Control of oscillations of a nonlinear system in the sense of a nonnegative functional
type: Item
instance of: scholarly article
title: Control of oscillations of a nonlinear system in the sense of a nonnegative functional
zbMATH Open document ID: 0963.93066
author: A. S. Shiryaev
published in: Doklady Mathematics
publication date: 2001-01-28T00:00:00Z
review text: The problem of determining a regulator to generate given oscillatory models in a closed-loop system is considered. One assumes that the control system is described by a nonlinear differential equation and a nonnegative functional is specified on the phase plane of system states. It is required to determine a regulator for a state under consideration such that any solution to a closed-loop system with initial data from a fixed set tends to the zero set of a preset functional. A family of regulators generated by the method of velocity gradient is taken as a set of feedbacks. For this set of generators, one obtains sufficient conditions which globally (locally) guarantee the achievement of the control goal. In the special case where the functional is positive definite, new conditions for global (local) asymptotic stability of the zero state of equilibrium of the nonlinear system are obtained.
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 49N35
Mathematics Subject Classification ID: 93B52
zbMATH DE Number: 1557666
zbMATH Keywords: oscillatory models
zbMATH Keywords: regulator
zbMATH Keywords: velocity gradient
reviewed by: Bozhidar Cheshankov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1557666