Parametric sensitivity functions for hybrid discrete/continuous systems
type: Item
instance of: scholarly article
title: Parametric sensitivity functions for hybrid discrete/continuous systems
zbMATH Open document ID: 0937.65137
DOI: 10.1016/S0168-9274(98)00125-1
author: Santos Galán
author: William F. Feehery
author: Paul I. Barton
published in: Applied Numerical Mathematics
publication date: 2000-05-17T00:00:00Z
review text: This paper is concerned with the study of the parameter sensitivity functions of some class of dynamical systems described either by ordinary differential equations (ODEs) or differential-algebraic equations (DAEs). The systems under consideration are assumed to be described by a state space \( S = \bigcup_k S_k\), so that the time evolution in each mode \( S_k\) from \(t_0^k\) to \(t_f^k\) is governed by a set of differential--algebraic equations \( f_k(\dot x^k, x^k, y^k, u^k, p^k, t)=0,\) where \(x^k\) and \(y^k\) are the differential and algebraic variables respectively, \(u^k = u^k(p^k,t)\) the controls and \(p^k\) the parameters. These equations are supplemented with some specification of the parameters \(p^k\) and consistent initial conditions. Further the transition conditions between two modes are properly defined. In the first part of the paper the equations which describe the parameter sensitivity are derived and different types of transitions between modes are given. Then in the case of systems described by pure ODEs the authors give some sufficient conditions which imply the continuity of the sensitivity functions \(\partial x^k/\partial p^k\). These results follow from well known properties about the dependence of the solutions of the differential equations on parameters. Next the authors extend these results to constant coefficients linear DAEs with index one. Further results are given for the case that the coefficients are parameter dependent. The paper ends presenting the numerical results obtained for some particular examples. Here the authors combine a numerical integrator with a state event location algorithm to model a complete evolution of the systems and point out some difficulties that may be found in the transitions.
Mathematics Subject Classification ID: 65P10
Mathematics Subject Classification ID: 37J05
Mathematics Subject Classification ID: 37M05
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 65L80
Mathematics Subject Classification ID: 37N35
zbMATH DE Number: 1367758
zbMATH Keywords: sensitivity of control systems
zbMATH Keywords: differential-algebraic equations
zbMATH Keywords: parametric sensitivities
zbMATH Keywords: dynamical systems
zbMATH Keywords: numerical results
reviewed by: Manuel Calvo
MaRDI profile type: Publication
full work available at URL: s0168-9274(98)00125-1
OpenAlex ID: W1979489469
description: scientific article; zbMATH DE number 1367758