Battery Energy Storage Systems (BESS) are important for applications related to both microgrids and electric vehicles. If BESS are used as the main energy source, then it is required to include adequate procedures for the estimation of critical variables such as the State of Charge (SoC) and the State of Health (SoH) in the design of Battery Management Systems (BMS). Furthermore, in applications where batteries are exposed to high charge and discharge rates it is also desirable to estimate the State of Maximum Power Available (SoMPA). In this regard, this paper presents a novel approach to the estimation of SoMPA in Lithium-Ion batteries. This method formulates an optimisation problem for the battery power based on a non-linear dynamic model, where the resulting solutions are functions of the SoC. In the battery model, the polarisation resistance is modelled using fuzzy rules that are function of both SoC and the discharge (charge) current. Particle filtering algorithms are used as an online estimation technique, mainly because these algorithms allow approximating the probability density functions of the SoC and SoMPA even in the case of non-Gaussian sources of uncertainty. The proposed method for SoMPA estimation is validated using the experimental data obtained from an experimental setup designed for charging and discharging the Lithium-Ion batteries. (C) 2015 Elsevier Ltd. All rights reserved.