Some approaches to ergodic and adaptive control of stochastic semilinear systems
type: Item
instance of: scholarly article
zbMATH Open document ID: 0982.93073
author: T. E. Duncan
publication date: 2001-10-30T00:00:00Z
Mathematics Subject Classification ID: 93E35
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 1594444
zbMATH Keywords: stochastic distributed systems
zbMATH Keywords: ergodic control
zbMATH Keywords: adaptive control
zbMATH Keywords: stochastic semilinear system
zbMATH Keywords: semigroup of contractions
MaRDI profile type: Publication
title: Some approaches to ergodic and adaptive control of stochastic semilinear systems
review text: The author considers some ergodic and adaptive control problems for the stochastic semilinear system NEWLINE\[NEWLINEdX(t)= (AX(t)+ f(\alpha, X(t))- u(t)) dt+ Q^{1/2} dW(t),NEWLINE\]NEWLINE where \(X(t)\), \(t\geq 0\), is an \(H\)-valued process, \(H\) is a Hilbert space, \(A\) is an infinitesimal operator of a Hilbert-Schmidt exponentially stable semigroup of contractions, \(W(t)\), \(t\geq 0\), is a standard cylindrical \(H\)-valued Wiener process, \(Q= (Q^{1/2})^* Q^{1/2}\) is an invertible linear operator, \(u\) is a control, and \(f(\alpha,\cdot):H\to H\) is a nonlinear function for each \(\alpha\) from a finite-dimensional compact set.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00050].
reviewed by: Grigori N. Milstein
description: scientific article