Solution of Delayed Mixed H2/H∞ Problem with Continuous-time System based on Nash Game Approach

In this paper, the mixed H
2
/H
∞
control problem with delayed continuous time system is considered. By applying the Nash game strategy, the delayed optimal control problem with a continuous time system is studied, and the optimal controller of the problem is obtained. Nash strategy suggests that the controllers’ structure are given in advance and are obtained simultaneously. The main contribution is the establishment of the maximum principle and processing the causality which is caused by delay. The Riccati equations are obtained by forward and backward differential equations(FBDEs).