1Infinite Horizon Differential Games for Multiparameter Singularly Perturbed Systems

Abstract- In this paper, we study the infinite horizon zero-sum differential games for both standard and nonstandard multiparameter singularly perturbed systems. A composite approximation of the full-order linear feedback saddle-point solution is obtained by decomposing the full-order game prob-lem into a slow game and two fast control problems. It is proven that such a composite approximation forms an O(||µ||) (near) saddle-point equilibrium of the full-order game, and the resulting value is O(||µ||2) over or below the exact value of the full-order game depending on the given game parameters