Analytical Solution Methods

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


This chapter focuses on analytical solutions for the powersplit control problem defined in the previous chapter. Two well known solution concepts will be considered: the method of Lagrange multipliers and Pontryagin’s Minimum Principle. Both concepts have in common that they obtain the necessary conditions for an optimal solution by evaluating where the first differential of the augmented objective function becomes equal to zero. Illustrative examples are used to introduce each solution concept. Next, analytical expressions will be derived that solve the optimal powersplit problem under consideration. This chapter ends with a summary for both solution concepts and demonstrates the coherence between their respective optimality conditions.


Lagrange Multiplier Performance Index Drive Cycle Brake Specific Fuel Consumption Optimal Control Input 
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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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