The Two-Level Multi-Player Dynamic Game Problems for Descrete-Time Descriptor System

Abstract

The present paper deals with the linear quadratic dynamic game problem for the descriptor systems Ex_k+1=Ax_k+Bu_k+Cv_k+Dw_k, where E is in general singular matrix and the system structure is noncausal. Condition are obtained under which a strategy of a leader controller forces the two other controllers (follower) to use a team-optimal solution while the follower controllers of the second-level are in fact a Nash equilibrium. Two different information structeres of the followers, that is, the open-loop infomation structure and the closed-loop infomation structure, are considered in the paper.