  Robust Optimal Control (ROC) with adjustable uncertainties has proven to be
effective in addressing critical challenges within modern energy networks,
especially the reserve and provision problem. However, prior research on ROC
with adjustable uncertainties has predominantly focused on the scenario of
uncertainties modeled as continuous variables. In this paper, we explore ROC
with binary adjustable uncertainties, where the uncertainties are modeled by
binary decision variables, marking the first investigation of its kind. To
tackle this new challenge, firstly we introduce a metric designed to
quantitatively measure the extent of binary adjustable uncertainties. Then, to
balance computational tractability and adaptability, we restrict control
policies to be affine functions with respect to uncertainties, and propose a
general design framework for ROC with binary adjustable uncertainties. To
address the inherent computational demands of the original ROC problem,
especially in large-scale applications, we employ strong duality (SD) and
big-M-based reformulations to create a scalable and computationally efficient
Mixed-Integer Linear Programming (MILP) formulation. Numerical simulations are
conducted to showcase the performance of our proposed approach, demonstrating
its applicability and effectiveness in handling binary adjustable uncertainties
within the context of modern energy networks.
