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H 2/H ∞ control problems of backward stochastic systems

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Abstract

This paper is concerned with the mixed H 2/H ∞ control problem for a new class of stochastic systems with exogenous disturbance signal. The most distinguishing feature, compared with the existing literatures, is that the systems are described by linear backward stochastic differential equations (BSDEs). The solution to this problem is obtained completely and explicitly by using an approach which is based primarily on the completion-of-squares technique. Two equivalent expressions for the H 2/H ∞ control are presented. Contrary to forward deterministic and stochastic cases, the solution to the backward stochastic H 2/H ∞ control is no longer feedback of the current state; rather, it is feedback of the entire history of the state.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Jinan, Jinan, 250022, China

    Qixia Zhang

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  1. Qixia Zhang
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Correspondence to Qixia Zhang.

Additional information

This research was supported by the Doctoral Foundation of University of Jinan under Grant No. XBS1213.

This paper was recommended for publication by Editor HONG Yiguang.

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Zhang, Q. H 2/H ∞ control problems of backward stochastic systems. J Syst Sci Complex 27, 899–910 (2014). https://doi.org/10.1007/s11424-014-2215-9

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  • DOI: https://doi.org/10.1007/s11424-014-2215-9

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