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Optimal control of electric vehicle by Short-term Costate Estimation method of Pontryagin’s minimum principle

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  • Kim, Sang Rak
  • Cha, Suk Won

Abstract

Pontryagin’s minimum principle (PMP) is a foundational theory to obtain optimal control of dynamic systems by the change of their state and cost function over time. Compared to programming-based optimization methods, it offers the advantage of providing rapid computation and an algebraic comprehension of the optimal solution. However, particularly for large-scale systems, constructing their costate dynamics and ensuring numerical stability is quite a difficult task. This study introduces a novel method called as the Short-term Costate Estimation method based on PMP (SCEMP). It aims to efficiently obtain optimal control for large-scale systems by employing an iterative algorithm cored by the PMP. The objective is to minimize energy consumption while a car is running, achieved by regulating the distribution ratio of traction torque between the front and rear wheels. The key concept of SCEMP lies in obtaining a discrete optimal control through the sequential process of forward integration of the state equation and backward integration of the costate equation within a pre-defined near-future time frame. Costate dynamics is formulated with a cost function evaluated within a surrogate model, which not only offers a simplified representation of the plant dynamics but also serves as a reference model for controlling the plant model. Verification is conducted within a simulation environment. The SCEMP achieved results that approached the global optimum obtained from Dynamic Programming (DP) within a margin of up to 1%, while requiring approximately one-tenth of the computation time needed by DP.

Suggested Citation

  • Kim, Sang Rak & Cha, Suk Won, 2025. "Optimal control of electric vehicle by Short-term Costate Estimation method of Pontryagin’s minimum principle," Applied Energy, Elsevier, vol. 380(C).
    • Handle: RePEc:eee:appene:v:380:y:2025:i:c:s0306261924021196
    DOI: 10.1016/j.apenergy.2024.124736
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    References listed on IDEAS

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    1. Lucas Böttcher & Nino Antulov-Fantulin & Thomas Asikis, 2022. "AI Pontryagin or how artificial neural networks learn to control dynamical systems," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    2. Bruce A. Conway, 2012. "A Survey of Methods Available for the Numerical Optimization of Continuous Dynamic Systems," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 271-306, February.
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