View Item 

Hamilton-Jacobi Equation for Optimal Control of Nonlinear Stochastic Distributed Parameter Systems Applied to Air Pollution Process

Access Status
Open access
Authors
Do, Khac Duc
Date
2014
Type
Journal Article

Metadata
Show full item record
Citation
Do, K.D. 2014. Hamilton-Jacobi equation for optimal control of nonlinear stochastic distributed parameter systems applied to air pollution process. Applied Mathematical Sciences. 8 (57): pp. 2801-2816.
Source Title
Applied Mathematical Sciences
DOI
ISSN
School
Department of Mechanical Engineering
Remarks

This article is published under the Open Access publishing model and distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/. Please refer to the licence to obtain terms for any further reuse or distribution of this work.

URI
Collection
Abstract

This paper derives Hamilton-Jacobi equation (HJE) in Hilbert space foroptimal control of stochastic distributed parameter systems (SDPSs) governedby partial differential equations (SPDEs) subject to both state-dependent andadditive stochastic disturbances. First, nonlinear SDPSs are transformed tostochastic evolution systems (SESs), which are governed by stochastic ordinarydifferential equations (SODEs) in Hilbert space, using functional analysis.Second, the Hamilton-Jacobi equation (HJE), of which the solution resultsin an optimal control law, is derived. Third, a problem of optimal control oflinear SDPSs, which include the air pollution process, with a quadratic costfunctional is addressed as an application of the HJE. After, the control designis done, the SESs are transformed back to Euclidean space for implementation.