On differential algebraic equations with discontinuities
type: Item
instance of: scholarly article
title: On differential algebraic equations with discontinuities
zbMATH Open document ID: 0755.34001
DOI: 10.1007/BF00946633
author: U. Pallaske
author: Ludger Brüll
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1992-09-27T00:00:00Z
review text: Many of the differential algebraic equations (DAEs) that arise in control problems take the form \(A(z,u)z'=f_ 1(z,u)\), \(0=f_ 2(z,u)\), \(z(0)=z_ 0\) where \(A\) is singular but has constant rank. This paper examines what the response of the state should be if the control \(u\) has a jump discontinuity at a time \(t_ 0\). This is done by defining a class of regularizations, that is, continuous controls which approach \(u\) in a neighborhood of \(t_ 0\). A ``genuine initial value'' is then defined in terms of a limit involving the regularization. The existence of genuine initial values is shown to be characterized by the equations defining the DAE arising from potentials.
reviewed by: Stephen L. Campbell
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 92E20
zbMATH DE Number: 63821
zbMATH Keywords: differential algebraic equations
zbMATH Keywords: control problems
zbMATH Keywords: jump discontinuity
zbMATH Keywords: regularizations
zbMATH Keywords: genuine initial value
MaRDI profile type: Publication
cites work: Differential Algebraic Equations, Indices, and Integral Algebraic Equations
cites work: ODE Methods for the Solution of Differential/Algebraic Systems
full work available at URL: https://doi.org/10.1007/bf00946633
OpenAlex ID: W1981923159
description: scientific article; zbMATH DE number 63821