In this paper, the theory of robust min–max control is extended to hierarchical and multiplayer dynamic games for linear quadratic discrete time systems. The proposed game model con- sists of one leader and many followers, while the performance of all players is affected by disturbance. The Stackelberg–Nash-saddle equilibrium point of the game is derived and a necessary and suffi- cient condition for the existence and uniqueness of such a solution is obtained. In the infinite time horizon, it is shown that the solution of the Riccati equation is upper bounded under a condition that is called individual controllability. By assuming such a condition and using a time-varying Lyapunov function the input-to-state stability of the hierarchical dynamic game is achieved, considering the opti- mal feedback strategies of the players and an arbitrary disturbance as the input.
|Titolo:||Discrete-time Robust Hierarchical Linear-Quadratic Dynamic Games|
|Data di pubblicazione:||2018|
|Appare nelle tipologie:||1.1 Articolo in rivista|