Robust Stackelberg Differential Game With Model Uncertainty
IEEE Transactions on Automatic Control(2022)
Abstract
This article formalizes two types of modeling uncertainties in a stochastic Stackelberg linear-quadratic (LQ) differential game and then discusses the associated robust Stackelberg strategy design for either the leader or follower. Both uncertainties are primarily motivated by practical applications in engineering and management. The first uncertainty is connected to a disturbance unknown to the follower but known to the leader. A
soft-constraint
min-max control is applied by the follower to determine the optimal response, and then an
augmented
LQ forward-backward stochastic differential equation control is solved by the leader to ensure a robust strategy design. The second uncertainty involves a disturbance, the realization of which can be completely observed by the follower, but only its distribution can be accessed by the leader. Thus, a
hard-constraint
min-max control on an
affine-equality-constraint
is studied by the leader to address the
exact-optimal
robust design. Moreover, based on a weak convergence technique, a minimizing sequence of
near-optimal
robust designs is constructed, which is more tractable in computation. Some numerical results of the abovementioned robust strategies are also presented.
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Key words
Forward-backward stochastic differential equation,hard-constraint,min-max control,near-optimal control,robust Stackelberg strategy,soft-constraint
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