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Infinite Horizon Optimal Control Problem for Stochastic Evolution Equations in Hilbert Spaces

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Abstract

The aim of the present paper is to study an infinite horizon optimal control problem in which the controlled state dynamics is governed by a stochastic evolution equation in Hilbert spaces and the cost functional has a quadratic growth. The existence and uniqueness of the optimal control are obtained by the means of an associated infinite horizon backward stochastic differential equations with quadratic growth. As an application, an optimal control of stochastic heat equation is also given.

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Authors and Affiliations

  1. College of Science, Northwest A&F University, Yangling, 712100, Shaanxi, People’s Republic of China

    Jianjun Zhou

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  1. Jianjun Zhou
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Corresponding author

Correspondence to Jianjun Zhou.

Additional information

This work was partially supported by the National Natural Science Foundation of China (Grant No. 11401474), Shaanxi Natural Science Foundation (Grant No. 2014JQ1035) and the Fundamental Research Funds for the Central Universities (Grant No. 2452015087 and Grant No. 2452015443)

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Zhou, J. Infinite Horizon Optimal Control Problem for Stochastic Evolution Equations in Hilbert Spaces. J Dyn Control Syst 22, 531–554 (2016). https://doi.org/10.1007/s10883-015-9307-2

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  • DOI: https://doi.org/10.1007/s10883-015-9307-2

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