Optimization and Systems Theory Seminar
Thursday, October 11, 2001, 13.15-14.15, Room 3721, Lindstedtsvägen 25


Professor Vladimir A. Yakubovich
St. Petersburg State University
St. Petersburg
Russia

Design of stabilizing controllers with system output independent of external disturbance

The problem of the design of a universal controller that makes the output of a control system invariant under any external disturbance has a long history. Before the Second World War a discussion about the possibility of developing such controllers took place among Russian specialists in control theory. The special commission of the Russian Academy of Sciences considered the arguments of the disputing sides. After the Second World War regular conferences on this subject were held in Russia.

In this talk a variant of this problem is considered. The simple formulas are obtained describing the set of all stabilizing controllers for the minimum-phase object. It is shown that the absolute invariance is possible under some conditions if the external disturbance is measured and if it is one of the inputs of the controller. It is also proved that the absolute invariance is impossible if the external disturbance is not measured. ( An example of the first case is the problem of automatic car steering.) It is shown that in the second case the approximate solution of the invariance problem is possible (with any precision) if the external disturbances belong to some sufficiently general classes. As an example of the second case the approach problem is considered (one moving object must approach the other).

Calendar of seminars
Last update: October 2, 2001 by Anders Forsgren, anders.forsgren@math.kth.se.