Current Status and Prospects for Model Predictive Energy Management in Hybrid Electric Vehicles

doi:10.3901/JME.2019.10.086

Abstract

Abstract: Energy management strategies are a core technology in hybrid electric vehicles and plug-in hybrid electric vehicles (HEVs/PHEVs), which directly determines fuel economy, power performance, and drivability. However, the uncertainty, and perturbation of realistic driving conditions greatly increase the difficulty of devising an effective energy management algorithm. It is therefore critical to develop efficient, adaptive, and resilient energy management algorithms. The model predictive energy management can reduce the impact of future operating disturbances on the optimization performance, improving the adaptability of driving conditions and vehicle economy due to the advantages of optimization over receding horizon and feedback compensation. It systematically surveys the state of the art in energy management strategies based on model predictive control (MPC). Their principles, advantages, and applicability are comprehensively analyzed. The advantages and disadvantages of different control methods are compared and summarized. A case study is conducted to illustrate features of MPC-based energy management for HEVs. Finally, future research trends are presented from different perspectives, in order to shed some light on the development of advanced supervisory energy management controllers in HEVs/PHEVs.

Key words: driving cycle prediction, energy management strategies, hybrid electric vehicles, internet of vehicles, model predictive control

CLC Number:

TH156

ZHANG Fengqi, HU Xiaosong, XU Kanghui, TANG Xiaolin, CUI Yahui. Current Status and Prospects for Model Predictive Energy Management in Hybrid Electric Vehicles[J]. Journal of Mechanical Engineering, 2019, 55(10): 86-108.

References

[1] 于秀敏,曹珊,李君,等. 混合动力汽车控制策略的研究现状及其发展趋势[J]. 机械工程学报,2006,42(11):10-16. YU Xiumin,CAO Shan,LI Jun,et al. Present study situation and developing trend of control strategies for hybrid electric vehicle[J]. Chinese Journal of Mechanical Engineering,2006,42(11):10-16.
[2] 陈清泉,孙逢春,祝嘉光. 现代电动汽车技术[M]. 北京:北京理工大学出版社,2002. CHEN Qingquan,SUN Fengchun,ZHU Jiaguang. Modern electric vehicle technology[M]. Beijing:Beijing Institute of Technology Press,2002.
[3] 王钦普,游思雄,李亮,等. 插电式混合动力汽车能量管理策略研究综述[J]. 机械工程学报,2017,53(16):1-19. WANG Qinpu,YOU Sixiong,LI Liang,et al. Survey on energy management strategy for plug-in hybrid electric vehicles[J]. Journal of Mechanical Engineering,2017,53(16):1-19.
[4] 苏岭,曾育平,秦大同. 插电式混合动力汽车能量管理策略研究现状和发展趋势[J]. 重庆大学学报,2017,40(2):10-15. SU Ling,ZENG Yuping,QIN Datong. Current situation and development trend of plug-in hybrid electric vehicle's energy management strategies[J]. Journal of Chongqing University,2017,40(2):10-15.
[5] PANDAY A,BANSAL H O. A review of optimal energy management strategies for hybrid electric vehicle[J]. International Journal of Vehicular Technology,2014,2014:1-19.
[6] HUANG Yanjun,WANG Hong,KHAJEPOUR A,et al. Model predictive control power management strategies for HEVs:A review[J]. Journal of Power Sources,2017,341:91-106.
[7] BANVAIT H,ANWAR S,CHEN Y. A rule-based energy management strategy for plug-in hybrid electric vehicle (PHEV)[C]//IEEE on American Control Conference. IEEE Press,2009:3938-3943.
[8] 周能辉,赵春明,辛明华,等. 插电式混合动力轿车整车控制策略的研究[J]. 汽车工程,2013,35(2):99-104. ZHOU Nenghui,ZHAO Chunming,XIN Minghua,et al. A research on the vehicle control strategy of a plug-in hybrid electric car[J]. Automotive Engineering,2013,35(2):99-104.
[9] 刘永刚,卢立来,解庆波,等. 基于道路坡度信息的插电式混合动力汽车能量管理策略[J]. 北京科技大学学报,2016,38(7):1025-1031. LIU Yonggang,LU Lilai,XIE Qingbo,et al. Energy management for plug-in hybrid electric vehicles based on road gradient[J]. Journal of University of Science and Technology Beijing,2016,38(7):1025-1031.
[10] 李卫民. 混合动力汽车控制系统与能量管理策略研究[D]. 上海:上海交通大学,2008. LI Weimin. Research of control system and energy management of hybrid electric vehicle[D]. Shanghai Shanghai:Jiao Tong University,2008.
