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Pontryagin’s Minimum Principle

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Hybrid Electric Vehicles

Part of the book series: SpringerBriefs in Electrical and Computer Engineering ((BRIEFSCONTROL))

Abstract

In Chap. 4 we presented the DP as a numerical tool to solve the optimal control problem for hybrid electric vehicles as defined in Sect. 3.4.

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Notes

  1. 1.

    The minimum principle was originally proposed (as maximum principle) by the Russian mathematician Lev Semenovich Pontryagin and his students in 1958 and later described in a textbook [3]. Some regard this theorem as the beginning of modern optimal control theory [4].

  2. 2.

    The reader can refer to [5] for other PMP formulations.

  3. 3.

    This approach is practical and reliable when the problem has a single state and the effect of the co-state on the solution is easily understood; in that case, the shooting method can be implemented with a simple iterative search, such as bisection, which converges in a relatively few steps.

  4. 4.

    As well as for further developments in the next chapters.

References

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  3. L. Pontryagin, V. Boltyanskii, R. Gamkrelidze, E. Mishchenko, The Mathematical Theory of Optimal Processes (Inderscience Publishers, New York, 1962)

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  4. H. Sussmann, J. Willems, 300 years of optimal control: from the brachystochrone to the maximum principle. IEEE Control Syst. Mag. 17(3), 32–44 (1997)

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Author information

Authors and Affiliations

  1. Automotive Engineering Department, Clemson University, Greenville, SC, USA

    Simona Onori

  2. Dana Mechatronics Technology Center, Dana Holding Corporation, Rovereto, Italy

    Lorenzo Serrao

  3. Department of Mechanical and Aerospace Engineering and Center for Automotive Research, The Ohio State University, Columbus, OH, USA

    Giorgio Rizzoni

Authors
  1. Simona Onori
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  2. Lorenzo Serrao
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  3. Giorgio Rizzoni
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Correspondence to Simona Onori .

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Onori, S., Serrao, L., Rizzoni, G. (2016). Pontryagin’s Minimum Principle. In: Hybrid Electric Vehicles. SpringerBriefs in Electrical and Computer Engineering(). Springer, London. https://doi.org/10.1007/978-1-4471-6781-5_5

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  • DOI: https://doi.org/10.1007/978-1-4471-6781-5_5

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-6779-2

  • Online ISBN: 978-1-4471-6781-5

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