Group differential game approach of H2/H∞ control for large-scale linear stochastic systems

The group differential game approach to the finite horizon H
₂
/H
_∞
control problem is considered for a class of large-scale stochastic linear systems. First, it is shown that the necessary conditions for the existence of a strategy set are established by means of cross-coupled stochastic Riccati differential equations (CSRDEs). Second, in order to compute the strategy set, an efficient numerical method for solving the CSRDEs is discussed. In particular, a reduced-order computational algorithm is derived based on the reduced-order differential equations to avoid full-dimensional calculations. Moreover, an approximate strategy set is proposed, and the performance degradation is indicated. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approximate strategy set.