Time-optimal control policy for a hybrid electric race car

Mauro Salazar, Philipp Elbert, Soren Ebbesen, Carlo Bussi, Christopher Onder

Research output: Contribution to journalArticleAcademicpeer-review

20 Citations (Scopus)


Since 2014, the Formula 1 car has been a hybrid electric vehicle with a turbocharged gasoline engine and electric motor/generator units connected to the axle, for kinetic energy recovery and boosting, and to the shaft of the turbocharger, mainly to recover waste heat from the exhaust gases. This system offers a new degree of freedom, namely, the power split, which is the ratio of power delivered by the electric traction motor in comparison to the overall propulsive power. In the straights, where the driver usually requests 100% acceleration, regulations allow the implementation of a thrust controller, since only by limiting the acceleration power, the maximum allowed fuel consumption of 100 kg gasoline per race can be achieved. The decisions of the corresponding energy management controller strongly influence the achievable lap time, and thus need to be carefully optimized. Furthermore, there exist several operational constraints imposed by the regulations that need to be tracked. This paper proposes a real-time implementable energy management strategy minimizing the lap time, by deriving the optimal control policy analytically. Optimality of the proposed controller is verified by comparing the results obtained with a benchmark simulator against the global optimal solution, while implementability and compatibility with the regulations are demonstrated using a high-fidelity nonlinear simulator.
Original languageEnglish
Article number7851070
Pages (from-to)1921 - 1934
Number of pages14
JournalIEEE Transactions on Control Systems Technology
Issue number6
Publication statusPublished - Nov 2017
Externally publishedYes


  • Energy management
  • Formula 1 (F1)
  • Pontryagin's minimum principle (PMP)
  • hybrid electric powertrain
  • optimal control
  • real-time implementation


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