[11] 庄伟超,丁洋,邱立琦,等. 插电式混合动力汽车控制策略的研究现状及发展趋势[J]. 机械设计与制造工程,2016,45(6):11-17. ZHUANG Weichao,DING Yang,QIU Liqi,et al. The research status and development trends of energy management strategy for plug-in hybrid electric vehicles[J]. Machine Design & Manufacturing Engineering,2016,45(6):11-17.
[12] LANGARI R,WON J S. Integrated drive cycle analysis for fuzzy logic based energy management in hybrid vehicles[C]//The 12th IEEE International Conference on Fuzzy Systems,2003. FUZZ'03. IEEE,2003,1:290-295.
[13] LI S G,SHARKH S M,WALSH F C,et al. Energy and battery management of a plug-In series hybrid electric vehicle using fuzzy logic[J]. IEEE Transactions on Vehicular Technology,2011,60(8):3571-3585.
[14] WON J S,LANGARI R. Fuzzy torque distribution control for a parallel hybrid vehicle[J]. Expert Systems,2010,19(1):4-10.
[15] LEE H D,SUL S K. Fuzzy-logic-based torque control strategy for parallel-type hybrid electric vehicle[J]. IEEE Transactions on Industrial Electronics,1998,45(4):625-632.
[16] PAGANELLI G,DELPRAT S,GUERRA T M,et al. Equivalent consumption minimization strategy for parallel hybrid powertrains[C]//IEEE 55th Vehicular Technology Conference. VTC Spring 2002(Cat. No. 02CH37367). IEEE,2002:2076-2081.
[17] TULPULE P,MARANO V,RIZZONI G. Effect of traffic,road and weather information on PHEV energy management[R]. SAE Technical Papers,2011-24-0162.
[18] VAJEDI M,TAGHAVIPOUR A,AZAD N L. Traction-motor power ratio and speed trajectory optimization for power split PHEVs using route information[C]//ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers,2012:301-308.
[19] VAJEDI M,TAGHAVIPOUR A,AZAD N L,et al. A comparative analysis of route-based power management strategies for real-time application in plug-in hybrid electric vehicles[C]//2014 American Control Conference. IEEE,2014:2612-2617.
[20] HE Yiming,CHOWDHURY M,PISU P,et al. An energy optimization strategy for power-split drivetrain plug-in hybrid electric vehicles[J]. Transportation Research Part C,2012,22(5):29-41.
[21] ZHANG Fengqi,LIU Haiou,HU Yuhui,et al. A supervisory control algorithm of hybrid electric vehicle based on adaptive equivalent consumption minimization strategy with fuzzy PI[J]. Energies,2016,9(11):26.
[22] KIM N,CHA S,PENG H. Optimal control of hybrid electric vehicles based on Pontryagin's minimum principle[J]. IEEE Transactions on Control Systems Technology,2011,19(5):1279-1287.
[23] CHEN Zheng,MI C C,XIA Bing,et al. Energy management of power-split plug-in hybrid electric vehicles based on simulated annealing and Pontryagin's minimum principle[J]. Journal of Power Sources,2014,272:160-168.
[24] TRIBIOLI L,BARBIERI M,CAPATA R,et al. A real time energy management strategy for plug-in hybrid electric vehicles based on optimal control theory[J]. Energy Procedia,2014,45:949-958.
[25] LI Liang,YANG Chao,ZHANG Yahui,et al. Correctional DP-based energy management strategy of plug-in hybrid electric bus for city-bus route[J]. IEEE Transactions on Vehicular Technology,2015,64(7):2792-2803.
[26] 张松,吴光强,郑松林. 插电式混合动力汽车能量管理策略多目标优化[J]. 同济大学学报,2011,39(7):99-103. ZHANG Song,WU Guangqiang,ZHENG Songlin. Multi-objective optimization of energy management strategy of plug-in hybrid electric vehicle[J]. Journal of Tongji University,2011,39(7):99-103.
[27] 杜常清,甘雯雯,张佩. 基于动态规划不同优化目标的HEV转矩分配策略对比研究[J]. 计算机应用研究,2017,34(5):1308-1310. DU Changqing,GAN Wenwen,ZHANG Pei. Comparison of torque distribution strategies with different optimization objective function for HEV based on dynamic programming[J]. Application Research of Computers,2017,34(5):1308-1310.
[28] YU Haifang,LIU Long,BAI Boxu,et al. A dynamic programming-based control strategy with optimum efficiency of hybrid energy storage system for HEV[J]. Advanced Materials Research,2015,1092-1093:165-168.
