Ergodic control of semilinear stochastic equations and the Hamilton-Jacobi equation
type: Item
instance of: scholarly article
title: Ergodic control of semilinear stochastic equations and the Hamilton-Jacobi equation
zbMATH Open document ID: 0939.93043
author: B. Goldys
author: B. Maslowski
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-11-12T00:00:00Z
review text: The authors consider an optimal control problem with an ergodic cost functional for a stochastic evolution equation in a Hilbert space driven by a cylindrical Brownian motion. The drift term of the controlled equation is defined as \(AX_t+ F(X_t)- u_t\), where \(A\) is the generator of a strongly continuous semigroup, \(F\) is a Lipschitz-continuous and Gateaux-differentiable dissipative mapping, \(u_t\) is a control having sufficiently small norm, and \(X_t\) is a solution of the equation. The optimal cost is characterized as a unique solution to the corresponding Hamilton-Jacobi equation in a space of polynomially increasing functions, and an optimal control is given in a feedback form. The proof is based on the analysis of an auxiliary discounted cost problem and the limit transition to the ergodic cost problem.
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 1334729
zbMATH Keywords: optimal control
zbMATH Keywords: ergodic cost functional
zbMATH Keywords: Hamilton-Jacobi equation
reviewed by: Henrikas Pragarauskas
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6387
OpenAlex ID: W2011279495
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DOI: 10.1006/JMAA.1999.6387
description: scientific article; zbMATH DE number 1334729