IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 23, NO. 3, MAY 2015 1197 Velocity Predictors for Predictive Energy Management in Hybrid Electric Vehicles Chao Sun, Xiaosong Hu, Member, IEEE, Scott J. Moura, Member, IEEE, and Fengchun Sun Abstract— The performance and practicality of predictive energy management in hybrid electric vehicles (HEVs) are highly dependent on the forecast of future vehicular velocities, both in terms of accuracy and computational efficiency. In this brief, we provide a comprehensive comparative analysis of three velocity prediction strategies, applied within a model predictive control framework. The prediction process is performed over each receding horizon, and the predicted velocities are utilized for fuel economy optimization of a power-split HEV. We assume that no telemetry or on-board sensor information is available for the controller, and the actual future driving profile is completely unknown. Basic principles of exponentially varying, stochastic Markov chain, and neural network-based velocity prediction approaches are described. Their sensitivity to tuning parameters is analyzed, and the prediction precision, computational cost, and resultant vehicular fuel economy are compared. Index Terms— Artificial neural network (NN), comparison, energy management, hybrid electric vehicle (HEV), model predictive control (MPC), velocity prediction. I. I NTRODUCTION S OPHISTICATED energy management strategies have been developed to provide better fuel economy perfor- mance in hybrid electric vehicles (HEVs) [1], [2]. This brief intends to facilitate the performance of predictive energy management through evaluating different horizon velocity predicting approaches. In the literature, dynamic programming (DP) and equiva- lent consumption minimization strategy (ECMS) are crucial in resolving the energy management problem for HEVs. Globally, DP can ensure an optimal result when complete knowledge of driving conditions is prescribed [3]. However, the exact future power demand is usually unknown and the computational burden is prohibitive. The DP solutions are often realized offline and deployed as benchmarks [2]. The ECMS is an instantaneous optimization for HEV energy management [4], [5]. By defining an equivalent fuel cost for battery energy, ECMS solves the optimal power split at each time instant rather than over a time horizon. It has Manuscript received May 9, 2014; accepted September 5, 2014. Date of publication October 7, 2014; date of current version April 14, 2015. Manuscript received in final form September 12, 2014. Recommended by Associate Editor F. Vasca. C. Sun was with the National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology, Beijing 100081, China. He is now with the Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720 USA (e-mail: chaosun.email@gmail.com). X. Hu and S. J. Moura are with the Department of Civil and Environmental Engineering, University of California at Berkeley, Berkeley, CA 94720 USA (e-mail: xiaosong@chalmers.se; smoura@berkeley.edu). F. Sun is with the National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology, Beijing 100081, China (e-mail: sunfch@bit.edu.cn). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCST.2014.2359176 demonstrated that given an appropriate equivalence factor, ECMS is comparable with DP [6]. Nevertheless, tuning the equivalence factor is nontrivial. The ECMS variants, such as telemetric-ECMS and adaptive-ECMS, are proposed to adjust the equivalence factor based on information from telemetry equipment or on-board sensors [7], [8]. Due to the uncertainty of future driving profiles, endowing the controller with an appropriate prediction ability can achieve better performance. The forecast ability in the adaptive-ECMS is different from the model predictive control (MPC) approach used in this brief. The MPC has attracted increasing attention in the HEV energy management research community. Given a finite moving horizon, an MPC controller can maintain computa- tional load within a practical range. An MPC controller solves a short-term energy management problem at each time step, via nonlinear programming [9], quadratic programming [10], Pontryagin’s minimum principle [11], or DP [12]. The performance of MPC strongly depends on the power reference provided in each prediction horizon. The precision of future power prediction is instrumental for the overall vehicle fuel economy. Considering that road grade information is static, we focus on the horizon velocity prediction. No telemetry devices or environment detecting sensors are assumed, and the future driving information is completely unknown. We investigated three velocity predicting approaches. In [9], we assumed power demand decreases exponentially over the prediction horizon. The aim of this simple method was to provide an intuitive understanding of how velocity predic- tion affects fuel economy. To systematically investigate this method, a generalized exponentially varying velocity predictor is considered in this brief. Markov-chain models are widely used for vehicular velocity modeling [13], [14]. An MPC controller with a stochastic Markov-chain velocity predictor is usually called stochastic MPC (SMPC) [12], [15]. The 1-stage Markov-chain process has proven to be effective in generating fixed-route driving patterns. However, when comprehensive driving tasks are considered, the accuracy of 1-stage Markov chain may decline. On the other hand, the predicted power demand relies not only on the present vehicle states, but also on the historical values [16]. Typically, the more historical data used, the more accurate the prediction. For SMPC, multistage Markov-chain processes can hence be formulated to enhance the velocity prediction accuracy. Artificial neural networks (NNs) are a successful method for time series forecasting [17]. Applications of NNs to predicting city power load [18], driving handling behaviors [19], and traf- fic flows [20] have verified its strong capability in predicting nonlinear dynamic behaviors. In [21], we also employed NN to predict the road type and traffic congestion to improve the 1063-6536 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.