BACKWARD STOCHASTIC H-2/H-infinity CONTROL WITH RANDOM JUMPS

作者：Zhang, Qixia^*

来源：Asian Journal of Control, 2014, 16(4): 1238-1244.

DOI：10.1002/asjc.779

• Backward stochastic H-2/H-infinity control
• backward stochastic differential equation (BSDE)
• forward backward stochastic differential equation (FBSDE)
• Riccati equation

This paper is concerned with H-2/H-infinity 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 Brownian motion and random jumps. It is shown that the backward stochastic H-2/H-infinity control under consideration is associated with the L-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 Brownian 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.

• 出版日期2014-7
• 单位济南大学