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

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2014
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Journal Article

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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.
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Applied Mathematical Sciences
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Department of Mechanical Engineering
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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.

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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.