There is an emerging concern that anthropogenic greenhouse warming may trigger climate tipping elements leading to irreversible climate changes, such as ice-free Arctic in Summer. Amidst such concerns, it is important to investigate the capacity of feedback control to arrest or even reverse the crossing of tipping points. As an example, here we study the control of an idealized diffusive energy balance model (EBM) for the earth’s climate with multiple tipping points associated with sea-ice. The EBM exhibits strong nonlinear behavior due to ice albedo feedback which leads to hysteresis and the existence of two tipping points. One of these tipping points is a 'large icecap' instability, which accelerates ice growth towards the equator under global cooling. The other is a 'small icecap' instability responsible for a rapid transition to an ice-free climate state under global warming.

We develop an optimal albedo-based control strategy for the EBM under different climate forcing scenarios, with the goal of reversing sea ice loss while minimizing costs. The cost of control is estimated in the vicinity of the tipping points. In particular, we find that the cost of control is nearly doubled for an initial state that is past the tipping point as compared to an initial state before the tipping point. Additionally, we demonstrate that the polar regions have the most efficacy for control. Finally, the same optimization approach to find the optimal control is also extended to the case with seasonal cycle.