Optimizing Regenerative Braking: A Variational Calculus Approach

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.