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Exact optimal solution for a class of dual control problems

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  • Suping Cao
  • Fucai Qian
  • Xiaomei Wang

Abstract

This paper considers a discrete-time stochastic optimal control problem for which only measurement equation is partially observed with unknown constant parameters taking value in a finite set of stochastic systems. Because of the fact that the cost-to-go function at each stage contains variance and the non-separability of the variance is so complicated that the dynamic programming cannot be successfully applied, the optimal solution has not been found. In this paper, a new approach to the optimal solution is proposed by embedding the original non-separable problem into a separable auxiliary problem. The theoretical condition on which the optimal solution of the original problem can be attained from a set of solutions of the auxiliary problem is established. In addition, the optimality of the interchanging algorithm is proved and the analytical solution of the optimal control is also obtained. The performance of this controller is illustrated with a simple example.

Suggested Citation

  • Suping Cao & Fucai Qian & Xiaomei Wang, 2016. "Exact optimal solution for a class of dual control problems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(9), pages 2078-2087, July.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:9:p:2078-2087
    DOI: 10.1080/00207721.2014.973469
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    References listed on IDEAS

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    1. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    2. Fucai Qian & Guo Xie & Ding Liu & Wenfang Xie, 2011. "Optimal control of LQG problem with an explicit trade-off between mean and variance," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(12), pages 1957-1964.
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