Controllability of semilinearstochastic delay evolution equations in Hilbert spaces
type: Item
instance of: scholarly article
title: Controllability of semilinearstochastic delay evolution equations in Hilbert spaces
zbMATH Open document ID: 1031.93023
DOI: 10.1155/S0161171202111318
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2002-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/50595
full work available at URL: S0161171202111318.html
review text: Semilinear stochastic control systems with time-variable delays in the state variables are considered. It is assumed that such systems are defined in an infinite-dimensional Hilbert space, that they contain both linear and nonlinear parts and that the admissible controls are unbounded with values in an infinite-dimensional Hilbert space. Using the well-known Banach fixed-point theorem and the semigroup theory of linear operators, a sufficient condition for exact global relative controllability in a given finite-time interval is formulated and proved. In the proof, methods taken from nonlinear functional analysis and the theory of stochastic differential equations are used. Finally, an illustrative example, namely a stochastic Burgers-type equation with one constant time delay, is investigated, and controllability conditions for this equation are stated. It should be pointed out that similar controllability problems have been recently considered in the publication [\textit{K. Balachandran}, \textit{P. Balasubramaniam} and \textit{J. P. Dauer}, Optim. Control Appl. Methods 16, 283-290 (1995; Zbl 0849.93008)].
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C23
Mathematics Subject Classification ID: 34K50
zbMATH DE Number: 1780412
zbMATH Keywords: infinite-dimensional systems
zbMATH Keywords: semilinear stochastic control systems
zbMATH Keywords: delays
zbMATH Keywords: sufficient condition
zbMATH Keywords: global relative controllability
zbMATH Keywords: stochastic Burgers-type equations
author: P. Balasubramaniam
author: J. P. Dauer
reviewed by: Jerzy Klamka
MaRDI profile type: Publication
OpenAlex ID: W2147942349
Recommended article: Controllability of semilinear stochastic delay systems with distributed delays in control
Recommended article: Controllability of semilinear stochastic control system with finite delay
Recommended article: Q4978172
Recommended article: Complete controllability of semi-linear stochastic system with delay
Recommended article: Approximate controllability of retarded semilinear stochastic system with non local conditions
Recommended article: Complete Controllability of a Delayed Semilinear Stochastic Control System
Recommended article: Controllability of nonlinear stochastic systems with multiple time-varying delays in control
Recommended article: Approximate controllability of semilinear stochastic system with multiple delays in control
Recommended article: Stochastic Controllability of Systems with Multiple Delays in Control
Recommended article: Controllability of stochastic systems with distributed delays in control
description: scientific article; zbMATH DE number 1780412