[29] 王慧璇. 基于动态规划的Plug-in混合动力汽车能量管理策略优化研究[D]. 济南:山东大学,2012. WANG Huixuan. Optimal energy management strategy of Plug-in hybrid electric vehicles based on dynamic programming[D]. Jinan:Shandong University,2012.
[30] MARTINEZ C M,HU Xiaosong,CAO Dongpu,et al. Energy management in plug-in hybrid electric vehicles:recent progress and a connected vehicles perspective[J]. IEEE Transactions on Vehicular Technology,2017,66(6):4534-4549.
[31] MURGOVSKI N,JOHANNESSON L,SJÖBERG J,et al. Component sizing of a plug-in hybrid electric powertrain via convex optimization[J]. Mechatronics,2012,22(1):106-120.
[32] NAFISI H,AGAH S M M,ABYANEH H A,et al. Two-stage optimization method for energy loss minimization in microgrid based on smart power management scheme of PHEVs[J]. IEEE Transactions on Smart Grid,2016,7(3):1268-1276.
[33] BOYD S,VANDENBERGHE L,FAYBUSOVICH L. Convex optimization[J]. IEEE Transactions on Automatic Control,2006,51(11):1859.
[34] ORSZAG S A. Comparison of pseudospectral and spectral approximation[J]. Studies in Applied Mathematics,1972,51(3):253-259.
[35] ZHOU Wei,ZHANG Chengning,LI Junqiu,et al. A pseudospectral strategy for optimal power management in series hybrid electric powertrains[J]. IEEE Transactions on Vehicular Technology,2016,65(6):4813-4825.
[36] HU Xiaosong,LI Shengbo,PENG Huei,et al. Charging time and loss optimization for LiNMC and LiFePO₄,batteries based on equivalent circuit models[J]. Journal of Power Sources,2013,239(10):449-457.
[37] QIN S J,BADGWELL T A. A survey of industrial model predictive control technology[J]. Control Engineering Practice,2003,11(7):733-764.
[38] 陈虹. 模型预测控制[M]. 北京:科学出版社,2013. CHEN Hong. Model predictive control[M]. Beijing:Science Press,2013.
[39] 崔高健,钟博浩. 基于模型预测控制的混合动力汽车能量管理策略研究综述[J]. 时代汽车,2016,12(8):33-34. CUI Gaijian,ZHONG Bohao. Review of model predictive control based energy management strategy for hybrid electric vehicles[J]. Auto Time,2016(8):33-34.
[40] MORARI M,BARIC M. Recent developments in the control of constrained hybrid systems[J]. Computers & Chemical Engineering,2006,30(10):1619-1631.
[41] 张洁丽. 基于模型预测控制的插电式混合动力客车能量管理策略研究[D]. 北京:北京理工大学,2016. ZHANG Jieli. Energy Management strategy for a plug-in hybrid electric bus based on model predictive control[D]. Beijing:Beijing Institute of Technology,2016.
[42] 邹涛,丁宝苍,张端. 模型预测控制工程应用导论[M]. 北京:化学工业出版社,2010. ZHOU Tao,DING Baocang,ZHANG Rui. Introduction to engineering application of model predictive control[M]. Beijing:Chemical Industry Press,2010.
[43] 孔宪光,殷磊. 自动控制原理与技术研究[M]. 北京:中国水利水电出版社,2014. KONG Xianguang,YIN Lei. Automatic control principle and technology research[M]. Beijing:China Water & Power Press,2014.
[44] SUN Chao,HU Xiaosong,MOURA S J,et al. Velocity predictors for predictive energy management in hybrid electric vehicles[J]. IEEE Transactions on Control Systems Technology,2015,23(3):1197-1204.
[45] 曾祥瑞,黄开胜,孟凡博. 具有实时运算潜力的并联混合动力汽车模型预测控制[J]. 汽车安全与节能学报,2012,3(2):165-172. ZENG Xiangrui,HUANG Kaisheng,MENG Fanbo. Model predictive control for parallel hybrid electric vehicles with potential real-time capability[J]. Journal of Automotive Safety & Energy,2012,3(2):165-172.
[46] ZHANG Shuo,XIONG Rui,SUN Fengchun. Model predictive control for power management in a plug-in hybrid electric vehicle with a hybrid energy storage system[J]. Applied Energy,2015,185:1654-1662.
[47] 张延安. 试论马尔可夫模型及应用[J]. 沈阳大学学报,2001,13(2):44-46. ZHANG Yanan. On the model and application of Markov[J]. Journal of Shenyang University,2001,13(2):44-46.
