Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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INFINITE HORIZON OPTIMAL CONTROL PROBLEMS OF BACKWARD STOCHASTIC DELAY DIFFERENTIAL EQUATIONS IN HILBERT SPACES

  • Liang, Hong (Institute of Applied Mathematics College of Science Northwest A&F University) ;
  • Zhou, Jianjun (Institute of Applied Mathematics College of Science Northwest A&F University)
  • Received : 2019.02.21
  • Accepted : 2019.05.16
  • Published : 2020.03.31
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Abstract

This paper investigates infinite horizon optimal control problems driven by a class of backward stochastic delay differential equations in Hilbert spaces. We first obtain a prior estimate for the solutions of state equations, by which the existence and uniqueness results are proved. Meanwhile, necessary and sufficient conditions for optimal control problems on an infinite horizon are derived by introducing time-advanced stochastic differential equations as adjoint equations. Finally, the theoretical results are applied to a linear-quadratic control problem.

Keywords

Acknowledgement

Supported by : Natural Science Foundation of Shaanxi Province, Central Universities

This work is partially supported by the Natural Science Foundation of Shaanxi Province (Grant No. 2017JM1016) and the Fundamental Research Funds for the Central Universities (Grant No. 2452019075).

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