer, A. M. Tsirlin, Optimal Control of Thermodynamic Processes. III, Avtomat. i Telemekh., 1983, 3,  50—64    Autom. Remote Control44:3 (1983), 314—326.
11. L. I. Rozonoer, A. M. Tsirlin, Optimal Control of Thermodynamic Processes. II, Avtomat. i Telemekh., 1983, 2,  88—101      Autom. Remote Control44:2 (1983), 209—220.
12. L. I. Rozonoer, A. M. Tsirlin, Optimal Control of Thermodynamic Processes. I, Avtomat. i Telemekh., 1983, 1,  70—79      Autom. Remote Control44:1 (1983), 55—62.
13. V. N. Orlov, L. I. Rozonoer, The Variational Principle for Equations of Macroscopic Dynamics and Its Application to Chemical Kinetics, Zh. Vychisl. Mat. Mat. Fiz.21:5 (1981),  1192—1205    U.S.S.R. Comput. Math. Math. Phys.21:5 (1981), 120—133.
14. L. I. Rozonoer, Extension Operators in General Theory of Dynamic Systems, Avtomat. i Telemekh., 1979, 6,  49—62      Autom. Remote Control40:6 (1979), 820—830.
15. L. I. Rozonoer, Y. I. Sedykh, On Evolution Mechanisms of Self-Reproducing Systems. III, Avtomat. i Telemekh., 1979, 5,  137—148    Autom. Remote Control40:5 (1979), 741—749.
16. L. I. Rozonoer, Y. I. Sedykh, On Evolution Mechanisms of Self-Reproducing Systems. II, Avtomat. i Telemekh., 1979, 3,  119—130    Autom. Remote Control40:3 (1979), 419—429.
17. L. I. Rozonoer, Ye. I. Sedykh, On Evolution Mechanisms of Self-Reproducing Systems. I, Avtomat. i Telemekh., 1979, 2,  110—119      Autom. Remote Control40:2 (1979), 243—251.
18. L. I. Rozonoer, A Generalized Thermodynamic Approach to Resource Exchange and Allocation. III, Avtomat. i Telemekh., 1973, 8,  82—103    Autom. Remote Control34:8 (1973), 1272—1289.
19. L. I. Rozonoer, A Generalized Thermodynamic Approach to Resource Exchange and Allocation. II, Avtomat. i Telemekh., 1973, 6,  65—79    Autom. Remote Control34:6 (1973), 915—927.
20. L. I. Rozonoer, Resource Exchange and Allocation (A Generalized Thermodynamic Approach. I, Avtomat. i Telemekh., 1973, 5,  115—132.  
21. A. M. Kogan, L. I. Rozonoer, Macroscopic Description of Kinetic Processes, Dokl. Akad. Nauk SSSR158:3 (1964),  566—569.  


The list of his papers in Avtomatika i Telemekhanika can be found at:

For their English versions, see the microfilm collection of Automation and Remote Control (1956—1994):
and the journal page at SpringerLink (2001—2022):

Articles about L.I. Rozonoer

1. The 80th Birthday of L.I. RozonoerAvtomat. i Telemekh., 2012, no. 4, 164—165.

Scopus Author ID: 6701824863