Necessary Optimality Conditions for Fast Lithium-ion Battery Charging via Hybrid Simulations

Fast yet health-conscious and safe optimal charging for lithium-ion batteries is essential for resource efficiency, increased battery lifetime, and overall usability. While quick and resource-efficient charging can be formulated as an optimal control problem, it often cannot be solved in real-time on computationally limited, embedded systems. We build upon a mathematical reformulation of the constrained optimal control problem into hybrid simulations, which allows for computationally efficient solutions and provides operation modes beyond existing charging profiles. We analyze under which conditions this mathematical reformulation can lead to the optimality of the resulting charging protocols. Physics-based battery models are analyzed from a systems theory perspective. Using controllability and flatness properties, necessary optimality conditions for the charging protocols are established.