[48] 周勇有. 基于马尔可夫预测的混合动力汽车控制策略[D]. 长春:吉林大学,2009. ZHOU Yongyou. Hybrid electric vehicle control strategy based on the Markov prediction[D]. Changchun:Jilin University,2009.
[49] 张昕,王松涛,张欣,等. 基于马尔可夫链的混合动力汽车行驶工况预测研究[J]. 汽车工程,2014,36(10):1216-1220. ZHANG Xin,WANG Songtao,ZHANG Xin,et al. A research on driving condition prediction for HEVs based on Markov chain[J]. Automotive Engineering,2014,36(10):1216-1220.
[50] SONG Xiaolin,CAO Haotian,HUANG Jiang. Influencing factors research on vehicle path planning based on elastic bands for collision avoidance[J]. SAE International Journal of Passenger Cars-Electronic and Electrical Systems,2012,5(2):625-637.
[51] 孟凡博,黄开胜,曾祥瑞,等. 基于马尔可夫链的混合动力汽车模型预测控制[J]. 中国机械工程,2014,25(19):2692-2697. MENG Fanbo,HUANG Kaisheng,ZENG Xiangrui,et al. Model predictive control for hybrid electric vehicle based on Markov chain approach[J]. China Mechanical Engineering,2014,25(19):2692-2697.
[52] ZENG Xiangrui,WANG Junming. A parallel hybrid electric vehicle energy management strategy using stochastic model predictive control with road grade preview[J]. IEEE Transactions on Control Systems Technology,2015,23(6):2416-2423.
[53] CAIRANO S D,BERNARDINI D,BEMPORAD A,et al. Stochastic MPC with learning for driver-predictive vehicle control and its application to HEV energy management[J]. IEEE Transactions on Control Systems Technology,2014,22(3):1018-1031.
[54] LIU Teng,ZOU Yuan,LIU Dexing. Energy management for battery electric vehicle with automated mechanical transmission[J]. International Journal of Vehicle Design,2016,70(1):98-112.
[55] XIE Shanshan,HE Hongwen,PENG Jiankun. An energy management strategy based on stochastic model predictive control for plug-in hybrid electric buses[J]. Applied Energy,2017,196:279-288.
[56] JOSEVSKI M,ABEL D. Energy management of parallel hybrid electric vehicles based on stochastic model predictive control[J]. IFAC Proceedings Volumes,2014,47(3):2132-2137.
[57] 钱立军,荆红娟,邱利宏. 基于随机模型预测控制的四驱混合动力汽车能量管理[J]. 中国机械工程,2018,29(11):1342-1348. QIAN Lijun,JING Hongjuan,QIU Lihong. Energy management of a 4WD HEV based on SMPC[J]. China Mechanical Engineering,2018,29(11):1342-1348.
[58] 赵韩,吴迪. 基于随机模型预测控制的并联式混合动力汽车控制策略研究[J]. 汽车工程,2014,36(11):1289-1294. ZHAO Han,WU Di. A research on the control strategy of a parallel HEV based on stochastic model predictive control[J]. Automotive Engineering,2014,36(11):1289-1294.
[59] XIE Shaobo,HU Xiaosong,XIN Zongke,et al. Time-efficient stochastic model predictive energy management for a plug-in hybrid electric bus with an adaptive reference state-of-charge advisory[J]. IEEE Transactions on Vehicular Technology,2018,67(7):5671-5682.
[60] LI Liang,YOU Sixiong,YANG Chao,et al. Driving-behavior-aware stochastic model predictive control for plug-in hybrid electric buses[J]. Applied Energy,2016,162:868-879.
[61] XIANG Changle,DING Feng,WANG Weida,et al. MPC-based energy management with adaptive Markov-chain prediction for a dual-mode hybrid electric vehicle[J]. Science China Technological Sciences,2017,60(5):737-748.
[62] ZAMARREñO J M,VEGA P. Neural predictive control. Application to a highly non-linear system[J]. Engineering Applications of Artificial Intelligence,1999,12(2):149-158.
[63] 厉建远,高建平. 人工神经网络在运行车速预测中的应用[J]. 重庆交通大学学报,2006,25(4):102-105. LI Jianyuan,GAO Jianping. The application of artificial neural network in operating speed forecast[J]. Journal of Chongqing Jiaotong University,2006,25(4):102-105.
[64] SUN Chao,MOURA S J,HU Xiaosong,et al. Dynamic traffic feedback data enabled energy management in plug-in hybrid electric vehicles[J]. IEEE Transactions on Control Systems Technology,2015,23(3):1075-1086.
[65] 孙超. 混合动力汽车预测能量管理研究[D]. 北京:北京理工大学,2016. SUAN Chao. Predictive energy management of hybrid electric vehicle powertrains[D]. Beijing:Beijing Institute of Technology,2016.
