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Unsolved Problems in Mathematical Systems and Control Theory by Vincent D. Blondel, Alexandre Megretski

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Problem 3.8

Determining of various asymptotics of

solutions of nonlinear time-optimal

problems via right ideals in the moment

algebra

G. M. Sklyar

Szczecin University

Wielkopolska str. 15, 70-451 Szczecin, Poland;

Kharkov National University

Svoboda sqr. 4, 61077 Kharkov

Ukraine

sklar@sus.univ.szczecin.pl, sklyar@univer.kharkov.ua

S. Yu. Ignatovich

Kharkov National University

Svoboda sqr. 4, 61077 Kharkov, Ukraine

bob@online.kharkiv.com

1 MOTIVATION AND HISTORY OF THE PROBLEM

The time-optimal control problem is one of the most natural and at the same time difficult problems in the optimal control theory.

For linear systems, the maximum principle allows to indicate a class of optimal controls. However, the explicit form of the solution can be ...

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