Asymptotic stackelberg optimal control design for an uncertain Euler Lagrange system

Game theory methods have advanced various disciplines from social science, notably economics and biology, and engineering. Game theory establishes an optimal strategy for multiple players in either a cooperative or noncooperative manner where the objective is to reach an equilibrium state among the players. A Stackelberg game strategy involves a leader and a follower that follow a hierarchy relationship where the leader enforces its strategy on the follower. In this paper, a general framework is developed for feedback control of an Euler Lagrange system using an open-loop Stackelberg differential game. A Robust Integral Sign of the Error (RISE) controller is used to cancel uncertain nonlinearities in the system and a Stackelberg optimal controller is used for stabilization in the presence of uncertainty. A Lyapunov analysis is provided to examine the stability of the developed controller.