On robust one-leader multi-followers linear quadratic dynamic games

In this paper, the theory of robust min-max control is extended to hierarchical and multi-player dynamic games for linear quadratic discrete time systems. The proposed game model consists of a leader and many followers, while the performance of all players is affected by disturbance. The followers play a Nash game with each other and each of them also plays a zero-sum game with the disturbance. In the higher level of the game, the leader plays a Stackelberg game with the followers and at the same time, plays a zero-sum game with disturbance. The Stackelberg-Nash-saddle point equilibrium of the game is derived using dynamic programming approach and some conditions for existence and uniqueness of the solution are given. Finally an illustrative example is given in the simulation results.