A Stackelberg Game Approach to Mixed $H_2/H_\infty$ Control
Résumé
The $H_2/H_\infty$ robust control problem is formulated as a Stackelberg differential game where the leader minimizes an $H_2$criterion while the follower deals with the $H_\infty$ constraint. For a closed loop information structure in the game, the necessary conditions to solve such a constrained optimization problem are derived for the finite time horizon case. It is shown that such an approach leads to a singular control and the Stackelberg strategy degenerates due to the omnipotence of the leader. Using conjugate times theory, we prove that the derived necessary conditions are also sufficient.
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