Time-Optimal Low-Level Control and Gearshift Strategies for the Formula 1 Hybrid Electric Powertrain

Today, Formula 1 race cars are equipped with complex hybrid electric powertrains that display significant cross-couplings between the internal combustion engine and the electrical energy recovery system. Given that a large number of these phenomena are strongly engine-speed dependent, not only the energy management but also the gearshift strategy significantly influence the achievable lap time for a given fuel and battery budget. Therefore, in this paper we propose a detailed low-level mathematical model of the Formula 1 powertrain suited for numerical optimization, and solve the time-optimal control problem in a computationally efficient way. First, we describe the powertrain dynamics by means of first principle modeling approaches and neural network techniques, with a strong focus on the low-level actuation of the internal combustion engine and its coupling with the energy recovery system. Next, we relax the integer decision variable related to the gearbox by applying outer convexification and solve the resulting optimization problem. Our results show that the energy consumption budgets not only influence the fuel mass flow and electric boosting operation, but also the gearshift strategy and the low-level engine operation, e.g., the intake manifold pressure evolution, the air-to-fuel ratio or the turbine waste-gate position.