Gamkrelidze convexification and Bogolyubov's theorem (Q2192002)

This work is dedicated to studying the so-called ``interconnection'' between an optimal control problem and its convexification in the sense of Gamkrelidze and Bogolyubov, by means of biconjugate functions, as a sort of counterpart to the classical Fenchel-Moreau theorem from convex analysis. As a special case of the main statement, the authors rediscover Bogolyubov's classical similar result concerning variational calculus problems. Some examples illustrate the theoretical achievements.