Several components of the Earth's system are at high risk of undergoing rapid, irreversible qualitative changes or "overturning" with increasing climate warming. Therefore, it is necessary to investigate the feasibility of stopping or even reversing the exceeding of tipping thresholds. Here, we study the feedback control of an idealized energy balance model (EBM) for Earth's climate that exhibits a “small ice sheet” instability responsible for the rapid transition to an ice-free climate under increasing greenhouse gas pressure. We develop an optimal control strategy for EBM under different forcing scenarios to reverse sea ice loss while minimizing costs. Control is achievable for this system, but the cost almost quadruples when the system flips. While thermal inertia can delay a rollover, leading to a critical force threshold being exceeded, this freedom comes with a steep increase in the control required when a rollover occurs. Furthermore, we found that the optimal control is localized in the polar region. (Parvathi Kooloth, Jian Lu, Adam Rupe, more at nature.com)