Asymptotic solution of zero-sum linear-quadratic differential game with cheap control for minimizer

A two-players zero-sum linear-quadratic differential game with the cheap control for the minimizer (the player which minimizes the cost functional) is considered. An asymptotic solution of the singularly perturbed matrix differential Riccati equation with singular terminal conditions for the "fast" variables, associated with this problem, is constructed. Based on this result, some asymptotic properties of suboptimal feedback strategies of the players are investigated. In particular, an asymptotic equilibrium of the suboptimal strategies is established.