Constrained optimal control of monotone systems with applications to battery fast-charging

Enabling fast charging for lithium ion batteries is critical to accelerating the green energy transition. As such, there has been significant interest in tailored fast-charging protocols computed from the solutions of constrained optimal control problems. Here, it is shown that as long as certain monotonicity assumptions are satisfied by these control problems then their optimal solutions satisfy bang-and-ride control with the input riding the maximal allowable constraint. It is then shown that several fast-charging problems are monotone in the desired sense, and hence are optimised by bang-and-ride control. This result can be used to characterise the solutions of fast-charging control problems and simplify how they are computed.