2019 Volume 2019 Pages 49-55
In this paper, we study Nash tracking game problems with preview for linear continuous-time systems over finite time intervals. We introduce cross-coupled differential Riccati equations (CDREs) to give solutions of the tracking problems with multi-players. Corresponding to the coupled properties of the CDREs, the forms of preview compensator dynamics are cross-coupled. In this paper, we focus on the derivation of the necessary conditions for the solvability of the tracking problems by variational approach.