Set-based state estimation of a Li-ion cell using DC programming and constrained zonotopes

Advanced battery management systems (ABMSs) rely on mathematical models to ensure high battery safety and performance. One of the key tasks of a BMS is state estimation. In the following, we consider a single lithium-ion cell described with a dual polarization equivalent circuit model. To consider a realistic scenario, where the parameters have been identified from experimentally collected data, both parametric and measurement uncertainties are taken into account in the model. In particular, unknown but bounded uncertainties are assumed. In this setup, we address state estimation through a set-based approach using Constrained Zonotopes (CZ). Due to the model nonlinearities, a method able to propagate CZ through nonlinear mappings is demanded. Within this context, mean value and first-order Taylor CZ-based extensions were proposed which, however, might lead to conservative overestimation due to the sensitivity to the wrapping and dependency effects inherited from interval arithmetic. In the following, we suggest the use of DC programming as an alternative. The effectiveness of the proposed scheme is demonstrated in simulation for the considered Li-ion model.