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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| Format: | Journal Article |
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HIKARI Ltd
2014
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| Online Access: | http://hdl.handle.net/20.500.11937/42571 |
| _version_ | 1848756456660140032 |
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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. |
| first_indexed | 2025-11-14T09:12:29Z |
| format | Journal Article |
| id | curtin-20.500.11937-42571 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:12:29Z |
| publishDate | 2014 |
| publisher | HIKARI Ltd |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |