### Optimization and Systems Theory Seminar

Friday, October 24, 1997, 11.00-12.00, Room 3721, Lindstedtsvägen 25

** Professor Vladimir A. Yakubovich**

St. Petersburg State University

St. Petersburg

Russia

####
Abstract theory of optimal control

This year may be considered as 40-th anniversary of remarkable achievement
of the mathematics of our century - the Pontrjagin maximum principle.
( It was formulated without proofs 41 years ago and the proofs were published
39 years ago. ) Almost all results of classical calculus of
variations follow from this principle and quite a lot of new
optimization control problems were solved by applying this
principle. Pontrjagin and coauthors considered only differential
equations. For those 40 years the new necessary conditions of
optimality were establish for other plant equations and these
conditions had form of the "maximum principle" also.
The talk is related to the main ideas of the "abstract theory of
optimal control" which is designed by author, further developed by A,
A.S.Matveev and is published in the book of the same title ( in
Russian ). This theory explains why the maximum principle is natural
form of the necessary condition of optimality. The theory formulates
the abstract maximum principle which allows to obtain the necessary (
and sufficient under some assumptions) conditions of optimality in the
uniform way and relatively simple. As well it allows to solve many new
problems.

Calendar of seminars

*Last update: October 20, 1997 by
Anders Forsgren,
andersf@math.kth.se.
*