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Optimal Control Using Pontryagin’s Maximum Principle and Dynamic Programming

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Automotive Model Predictive Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 402))

Abstract

This chapter describes the application of Pontryagin’s Maximum Principle and Dynamic Programming for vehicle drivingwith minimum fuel consumption. The focus is on minimum-fuel accelerations. For the fuel consumption modeling, a six-parameter polynomial approximation is proposed. With the Maximum Principle, this consumption model yields optimal accelerations with a linearly decreasing acceleration as a function of the velocity. This linear acceleration behavior is also observed in real traffic situations by other researchers. Dynamic Programming is implemented with a backward recursion on a specially chosen distance grid. This grid enables the calculation of realistic gear shifting behaviour during vehicle accelerations. Gear shifting dynamics are taken into account.

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Katholieke Universiteit Leuven, Celestijnenlaan 300, B-3001, Heverlee, Belgium

    Bart Saerens & Eric Van den Bulck

  2. Optimization in Engineering Center (ESAT/SCD), Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, B-3001, Heverlee, Belgium

    Moritz Diehl

Authors
  1. Bart Saerens
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  2. Moritz Diehl
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  3. Eric Van den Bulck
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Editor information

Editors and Affiliations

  1. Institute for Design and Control of Mechatronical Systems, Johannes Kepler University Linz, Altenbergerstr. 69, 4040, Linz

    Luigi del Re

  2. Institute for Systems Theory and Automatic Control, University of Stuttgart, Pfaffenwaldring 9, 70550, Stuttgart

    Frank Allgöwer

  3. Facoltà di Ingegneria, Università del Sannio in Benevento, Corso Garibaldi 107, 82100, Benevento

    Luigi Glielmo

  4. Departamento de Máquinas y Motores Térmicos, Universidad Politécnica de Valencia (UPV), Camino de Vera, s/n., 46022, Valencia, (Spain)

    Carlos Guardiola

  5. Ford Research and Adv. Engineering, Ford Motor Company, Technical Leader, Powertrain Control R&A, 2101 Village Road Dearborn, 48124, MI

    Ilya Kolmanovsky

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Saerens, B., Diehl, M., Van den Bulck, E. (2010). Optimal Control Using Pontryagin’s Maximum Principle and Dynamic Programming. In: del Re, L., Allgöwer, F., Glielmo, L., Guardiola, C., Kolmanovsky, I. (eds) Automotive Model Predictive Control. Lecture Notes in Control and Information Sciences, vol 402. Springer, London. https://doi.org/10.1007/978-1-84996-071-7_8

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  • DOI: https://doi.org/10.1007/978-1-84996-071-7_8

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84996-070-0

  • Online ISBN: 978-1-84996-071-7

  • eBook Packages: EngineeringEngineering (R0)

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