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

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.