Main topic of research:
-- theory of optimal control. Yu. Petrov published 12
monographes, xxx textbooks and xxx journal articles.
Currently, Yu. Petrov works in the field of guaranteed
control and the recently discovered intriguing third class of
problems of applied mathematics -- the class which is intermediary
between the previously known classes, class of correct and incorrect
problems. Several papers were publish on this topic, and they
are accessible on-line. The principle
importance of this discovery is that traditional
mathematical transformations used during investigation of stability
of mathematical models of various technical devices which are
routinely used in all projecting companies in Russia and abroad can
be the reason of errors which may lead to serious catastrophes. There
are grounds to believe that some of recent famous catastrophes had
just that reason. Yu. Petrov is intensively working on methods of
verification of stability of mathematical models which fall in this
class of problems. You can learn more
details about this topic
here.
