## 1 Introduction
The task of updating the co-state is implemented in several ways and with different information sources. Ref. [18] shows the adaption based on driving cycle prediction implementing an on-the-fly algorithm for the estimate of the equivalent factor according to the driving conditions, combining past and predicted data to periodically refresh the equivalent factor. Ref. [19] uses an adaptive-ECMS in an HEV with continuously variable transmission based on driving pattern recognition. The proposed method considers the type of driving pattern and the battery state of charge (SOC) to adapt the equivalent factor. Ref. [17] presents an online co-state adaptation rule based on the SOC. In a similar way, authors in [20] employ a Markov chain model for vehicle-speed forecasting, and adapt the equivalent factor to the expected driving cycle. The main advantages of the previous approaches are the physical interpretability and their low computational cost; on the other hand, they need substantial calibration effort (specially for the equivalent factor) and sacrifice optimality in order to be applicable in cases where the conditions of the driving cycle are not well defined [21]. Another method developed to tackle the limitations of the driving-cycle information dependency of DP is the model predictive control (MPC). The main advantages of MPC are its ability to deal with system constraints and the capability of leveraging driving cycle estimations in a prediction horizon (e.g., traffic data, preceding vehicles and traffic lights) for optimization [22; 23; 24]. Although previous techniques have been developed, in general, for the passenger-car application, most of them have been adapted to the particular case of urban buses. In this sense, ref. [25] compare different architectures for HEV hybrid buses and employ DP to perform this comparison with optimal energy management for every architecture. In the same line [26] propose the use of DP to calibrate a heuristic energy management strategy for a hybrid bus. Regarding methods that can be applied for control, several variations of the ECMS have been applied to the field of hybrid buses. For example, in [27], authors approach the optimization of emissions by applying ECMS with an engine map that combines fuel consumption and emissions. In [28], authors proposed a ECMS strategy where the equivalence factor is adapted to driving condition of the bus by means of neuro-fuzzy inference techniques. Similarly, in [29], the equivalence factor of the ECMS in a HEV bus is adapted by means of genetic algorithms. A model predictive control based on [PERSON]'s minimum principle is applied in [30] to a hybrid electric bus, with a fuel consumption that exceed the theoretical optimum of 6% according to simulation results. In line with previous papers, this article presents an EMS for a parallel hybrid electric urban bus. The objective of the proposed strategy is to be applicable for control purposes and have a performance close to the theoretical optimum. As in previous literature [7], the criteria to judge the performance of the strategy is the fuel consumption and the deviation between the initial and final energy stored in the battery, which must be minimized to ensure the charge sustainability. To approximate the theoretical optimum, the proposed strategy is based on model-based optimization. On the other hand, to be applicable for control purposes, the proposed strategy must meet two main conditions:  
* The computation time should be low enough to be applied in real time. To this aim, the developed EMS is based on a simplified powertrain model as in the previously cited papers. * The strategy should not rely on future information. The proposed method exploits the periodicity in the route covered to reduce the dependence of the optimal control technique on the information about the future driving conditions.