National achievements in control theory: The aerospace perspective

Abstract

It is well known that among the first motivations for modern control theory were dynamic optimization problems in rocket launching and navigation in aerospace. These problems had become especially important in the 1940s and 1950s due to requirement to minimize various costly resources and design parameters, such as flight time, amount (mass) of fuel, weight of the spacecraft, the drag forces and other items. This had to be done under various restrictions on control capacities and other complicating factors, such for example, as incomplete information on the system. Among the precious techniques of applied mathematics there had long been developed an adequate tool for such problems which is the Calculus of Variations. Problems in flight dynamics had become the earliest serious technical object for its application. A large number of new basic ideas for adapting Calculus of Variations to modern control problems and synthesizing them into modern control theory were elaborated in the course of investigations in flight dynamics. This presentation traces some seminal investigations, which were crucial for related theoretical developments in former Soviet Union and present Russia and had also influenced related research beyond national borders. Such investigations had good historical precursors in the earlier mathematical works of P.L. Chebyshev, A.M. Lyapunov, A.A. Markov, the works in mechanics by N.E. Zhukovski and S.A. Chaplygin and the activities in dynamic systems theory of the 1930s (A.A. Andronov, L.S. Pontryagin, et al.). The present paper is confined only to deterministic problems in trajectory analysis, control and optimization within the framework of mathematical theory of controlled processes. The national community of researchers involved in these topics was enormous, including those in the Academy of Sciences, the Universities and the numerous institutions and plants supervised by related industrial ministries. While giving tribute to all those involved, this paper does not claim to give a full review of available publications, concentrating on what the authors believe to be the seminal issues in the field. This publication will therefore inevitably have a subjective flavor. We sincerely apologize to all those whose contributions may have been missed.