Schwartz' distributions in nonlinear setting: Applications to differential equations, filtering and optimal control
type: Item
instance of: scholarly article
title: Schwartz' distributions in nonlinear setting: Applications to differential equations, filtering and optimal control
zbMATH Open document ID: 1066.93023
DOI: 10.1080/10241230306723
author: Yanyan Li
published in: Mathematical Problems in Engineering
publication date: 2004-11-16T00:00:00Z
review text: This paper is intended to be of tutorial value for Schwartz distributions theory in a nonlinear setting. Mathematical models are presented for nonlinear systems which admit both standard and impulsive inputs. These models are governed by differential equations in distributions whose meaning is generalized to involve nonlinear, non-single-valued objects operating over distributions. The set of generalized solutions to these differential equations is defined via closure, in a certain topology, of the set of the conventional solutions corresponding to standard integrable inputs. The theory is exemplified by mechanical systems with impulsive phenomena, optimal impulsive feedback synthesis, sampled-data filtering of stochastic and deterministic dynamic systems.
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 46F10
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 93C57
Mathematics Subject Classification ID: 49N20
zbMATH DE Number: 2115995
zbMATH Keywords: nonlinear dynamics
zbMATH Keywords: distribution
zbMATH Keywords: instantaneous impulse response
zbMATH Keywords: generalized solution
zbMATH Keywords: generalized feedback
zbMATH Keywords: Schwartz distributions
zbMATH Keywords: sampled-data filtering
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1080/10241230306723
OpenAlex ID: W2076479927
description: scientific article; zbMATH DE number 2115995