Optimizing Regenerative Braking: A Variational Calculus Approach

L. Q. English, A. Mareno, Xuan Lin Chen

Research output: Contribution to journalArticlepeer-review


We begin by analyzing, using basic physics considerations, under what conditions it becomes energetically favorable to use aggressive regenerative braking to reach a lower speed over "coasting"where one relies solely on air drag to slow down. We then proceed to reformulate the question as an optimization problem to find the velocity profile that maximizes battery charge. Making a simplifying assumption on battery-charging efficiency, we express the recovered energy as an integral quantity, and we solve the associated Euler-Lagrange equation to find the optimal braking curves that maximize this quantity in the framework of variational calculus. Using Lagrange multipliers, we also explore the effect of adding a fixed-displacement constraint.

Original languageEnglish (US)
Article number8002130
JournalMathematical Problems in Engineering
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Engineering


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