[66] SUN Chao,HU Xiaosong,MOURA S J,et al. Comparison of velocity forecasting strategies for predictive control in HEVs[C]//ASME 2014 Dynamic Systems and Control Conference. American Society of Mechanical Engineers,2014:V002T20A003-V002T20A003.
[67] XIANG Changle,DING Feng,WANG Weida,et al. Energy management of a dual-mode power-split hybrid electric vehicle based on velocity prediction and nonlinear model predictive control[J]. Applied Energy,2017,189:640-653.
[68] CHEN Zheng,GUO Ningyuan,SHEN Jiangwei,et al. A hierarchical energy management strategy for power-split plug-in hybrid electric vehicles considering velocity prediction[J]. IEEE Access,2018(6):33261-33274.
[69] 连静,刘爽,李琳辉,等. 插电式混合动力汽车车速预测及整车控制策略[J]. 控制理论与应用,2017,34(5):564-574. LIAN Jing,LIU Shuang,LI Linhui,et al. Plug-in hybrid electric vehicle speed prediction and control strategy[J]. Control Theory & Applications,2017,34(5):564-574.
[70] ZHANG Shuwei,LUO Yugong,WANG Junming,et al. Predictive energy management strategy for fully electric vehicles based on preceding vehicle movement[J]. IEEE Transactions on Intelligent Transportation Systems,2017,18(11):3049-3060.
[71] 陆化普,李瑞敏. 城市智能交通系统的发展现状与趋势[J]. 工程研究-跨学科视野中的工程,2014(1):6-19. LU Huapu,LI Ruimin. Development status and trend of urban intelligent transportation system[J]. Engineering Research-Engineering in an Interdisciplinary Perspective,2014(1):6-19.
[72] 赵娜,袁家斌,徐晗. 智能交通系统综述[J]. 计算机科学,2014,41(11):7-11. ZHAO Na,YUAN Jiabin,XU Han. Survey on intelligent transportation system[J]. Computer Science,2014,41(11):7-11.
[73] KAMAL M A S,MUKAI M,MURATA J,et al. Model predictive control of vehicles on urban roads for improved fuel economy[J]. IEEE Transactions on Control Systems Technology,2013,21(3):831-841.
[74] KOHUT N J,HEDRICK J K,BORRELLI F. Integrating traffic data and model predictive control to improve fuel economy[J]. IFAC Proceedings Volumes,2009,42(15):155-160.
[75] 余开江,许孝卓,胡治国,等. 基于交通信号灯信息的混合动力汽车节能预测控制方法[J]. 河北科技大学学报,2015,36(5):480-486. YU Kaijiang,XU Xiaozhuo,HU Zhiguo,et al. Predictive control strategies for energy saving of hybrid electric vehicles based on traffic light information[J]. Journal of Hebei University of Science and Technology,2015,36(5):480-486.
[76] JOHANNESSON L,MURGOVSKI N,JONASSON E,et al. Predictive energy management of hybrid long-haul trucks[J]. Control Engineering Practice,2015,41:83-97.
[77] SHEN Daliang,BENSCH V,MⅡLLER S. Model predictive energy management for a range extender hybrid vehicle using map information[J]. Ifac Papersonline,2015,48(15):263-270.
[78] YU Kaijiang,YANG Junqi,YAMAGUCHI D. Model predictive control for hybrid vehicle ecological driving using traffic signal and road slope information[J]. Control Theory and Technology,2015,13(1):17-28.
[79] ASADI B,VAHIDI A. Predictive cruise control:utilizing upcoming traffic signal information for improving fuel economy and reducing trip time[J]. IEEE Transactions on Control Systems Technology,2011,19(3):707-714.
[80] 陈艳,何春明. 智能交通系统应用现状及其存在问题分析[J]. 交通标准化,2007(8):62-65. CHEN Yan,HE Chunming. Application situation and existed problem of intelligent transport system[J]. Communications Standardization,2007(8):62-65.
[81] 苏静,王冬,张菲菲. 车联网技术应用综述[J]. 物联网技术,2014,3(6):69-72. SU Jing,WANG Dong,ZHANG Feifei. Review of vehicle networking technology application[J]. Internet of Things Technologies,2014(6):69-72.
[82] 武文科. 车联网技术发展与应用综述[J]. 汽车实用技术,2017,41(3):88-91. WU Wenke. Review of the development and application of connected vehicles technology[J]. Automobile Applied Technology,2017,41(3):88-91.
