A Non-Convex Control Allocation Strategy as Energy-Efficient Torque Distributors for On-Road and Off-Road Vehicles

A M Dizqah, Brandon Ballard, Mike Blundell, Stratis Kanarachos, Mauro Innocente

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
40 Downloads (Pure)


A vehicle with multiple drivetrains, like a hybrid electric one, is an over-actuated system that means there is an infinite number of combinations of torques that individual drivetrains can supply to provide a given total torque demand. Energy efficiency is considered as the secondary objective to determine the optimum solution among these feasible combinations. The resulting optimisation problem, which is nonlinear due to the multimodal operation of electric machines, must be solved quickly to comply with the stability requirements of the vehicle dynamics. A theorem is developed for the first time to formulate and parametrically solve the energy-efficient torque distribution problem of a vehicle with multiple different drivetrains. The parametric solution is deployable on an ordinary electronic control unit (ECU) as a small-size lookup table that makes it significantly fast in operation. The fuel-economy of combustion engines, load transformations due to longitudinal and lateral accelerations, and traction efficiency of the off-road conditions are integrated into the developed theorem. Simulation results illustrate the effectiveness of the provided optimal strategy as torque distributors of on-road and off-road electrified vehicles with multiple different drivetrains.
Original languageEnglish
Article number104256
Number of pages10
JournalControl Engineering Practice
Early online date27 Nov 2019
Publication statusPublished - Feb 2020

Bibliographical note

NOTICE: this is the author’s version of a work that was accepted for publication in , Control Engineering Practice. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Control Engineering Practice, 95 (2020)
DOI: 10.1016/j.conengprac.2019.104256


This research is partially supported by a NATO project under the grant [NATO SPS MYP, G5176].


  • Traction efficiency
  • Control allocation
  • Energy management strategies
  • Hybrid electric vehicles
  • Power loss
  • Multiple drivetrains


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