# Adaptive MPC Based Real-Time Energy Management Strategy of the Electric Sanitation Vehicles
## 1 Introduction
### Literature Review and Motivation  
Recently, many EMSs have emerged to improve the energy efficiency of electric vehicles [1; 2], which can be generally divided into two categories: rule-based strategies and optimization-based ones. The rule-based strategies are designed based on expert experience and can be simply implemented online [3; 4], however, these deterministic methods fail to adapt to diverse driving conditions [5]. Due to a lack of sufficient optimality and adaptability, attempts to substitute or recalibrate the rule-based strategies with optimization methods were made by some researchers [3; 6]. One of the most widely used optimization EMSs is dynamic programming (DP) [7; 8], of which the result is globally optimal andthus is regarded as a benchmark. Unfortunately, because of requiring full knowledge of the driving cycle and high computation burden along with great data storing demands, DP is hardly implemented in real time in vehicles. Hence, some researchers explored compromised methods such as model predictive control (MPC), which can maintain computational load within a practical range [9; 10]. The essence of the MPC used in an EMS is to acquire sufficiently accurate predicted values related to driving cycles, which are mainly the vehicle velocity or road gradients [11] and information of transportation [11; 12], to guarantee a better energy economy [13]. Consequently, tremendous research has been conducted on the prediction method [14]. Some researchers adopted the exponentially varying approximation assuming the future velocity changes exponentially [11], which aims to intuitively display how the predicted values interact with the result. Practically, this method is too generalized to adapt to the flexible velocity variation. The Markov chain is also widely used to develop stochastic MPC [15; 16], which predicts the future value based on the transition probability matrices. Although proven to be effective in fixed-route driving cycles, the most used 1-stage Markov chain has poor performance when confronting comprehensive driving tasks due to not including historical data. Furthermore, the artificial neural network (ANN) revealed desirable prediction accuracy [10; 13; 17], which verified its strong capability to drive behavior pattern recognition [18], traffic flows [19], road type, and traffic congestion prediction [20]. Nevertheless, if sensitivity to the parameter tuning of ANN is not well ensured, unreliable performance might be obtained. Moreover, the autoregressive integrated moving average (ARIMA) is also taken into consideration to predict the time series [11].  
All the EMSs mentioned above, especially MPC-based EMSs with different prediction methods, proved to be effective to improve the energy economy of various electric vehicles. However, the time series to be modeled and predicted featured high nonlinearity and nonstationarity, which is different from those ordinary predicted time series such as velocity profiles. Thus, the existing MPC-based EMSs may perform poorly. Moreover, to the best of our knowledge, a few existing studies, which either focused on macroscopic clean route planning [21] or the specific parameter matching [22], were related to electric sanitation vehicles.  
Therefore, considering the fixed routes and environments sanitation vehicles work in, the garbage conditions on the road can be predicted. Otherwise, a dual-motor power system makes energy consumption optimization possible because the two motors have power coupled relationships from the aspects of the clean effects on the road surface. To realize an optimal power distribution on the premise that a clean task is guaranteed, the vehicle acceleration and the rotating speed of the working motor need to be optimized. Consequently, an MPC-based EMS is explored in this paper to solve the problem.