Vladimir S. Pugachev

Vladimir S. Pugachev


Saturday, March 25, 1911

Passed away: 

Wednesday, March 25, 1998

Vladimir Pugachev, in full Vladimir Semenovich Pugachev, was an outstanding Russian scientist and a remarkable educator, the founder of the statistical theory of controlled systems, and the author of fundamental research in aeronautical ballistics and flight dynamics, control theory, and theory of differential equations. He organized world-known scientific schools in aeronautical ballistics and statistical theory of controlled systems.

Pugachev was born on March 25, 1911, in the city of Ryazan. After graduating from Zhukovsky Air Force Academy, he actively participated in the rapid development of aviation technology in the 1930s. Pugachev compiled ballistic tables for air bombs and developed a new method for calculating air bomb trajectories, for the first time in world science, applying Poincaré’s small parameter method to the problems of ballistics.

In 1935, Pugachev was appointed Head of the Air Firing Department at Zhukovsky Air Force Academy. In a short period, he developed the foundations of a new branch in aviation science (the theory of air firing). The results were presented in the book Osnovy teorii vozdushnoi strel’by (Foundations of the Theory of Air Firing), Moscow, 1937.

In 1935, Pugachev comprehensively assessed the firing efficiency in air combat, for the first time applying the methods of operations research and system analysis to justify the trends of aviation technology development. He became the founder of operations research and system analysis in the USSR, several years ahead of similar studies abroad.

In 1939, Pugachev was conferred Dr. Sci. (Eng.) for his dissertation entitled The General Problem of Rotating Shell Motion in the Air.

While searching for new methods for the problems of ballistics, Pugachev significantly contributed to the analytic theory of differential equations by elaborating the theory of asymptotic expansions of solutions of linear differential equations with a parameter.

For improving the firing and bombing efficiency, it was necessary to study control processes under random disturbances. At that time, no adequate methods for analyzing and solving such problems were available in the world literature. Pugachev made the first successful attempt to elaborate a general theory of systems described by stochastic differential equations. His paper “Random Functions Defined by Ordinary Differential Equations” (1944) laid the foundation for a new science: the statistical theory of control processes (statistical dynamics). It appeared many years before similar foreign publications.

In the post-war period, Pugachev’s R&D activities were connected with the further development of the statistical theory of control processes and its applications in various fields of science and technology. In 1947, he completed research on the general statistical theory of linear systems and approximate methods for analyzing the accuracy of nonlinear systems. The control theory methods developed by Pugachev underlay his subsequent research in controlled flight dynamics (1947–1952). During those years, a scientific consultant, Pugachev worked in a specialized design bureau to develop air weapons control systems and became one of the supervisors of the Moscow Air Defense System. In 1948, he was awarded the USSR State Prize for theoretical research in ballistics.

In 1956, Pugachev was invited to the Institute of Automation and Remote Control, the USSR Academy of Sciences (nowadays, Institute of Control Sciences RAS) to organize a laboratory and research on statistical methods in control theory. Here, he supervised the well-known Moscow Seminar on Statistical Problems in Cybernetics. The seminar became an excellent school that raised many experts in the area.

In the 1950s, Pugachev laid the foundations of the statistical theory of optimal systems. Pugachev’s general methods for determining optimal linear systems based on his theory of canonical expansions of random functions played a special role. In addition, he developed general methods for optimizing dynamic systems by any statistical criteria. Pugachev’s research works in the statistical theory of optimal systems became widespread, making him a true classic of world control science. Pugachev published more than 70 papers on the statistical dynamics of controlled systems. All those fundamental results were summarized in his famous monograph Teoriya sluchainykh funktsii i ee primenenie k zadacham avtomaticheskogo upravleniya (Theory of Random Functions and Its Application to Automatic Control Problems), Moscow: Fizmatlit, 1960. The monograph was republished twice, in 1960 and 1962, and translated into English, French, Polish, and German.

