  Batteries are nonlinear dynamical systems that can be modeled by Porous
Electrode Theory models. The aim of optimal fast charging is to reduce the
charging time while keeping battery degradation low. Most past studies assume
that model parameters and ambient temperature are a fixed known value and that
all PET model parameters are perfectly known. In real battery operation,
however, the ambient temperature and the model parameters are uncertain. To
ensure that operational constraints are satisfied at all times in the context
of model-based optimal control, uncertainty quantification is required. Here,
we analyze optimal fast charging for modest uncertainty in the ambient
temperature and 23 model parameters. Uncertainty quantification of the battery
model is carried out using non-intrusive polynomial chaos expansion and the
results are verified with Monte Carlo simulations. The method is investigated
for a constant current--constant voltage charging strategy for a battery for
which the strategy is known to be standard for fast charging subject to
operating below maximum current and charging constraints. Our results
demonstrate that uncertainty in ambient temperature results in violations of
constraints on the voltage and temperature. Our results identify a subset of
key parameters that contribute to fast charging among the overall uncertain
parameters. Additionally, it is shown that the constraints represented by
voltage, temperature, and lithium-plating overpotential are violated due to
uncertainties in the ambient temperature and parameters. The C-rate and charge
constraints are then adjusted so that the probability of violating the
degradation acceleration condition is below a pre-specified value. This
approach demonstrates a computationally efficient approach for determining
fast-charging protocols that take probabilistic uncertainties into account.
