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

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 tost...

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Main Author: Do, Khac Duc
Format: Journal Article
Published: HIKARI Ltd 2014
Subjects:
Online Access:http://hdl.handle.net/20.500.11937/42571
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author Do, Khac Duc
author_facet Do, Khac Duc
author_sort Do, Khac Duc
building Curtin Institutional Repository
collection Online Access
description 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.
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spelling curtin-20.500.11937-425712017-10-02T02:28:05Z Hamilton-Jacobi Equation for Optimal Control of Nonlinear Stochastic Distributed Parameter Systems Applied to Air Pollution Process Do, Khac Duc Hilbert space Hamilton-Jacobi Equation stochastic distributed - parameter system optimal control stochastic evolution equation air pollution 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. 2014 Journal Article http://hdl.handle.net/20.500.11937/42571 10.12988/ams.2014.4161 HIKARI Ltd fulltext
spellingShingle Hilbert space
Hamilton-Jacobi Equation
stochastic distributed - parameter system
optimal control
stochastic evolution equation
air pollution
Do, Khac Duc
Hamilton-Jacobi Equation for Optimal Control of Nonlinear Stochastic Distributed Parameter Systems Applied to Air Pollution Process
title Hamilton-Jacobi Equation for Optimal Control of Nonlinear Stochastic Distributed Parameter Systems Applied to Air Pollution Process
title_full Hamilton-Jacobi Equation for Optimal Control of Nonlinear Stochastic Distributed Parameter Systems Applied to Air Pollution Process
title_fullStr Hamilton-Jacobi Equation for Optimal Control of Nonlinear Stochastic Distributed Parameter Systems Applied to Air Pollution Process
title_full_unstemmed Hamilton-Jacobi Equation for Optimal Control of Nonlinear Stochastic Distributed Parameter Systems Applied to Air Pollution Process
title_short Hamilton-Jacobi Equation for Optimal Control of Nonlinear Stochastic Distributed Parameter Systems Applied to Air Pollution Process
title_sort hamilton-jacobi equation for optimal control of nonlinear stochastic distributed parameter systems applied to air pollution process
topic Hilbert space
Hamilton-Jacobi Equation
stochastic distributed - parameter system
optimal control
stochastic evolution equation
air pollution
url http://hdl.handle.net/20.500.11937/42571