Numerical Solutions for Known Trajectories

  • Bram de Jager
  • Thijs van Keulen
  • John Kessels
Part of the Advances in Industrial Control book series (AIC)


This chapter deals with numerical solutions for the powersplit problem for hybrid vehicles using predefined power and velocity trajectories. Two numerical solution methods are pursued: an indirect method that uses the necessary conditions for optimality obtained with Pontryagin’s Minimum Principle, and a direct method using the Dynamic Programming algorithm which is based on Bellman’s Principle of Optimality. Both methods are illustrated with an example.


Fuel Consumption Optimal Control Problem Dynamic Programming Algorithm Hybrid Vehicle Drive Cycle 
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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Bram de Jager
    • 1
  • Thijs van Keulen
    • 2
  • John Kessels
    • 3
  1. 1.Department of Mechanical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.DAF Trucks N.V.EindhovenThe Netherlands
  3. 3.Department of Electrical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands

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