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.

Since 2014, the Fédération Internationale de l'Automobile has prescribed a parallel hybrid powertrain for the Formula 1 race cars. The complex low-level interactions between the thermal and the electrical part represent a non-trivial and challenging system to be controlled online. We present a novel controller architecture composed of a supervisory controller for the energy management, a feedforward cylinder deactivation controller, and a track region-dependent low-level nonlinear model predictive controller to optimize the engine actuators. Except for the nonlinear model predictive controller, the proposed controller subsystems are computationally inexpensive and are real time capable. The framework is tested and validated in a simulation environment for several realistic scenarios disturbed by driver actions or grip conditions on the track. In particular, we analyze how the control architecture deals with an unexpected gearshift trajectory during an acceleration phase. Further, we demonstrate how an increased maximum velocity trajectory impacts the online low-level controller. Our results show a suboptimality over an entire lap with respect to the benchmark solution of 49 ms and 64 ms, respectively, which we deem acceptable. Compared to the same control architecture with full knowledge of the disturbances, the suboptimality amounted to only 2 ms and 17 ms. For all case studies we show that the cylinder deactivation capability decreases the suboptimality by 7 to 8 ms.