Optimal Control of Battery Fast Charging Based-on Pontryagin’s Minimum Principle

This paper derives provably optimal control trajectories for the Li-ion battery fast charging problem. Conventionally, battery charging protocols must satisfy safety constraints while maximizing the state of charge (SoC) level. In the literature, both computational and experimental studies promote a diversity of algorithms, including pulse charging, multi-step constant currents, and more. Although these approaches yield applicable charging algorithms, the literature lacks a rigorous analytical insight into optimal charging trajectories. In this paper, we focus on the Pontryagin's Minimum Principle for solving optimal control problem for battery fast charging. Specifically, we characterize the optimal control solution with respect to the state constraint bound. The optimal input is analytically derived for a reduced-order electrochemical model. The optimal solutions follow a Bang or Bang-Ride trajectory. Numerical simulations validate the analytical solutions.