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Backward Stochastic H 2 /H ∞ Control with Random Jumps
Author(s) -
Zhang Qixia
Publication year - 2014
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.779
Subject(s) - stochastic differential equation , mathematics , stochastic control , riccati equation , differential equation , stochastic partial differential equation , mathematical analysis , control theory (sociology) , optimal control , control (management) , mathematical optimization , computer science , artificial intelligence
This paper is concerned with H 2 / H ∞ control of a new class of stochastic systems. The most distinguishing feature, compared with the existing literature, is that the systems are described by backward stochastic differential equations ( BSDEs ) with B rownian motion and random jumps. It is shown that the backward stochastic H 2 / H ∞ control under consideration is associated with theL 2 -gain of the corresponding uncontrolled backward stochastic perturbed system. A necessary and sufficient condition for the existence of a unique solution to the control problem under consideration is derived. The resulting solution is characterized by the solution of an uncontrolled forward backward stochastic differential equation ( FBSDE ) with B rownian motion and random jumps. When the coefficients are all deterministic, the equivalent linear feedback solution involves a pair of Riccati‐type equations and an uncontrolled BSDE . In addition an uncontrolled forward stochastic differential equation ( SDE ) is given.