{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T04:20:38Z","timestamp":1768278038320,"version":"3.49.0"},"reference-count":37,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,5,8]],"date-time":"2023-05-08T00:00:00Z","timestamp":1683504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation (NNSF) of China","doi-asserted-by":"publisher","award":["61503127"],"award-info":[{"award-number":["61503127"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation (NNSF) of China","doi-asserted-by":"publisher","award":["2021-KYYWF-0027"],"award-info":[{"award-number":["2021-KYYWF-0027"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"University Basic Research foundation of Heilongjiang Province","award":["61503127"],"award-info":[{"award-number":["61503127"]}]},{"name":"University Basic Research foundation of Heilongjiang Province","award":["2021-KYYWF-0027"],"award-info":[{"award-number":["2021-KYYWF-0027"]}]},{"name":"Outstanding Youth Foundation of Heilongjiang University","award":["61503127"],"award-info":[{"award-number":["61503127"]}]},{"name":"Outstanding Youth Foundation of Heilongjiang University","award":["2021-KYYWF-0027"],"award-info":[{"award-number":["2021-KYYWF-0027"]}]},{"name":"Key Laboratory of Information Fusion Estimation and Detection, Heilongjiang Province","award":["61503127"],"award-info":[{"award-number":["61503127"]}]},{"name":"Key Laboratory of Information Fusion Estimation and Detection, Heilongjiang Province","award":["2021-KYYWF-0027"],"award-info":[{"award-number":["2021-KYYWF-0027"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Energy-optimal adaptive cruise control (EACC) is becoming increasingly popular due to its ability to save energy. Considering the negative impacts of system noise on the EACC, an improved modified model predictive control (MPC) is proposed, which combines the Sage-Husaadaptive Kalman filter (SHAKF), the cubature Kalman filter (CKF), and the back-propagation neural network (BPNN). The proposed MPC improves safety and tracking performance while further reducing energy consumption. The final simulation results show that the proposed algorithm has a stronger energy-saving capability compared to previous studies and always maintains an appropriate relative distance and relative speed to the vehicle in front, verifying the effectiveness of the proposed algorithm.<\/jats:p>","DOI":"10.3390\/s23094568","type":"journal-article","created":{"date-parts":[[2023,5,9]],"date-time":"2023-05-09T01:34:26Z","timestamp":1683596066000},"page":"4568","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Energy-Optimal Adaptive Control Based on Model Predictive Control"],"prefix":"10.3390","volume":"23","author":[{"given":"Yuxi","family":"Li","sequence":"first","affiliation":[{"name":"School of Electronic Engineering, Heilongjiang University, Harbin 150080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1252-5771","authenticated-orcid":false,"given":"Gang","family":"Hao","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Heilongjiang University, Harbin 150080, China"},{"name":"Key Laboratory of Information Fusion Estimation and Detection, Harbin 150080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"123543","DOI":"10.1016\/j.energy.2022.123543","article-title":"Energy recovery strategy optimization of dual-motor drive electric vehicle based on braking safety and efficient recovery","volume":"248","author":"He","year":"2022","journal-title":"Energy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"120369","DOI":"10.1016\/j.energy.2021.120369","article-title":"Optimal production and pricing strategies in auto supply chain when dual credit policy is substituted for subsidy policy","volume":"226","author":"Yu","year":"2021","journal-title":"Energy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"115081","DOI":"10.1016\/j.apenergy.2020.115081","article-title":"Microsimulation of electric vehicle energy consumption and driving range","volume":"267","author":"Xie","year":"2020","journal-title":"Appl. Energy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"117237","DOI":"10.1016\/j.energy.2020.117237","article-title":"Adaptive real-time optimal energy management strategy for extender range electric vehicle","volume":"197","author":"Yang","year":"2020","journal-title":"Energy"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.egyr.2022.10.259","article-title":"Research on the influence factors of brake regenerative energy of pure electric vehicles based on the CLTC","volume":"8","author":"Zhang","year":"2022","journal-title":"Energy Rep."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Hidalgo, C., Lattarulo, R., Flores, C., and Perez Rastelli, J. (2021). Platoon Merging Approach Based on Hybrid Trajectory Planning and CACC Strategies. Sensors, 21.","DOI":"10.3390\/s21082626"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1109\/TCST.2017.2658193","article-title":"Flexible Spacing Adaptive Cruise Control Using Stochastic Model Predictive Control","volume":"26","author":"Moser","year":"2018","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ren, P., Jiang, H., and Xu, X. (2023). Research on a Cooperative Adaptive Cruise Control (CACC) Algorithm Based on Frenet Frame with Lateral and Longitudinal Directions. Sensors, 23.","DOI":"10.3390\/s23041888"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Kim, H., Min, K., and Sunwoo, M. (2020). Driver Characteristics Oriented Autonomous Longitudinal