[83] 张建华,邹常丰. 车联网技术及其在交通管理中的应用[J]. 交通科技与经济,2014,16(6):91-94. ZHANG Jianhua,ZOU Changfeng. Car networking technology and its application in traffic management[J]. Technology & Economy in Areas of Communications,2014,16(6):91-94.
[84] HOMCHAUDHURI B,LIN Runing,PISU P. Hierarchical control strategies for energy management of connected hybrid electric vehicles in urban roads[J]. Transportation Research Part C Emerging Technologies,2016,62:70-86.
[85] 钱立军,邱利宏,司远,等. 智能网联环境下的混合动力汽车分层能量管理[J]. 汽车工程,2017,39(6):621-629. QIAN Lijun,QIU Lihong,SI Yuan,et al. Hierarchical energy management of hybrid electric vehicles under the environment of intelligent and connected vehicles[J]. Automotive Engineering,2017,39(6):621-629.
[86] 邱利宏,钱立军,杜志远,等. 车联网环境下车辆最优车速闭环快速模型预测控制[J]. 中国机械工程,2017,28(10):1245-1252. QIU Lihong,QIAN Lijun,DU Zhiyuan. et al. A closed-loop FMPC of optimal velocities for connected vehicles[J]. China Mechanical Engineering,2017,28(10):1245-1252.
[87] HOMCHAUDHURI B,VAHIDI A,PISU P. A fuel economic model predictive control strategy for a group of connected vehicles in urban roads[C]//2015 American Control Conference (ACC). IEEE,2015:2741-2746.
[88] 钱立军,邱利宏,林如宁,等. 基于V2X的混合动力汽车分层能量管理及优化[J]. 农业工程学报,2016,32(19):74-81. QIAN Lijun,QIU Lihong,LIN Runing,et al. Hierarchical energy management and optimization of hybrid electric vehicles based on V2X[J]. Transactions of the Chinese Society of Agricultural Engineering,2016,32(19):74-81.
[89] LIN Runing,HOMCHAUDHURI B,PISU P. Fuel efficient control strategies for connected hybrid electric vehicles in urban roads[C]//ASME 2015 Dynamic Systems and Control Conference. American Society of Mechanical Engineers,2015:V001T17A003-V001T17A003.
[90] 刘宗巍,匡旭,赵福全. 中国车联网产业发展现状、瓶颈及应对策略[J]. 科技管理研究,2016,36(4):121-127. LIU Zongwei,KUANG Xu,ZHAO Fuquan. The current situation,problems and countermeasures in Chinese internet of vehicles industrialization development[J]. Science & Technology Management Research,2016,36(4):121-127.
[91] 廖慧芬,邵小兵. 动态规划算法的原理及应用[J]. 中国科技信息,2005,16(21):42. LIAO Huifen,SHAO Xiaobing. Principle and application of dynamic programming algorithm[J]. China Science and Technology Information,2005,16(21):42.
[92] 孙延秋. 基于模型预测控制的HEV能量管理策略的研究[D]. 大连:大连理工大学,2017. SUN Yanqiu. Energy management strategy of HEV based on model predictive control[D]. Dalian:Dalian University of Technology,2017.
[93] LUO Yugong,CHEN Tao,ZHANG Shuwei,et al. Intelligent hybrid electric vehicle ACC with coordinated control of tracking ability,fuel economy,and ride comfort[J]. IEEE Transactions on Intelligent Transportation Systems,2015,16(4):2303-2308.
[94] 舒红,聂天雄,邓丽君,等. 插电式并联混合动力汽车模型预测控制[J]. 重庆大学学报,2011,34(5):36-41. SHU Hong,NIE Tianxiong,DENG Lijun,et al. Model predictive control for a plug-in hybrid electric vehicle[J]. Journal of Chongqing University,2011,34(5):36-41.
[95] BORHAN H,VAHIDI A,PHILLIPS A M,et al. MPC-based energy management of a power-split hybrid electric vehicle[J]. IEEE Transactions on Control Systems Technology,2012,20(3):593-603.
[96] FERREAU H J,KIRCHES C,POTSCHKA A,et al. QPOASES:A parametric active-set algorithm for quadratic programming[J]. Mathematical Programming Computation,2014,6(4):327-363.
[97] 宋巨龙,王香柯,冯晓慧. 最优化方法[M]. 西安:西安电子科技大学出版社,2012. SONG Julong,WANG Xiangke,FENG Xiaohui. Optimization method[M]. Xi'an:Xi'an University of Electronic Science and Technology Press,2012.
[98] 陈薇. 非线性预测控制快速算法的研究与应用[D]. 合肥:中国科学技术大学,2007. CHEN Wei. Study and application of nonlinear model predictive control fast algorithm[D]. Hefei:University of Science and Technology of China,2007.
