Time-optimal Energy Management of the Formula 1 Power Unit with Active Battery Path Constraints

Modern Formula 1 racing cars are high-performance hybrid-electric vehicles whose battery acts as an energy storage. When the powertrain is operated close to the lower or upper state-of-charge bound of the battery, its finite size limits the electric boosting and recuperation capacity, respectively. Given the detrimental effect on the achievable lap time, such scenarios call for a careful optimization of the energy management strategies. Based on a convex model of the car’s powertrain, we first study the impact of battery path constraints on the optimal control policy analytically, using a non-smooth version of Pontryagin’s minimum principle. We then corroborate the derivations with the numerical solution obtained from a convex optimization framework and discuss the time-optimal energy management strategy when the lower bound on the battery state-of-charge is active. Finally, we leverage the non-causal results to improve an existing online controller in the case of an overtake maneuver. Our simulations yield a lap time gain of about 370 ms over three laps.