On a stochastic differential game and its relationship with mixed H2/H∞ control

In this report, we study a stochastic differential game motivated from a control problem in which two types of disturbance are considered: disturbance with respect to which we have to be robust and disturbance which can be modeled as random processes. We show that the solution can be obtained by solving three coupled Riccati equations with mixed boundary conditions; an algorithm is presented. Finally, we show that, in the time-invariant, infinite-horizon case, the controller that we obtain is a mixed-norm H₂/H_∞ controller.