[99] UTHAICHANA K,DECARLO R,BENGEA S,et al. Hybrid optimal theory and predictive control for power management in hybrid electric vehicle[J]. Journal of Nonlinear Systems and Applications,2011,2(2):96-110.
[100] 丁峰,王伟达,马文杰,等. 基于模型预测控制的混联式混合动力车辆能量管理策略[J]. 北京汽车,2015(3):1-5. DING Feng,WANG Weida,MA Wenjie,et al. Model predictive control based energy management strategy for power-split hybrid electric vehicles[J]. Beijing Automotive Engineering,2015(3):1-5.
[101] WANG Yang,BOYD S. Fast model predictive control using online optimization[J]. IFAC Proceedings Volumes,2008,41(2):6974-6979.
[102] HOMCHAUDHURI B,VAHIDI A,PISU P. Fast model predictive control-based fuel efficient control strategy for a group of connected vehicles in urban road conditions[J]. IEEE Transactions on Control Systems Technology,2017,25(2):760-767.
[103] OHTSUKA T. A continuation/GMRES method for fast computation of nonlinear receding horizon control[J]. Automatica,2004,40(4):563-574.
[104] KELLEY C T. Iterative methods for linear and nonlinear equations[M]. Philadelphia:Society for Industrial and Applied Mathematics,1995.
[105] YU Kaijiang,XU Xiaozhuo,LIANG Qing,et al. Model predictive control for connected hybrid electric vehicles[J]. Mathematical Problems in Engineering,2015(1):1-15.
[106] YU Kaijiang,YANG Haizhu,TAN Xingguo,et al. Model predictive control for hybrid electric vehicle platooning using slope information[J]. IEEE Transactions on Intelligent Transportation Systems,2016,17(7):1894-1909.
[107] ZHANG Jiangyan,SHEN Tielong. Real-time fuel economy optimization with nonlinear MPC for PHEVs[J]. IEEE Transactions on Control Systems Technology,2016,24(6):2167-2175.
[108] 张聪. 混合动力汽车实时能量优化管理策略研究[D]. 天津:天津大学,2016. ZHANG Con. Real time optimization energy management strategy for hybrid electric vehicle[D]. Tianjin:Tianjin University,2016.
[109] GUO Lulu,GAO Bingzhao,GAO Ying,et al. Optimal energy management for HEVs in eco-driving applications using bi-level MPC[J]. IEEE Transactions on Intelligent Transportation Systems,2017,18(8):2153-2162.
[110] XIE Shaobo,HU Xiaosong,XIN Zongke,et al. Pontryagin's minimum principle based model predictive control of energy management for a plug-in hybrid electric bus[J]. Applied Energy,2019,236:893-905.
[111] 张鹏. 基于混合逻辑动态的混杂系统建模及其模型预测控制[D]. 长春:吉林大学,2007. ZHANG Peng. Model predictive control for hybrid systems based on mixed logic dynamical model[D]. Changchun:Jilin University,2007.
[112] 赵旭. 基于MLD模型的混杂预测控制研究[D]. 北京:中国石油大学,2010. ZHAO Xu. Research of hybrid predictive control based on MLD model[D]. Beijing:China University of Petroleum,2010.
[113] LI Guoqiang,GOERGES D. Hybrid modeling and predictive control of the power split and gear shift in hybrid electric vehicles[J]. IEEE Vehicle Power and Propulsion Conference (VPPC),2017:1-6.
[114] HERCEG M,KVASNICA M,JONES C N,et al. Multi-parametric toolbox 3.0[J]. Lecture Notes in Computer Science,2013,415(4):502-510.
[115] RIPACCIOLI G,BEMPORAD A,ASSADIAN F,et al. Hybrid modeling,identification,and predictive control:an application to hybrid electric vehicle energy management[C]//International Workshop on Hybrid Systems:Computation and Control. Springer,Berlin,Heidelberg,2009:321-335.
[116] VADAMALU R S,BUCH D,XIAO Hong,et al. Energy management of hybrid electric powertrain using predictive trajectory planning based on direct optimal control[J]. IFAC Papersonline,2015,48(25):236-241.
[117] LIAN Jing,LIU Shuang,LI Linhui,et al. A mixed logical dynamical-model predictive control (MLD-MPC) energy management control strategy for plug-in hybrid electric vehicles (PHEVs)[J]. Energies,2017,10(1):74.
[118] AIBERTO B. Hybrid toolbox for Matlab[EB/OL]. (2019-02-07). http://cse.lab.imtlucca.it/~bemporad/hybrid/toolbox/.