In the early 1960s, Pugachev prepared and read a new course on automatic control theory at Zhukovsky Air Force Academy. In 1963, Pugachev and his students published the monograph Osnovy avtomaticheskogo upravleniya (Foundations of Automatic Control), Moscow: Fizmatlit, 1963. It was the first to systematically describe analysis methods for automatic systems applied at that time, including statistical methods. In 1968 and 1974, the book was republished.

From 1965 to 1970, the main line of Pugachev’s research was the statistical theory of automatic learning systems. In 1976, he was awarded the USSR State Prize for creating an adaptive control system for a complex industrial process (hot rolling of pipes). The system was based on Pugachev’s methods of learning systems.

From the late 1970s to the early 1980s, Pugachev laid the foundations of a new branch in stochastic control: the theory of conditionally optimal filtering and control.

Since 1984 (and till the last days of his life), Pugachev worked at the Institute of Informatics Problems, the USSR (Russian) Academy of Sciences.

The results of many-years research in the theory of probability and stochastic systems were generalized and systematically described in the book Teoriya veroyatnosti i matematicheskaya statistika (Probability Theory and Mathematical Statistics) (1979, 1982, and 1984) and the monograph Stokhasticheskie differentsial’nye sistemy (Stochastic Differential Systems) (1985, 1987, and 1990), coauthored by I.N. Sinitsyn. In 1990, Pugachev was awarded the Lenin Prize for his research on the statistical theory of controlled systems.

Today, Pugachev’s followers and students develop his scientific ideas and create new methods, working in various research organizations, the industry, the Russian Academy of Sciences and the Academies of CIS countries, and universities.

Pugachev’s main books are as follows:

  1. Stochastic Systems: Theory and Applications, World Scientific, 2002. – 928 p. (coauthor I.N. Sinitsyn);
  2. Teoriya stokhasticheskikh sistem (Theory of Stochastic Systems), Moscow: Logos, 2000. – 1000 p. (coauthor I.N. Sinitsyn);
  3. Lectures on Functional Analysis and Applications, World Scientific, 1999. – 752 p. (coauthor I.N. Sinitsyn);
  4. Stochastic Differential Systems: Analysis and Filtering, 1st ed., Wiley, 1987. – 570 p. (coauthor I.N. Sinitsyn);
  5. Stokhasticheskie differentsial’nye sistemy (Stochastic Differential Systems), Moscow: Nauka, 1985. – 560 p. (coauthor I.N. Sinitsyn);
  6. Probability Theory and Mathematical Statistics for Engineers, Pergamon, 1984. – 468 p.;
  7. Teoriya veroyatnostei i matematicheskaya statistika (Probability Theory and Mathematical Statistics), Moscow: Nauka, 1979. – 496 p.;
  8. Osnovy statisticheskoi teorii avtomaticheskikh sistem (Foundations of the Statistical Theory of Automatic Systems), Moscow: Mashinostroenie, 1974. – 400 p.;
  9. Statisticheskie metody v tekhnicheskoi kibernetike (Statistical Methods in Engineering Cybernetics), Moscow: Sovetskoe Radio, 1971. – 192 p.;
  10. Vvedenie v teoriyu veroyatnostei (An Introduction to Probability Theory), Moscow: Nauka, 1968. – 368 p.;
  11. Theory of Random Functions (International Series of Monographs on Automation & Automatic Control), Elsevier, 1965. – 852 p.;
  12. Teoriya sluchainykh funktsii i ee primenenie k zadacham avtomaticheskogo upravleniya (Theory of Random Functions and Its Application to Automatic Control Problems), 2nd. ed., Moscow: GIFML, 1960. – 883 p.;
  13. Osnovy obshchei teorii sluchainykh funktsii (Foundations of the General Theory of Random Functions), Moscow: the Academy of Artillery Sciences, 1952. – 343 p.

The list of 36 journal papers by Pugachev is available at:


His publications can be found at:


Also, see the Wikipedia page devoted to Pugachev:


Scopus Author ID: 7006323384