  This paper studies a class of dynamic Stackelberg games under open-loop
information structure with constrained linear agent dynamics and quadratic
utility functions. We show two important properties for this class of dynamic
Stackelberg games. First, we prove that under mild conditions, the optimal
control of individual agents at the solution of the Stackelberg game coincides
with the solution to the team problem, where all agents cooperatively achieve
the coordinator's objective. Second, we show that the the agent's control at
each time step is non-increasing with respect to the coordinator's control at
the same step, and non-decreasing with respect the coordinator's control at
other steps. These properties enable us to develop an algorithm that converges
to the globally optimal solution to the dynamic Stackelberg game. The proposed
algorithm is illustrated by two demand response applications: the coordination
of electric vehicle charging and the coordination of thermostatically
controlled loads. Numerical examples are shown to demonstrate the effectiveness
of the proposed approach.