[119] JOŠEVSKI M,ABEL D. Distributed predictive control approach for fuel efficient gear shifting in hybrid electric vehicles[C]//2016 European Control Conference (ECC). IEEE,2016:2366-2373.
[120] JOŠEVSKI M,ABEL D. Gear shifting and engine on/off optimal control in hybrid electric vehicles using partial outer convexification[C]//2016 IEEE Conference on Control Applications (CCA). IEEE,2016:562-568.
[121] 戴荔. 分布式随机模型预测控制方法研究[D]. 北京:北京理工大学,2016. DAI Li. Distributed stochastic model predictive control[D]. Beijing:Beijing Institute of Technology,2016.
[122] REZAEI A,BURL J B. Effects of time horizon on model predictive control for hybrid electric vehicles[J]. IFAC Papersonline,2015,48(15):252-256.
[123] 彭剑坤. 插电式混合动力公交车工况构建和变时域预测能量管理[D]. 北京:北京理工大学,2016. PENG Jiankun. Driving cycle construction and variable-horizon predictive energy management for plug-in hybrid electric bus[D]. Beijing:Beijing Institute of Technology,2016.
[124] CAO Jianfei,PENG Jiankun,HE Hongwen. Research on model prediction energy management strategy with variable horizon[J]. Energy Procedia,2017,105:3565-3570.
[125] LI Yuecheng,HE Hongwen,PENG Jiankun. An adaptive online prediction method with variable prediction horizon for future driving cycle of the vehicle[J]. IEEE Access,2018,6:33062-33075.
[126] JOŠEVSKI M,ABEL D. Tube-based MPC for the energy management of hybrid electric vehicles with non-parametric driving profile prediction[C]//2016 American Control Conference (ACC). IEEE,2016:623-630.
[127] ZHOU Fang,XIAO Feng,CHANG Cheng,et al. Adaptive model predictive control-based energy management for semi-active hybrid energy storage systems on electric vehicles[J]. Energies,2017,10(7):1063.
[128] FU Jiangtao,SONG Shuzhong,FU Zhumu,et al. Hierarchical model predictive control for parallel hybrid electrical vehicles[J]. Asian Journal of Control,2018,20(6):2331-2342.
[129] JOŠEVSKI M,ABEL D. Multi-time scale model predictive control framework for energy management of hybrid electric vehicles[C]//53rd IEEE Conference on Decision and Control. IEEE,2014:2523-2528.
[130] MESBAH A. Stochastic model predictive control:An overview and perspectives for future research[J]. IEEE Control Systems Magazine,2016,36(6):30-44.
[131] HEIRUNG T A N,PAULSON J A,O'LEARY J,et al. Stochastic model predictive control-how does it work?[J]. Computers & Chemical Engineering,2018,114:158-170.
[132] MESBAH A. Stochastic model predictive control with active uncertainty learning:A survey on dual control[J]. Annual Reviews in Control,2018,45:107-117.
[133] BAVDEKAR V A,EHLINGER V,GIDON D,et al. Stochastic predictive control with adaptive model maintenance[C]//2016 IEEE 55th Conference on Decision and Control (CDC). IEEE,2016:2745-2750.
[134] ASWANI A,MASTER N,TANEJA J,et al. Energy-efficient building HVAC control using hybrid system LBMPC[J]. IFAC Proceedings Volumes,2012,45(17):496-501.
[135] ASWANI A,BOUFFARD P,ZHANG Xiaojing,et al. Practical comparison of optimization algorithms for learning-based MPC with linear models[J]. Mathematics,2014:1-7.
[136] ASWANI A,BOUFFARD P,TOMLIN C. Extensions of learning-based model predictive control for real-time application to a quadrotor helicopter[C]//2012 American Control Conference (ACC). IEEE,2012:4661-4666.
[137] BOUFFARD P,ASWANI A,TOMLIN C. Learning-based model predictive control on a quadrotor:onboard implementation and experimental results[C]//2012 IEEE International Conference on Robotics and Automation. IEEE,2012:279-284.
[138] ROSOLIA U,ZHANG Xiaojing,BORRELLI F. Data-driven predictive control for autonomous systems[J]. Annual Reviews on Control,Robotics,and Autonomous Systems,2018,1(1):259-286.
[139] ROSOLIA U,CARVALHO A,BORRELLI F. Autonomous racing using learning model predictive control[J]. American Control Conference (ACC),2017:5115-5120.
[140] ROSOLIA U,BORRELLI F. Learning model predictive control for iterative tasks. A data-driven control framework[J]. IEEE Transactions on Automatic Control,2017,63(7):1883-1896.