Universal controllers for optimal damping of forced oscillations in linear discrete systems
type: Item
instance of: scholarly article
title: Universal controllers for optimal damping of forced oscillations in linear discrete systems
zbMATH Open document ID: 0960.93035
author: A. Lindkvist
author: V. A. Yakubovich
published in: Doklady Mathematics
publication date: 2001-02-13T00:00:00Z
review text: The paper deals with the difference linear system \[ x_{n+1}=Ax_n+Bu_n+Ew_n,\quad y_n=Cx_n, \] where \(x_n\) is the state, \(y_n\) is the output, \(u_n\) is a control, \(w_n\) is the unobserved external action. The aim of the control is to minimize a functional \(F\) which characterizes the level of oscillations in a system with a given real quadratic form. The functional \(F\) depends on the unknowns \(w_n.\) Since their values are not known, the authors state the problem of finding an optimal controller that does not depend on these values. Such a controller is called an optimal universal controller. Three theorems give existence conditions for the universal controller in some classes of controllers. Moreover stochastic external actions are considered.
Mathematics Subject Classification ID: 93C73
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93D15
zbMATH DE Number: 1564297
zbMATH Keywords: oscillation
zbMATH Keywords: external perturbation
zbMATH Keywords: optimization problem
zbMATH Keywords: characteristic polynomial
zbMATH Keywords: stochastic action
zbMATH Keywords: discrete system
zbMATH Keywords: optimal universal controller
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1564297