Time-optimal control strategies for a hybrid electric race car

Recently, the Formula 1 propulsion system has evolved from being a conventional combustion engine toward a highly integrated hybrid electric powertrain. Since 2014, the vehicles have been equipped with an electric motor for extra boosting and regenerative braking, and an electrified turbocharger to improve the engine's torque response and to recover waste heat from the exhaust gas. The powertrain is controlled with a dedicated energy management system, which significantly influences the vehicle's acceleration performance as well as its fuel and electric energy consumption. Therefore, the strategy must be carefully optimized. In this paper, we propose a computationally efficient method to evaluate the theoretic, optimal energy management strategy leading to the best possible lap time. Since the driving path cannot be influenced by the energy management strategy, but is rather determined by the driver's steering's input, we separate the optimization of velocity profile and energy management from the problem of finding the optimal driving path. By carefully introducing convex approximations and relaxations, we formulate the problem as a convex optimal control problem that can be solved efficiently using dedicated numerical solvers. The proposed method allows parameter studies to be conducted within a reasonable time frame of a few minutes, while the optimization results serve as a benchmark for any real-time energy management strategy ultimately to be used during a real race.