Driving System in Car-Following Situation. Sensors, 20.","DOI":"10.3390\/s20216376"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/j.trc.2019.01.025","article-title":"Typical-driving-style-oriented Personalized Adaptive Cruise Control design based on human driving data","volume":"100","author":"Zhu","year":"2019","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"145056","DOI":"10.1109\/ACCESS.2020.3015349","article-title":"A Personalized Human Drivers\u2019 Risk Sensitive Characteristics Depicting Stochastic Optimal Control Algorithm for Adaptive Cruise Control","volume":"8","author":"Jiang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"105344","DOI":"10.1016\/j.conengprac.2022.105344","article-title":"Fast warm-start of F-MPC strategy for automotive cruise control with mode switching","volume":"128","author":"Liu","year":"2022","journal-title":"Control Eng. Pract."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"231200","DOI":"10.1016\/j.jpowsour.2022.231200","article-title":"Stochastically predictive co-optimization of the speed planning and powertrain controls for electric vehicles driving in random traffic environment safely and efficiently","volume":"528","author":"Zhou","year":"2022","journal-title":"J. Power Sources"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.conengprac.2017.12.001","article-title":"Energy-optimal adaptive cruise control combining model predictive control and dynamic programming","volume":"72","author":"Lin","year":"2018","journal-title":"Control Eng. Pract."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"122793","DOI":"10.1016\/j.energy.2021.122793","article-title":"Energy-optimal adaptive cruise control strategy for electric vehicles based on model predictive control","volume":"241","author":"Pan","year":"2022","journal-title":"Energy"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4326","DOI":"10.1109\/TSMC.2018.2850367","article-title":"Compensating Delays and Noises in Motion Control of Autonomous Electric Vehicles by Using Deep Learning and Unscented Kalman Predictor","volume":"50","author":"Li","year":"2020","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"103801","DOI":"10.1016\/j.trc.2022.103801","article-title":"Congestion-mitigating MPC design for adaptive cruise control based on Newell\u2019s car following model: History outperforms prediction","volume":"142","author":"Zhou","year":"2022","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"661","DOI":"10.3390\/s110100661","article-title":"Ultrasonic sensors in urban traffic driving-aid systems","volume":"11","author":"Alonso","year":"2011","journal-title":"Sensors"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"105002","DOI":"10.1016\/j.conengprac.2021.105002","article-title":"Generic stochastic particle filter algorithm for predictive energy optimization of a Plug-in Hybrid Electric Vehicle extended by a battery temperature control and implemented on a Hardware-in-the-Loop system","volume":"120","author":"Aubeck","year":"2022","journal-title":"Control Eng. Pract."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.isatra.2022.09.021","article-title":"Robust control strategy for multi-UAVs system using MPC combined with Kalman-consensus filter and disturbance observer","volume":"135","author":"Yan","year":"2023","journal-title":"ISA Trans."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/j.conengprac.2014.01.016","article-title":"Nonlinear Model Predictive Control approach in design of Adaptive Cruise Control with automated switching to cruise control","volume":"26","author":"Shakouri","year":"2014","journal-title":"Control Eng. Pract."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"934","DOI":"10.1002\/batt.202100046","article-title":"High-Energy Nickel-Cobalt-Aluminium Oxide (NCA) Cells on Idle: Anode- versus Cathode-Driven Side Reactions","volume":"4","author":"Li","year":"2021","journal-title":"Batter. Supercaps"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"670","DOI":"10.1016\/j.renene.2021.01.040","article-title":"Real-time rotor effective wind speed estimation using Gaussian process regression and Kalman filtering","volume":"169","author":"Lio","year":"2021","journal-title":"Renew. Energy"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Bar-Shalom, Y., Kirubarajan, T., and Li, X.R. (2001). Estimation with Applications to Tracking and Navigation, Estimation with Applications to Tracking and Navigation.","DOI":"10.1002\/0471221279"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wan, R., Song, Y., Mu, T., and Wang, Z. (2019, January 5\u20137). Moving Target Detection Using the 2D-FFT Algorithm for Automotive FMCW Ra-dars. Proceedings of the 2019 International Conference on Communications, Information System and Computer Engineering (CISCE), Haikou, China.","DOI":"10.1109\/CISCE.2019.00062"},{"key":"ref_26","first-page":"100431","article-title":"Pavement slipperiness detection using wheel speed and acceleration sensor data","volume":"11","author":"Jang","year":"2021","journal-title":"Transp. Res. Interdiscip. Perspect."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"012081","DOI":"10.1088\/1742-6596\/1236\/1\/012081","article-title":"The signal processing algorithm of automotive FMCW radars with an extended range of speed estimation","volume":"1236","author":"Ivanov","year":"2019","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_28","unstructured":"Drummond, O.E., Gale, N., Hong, L., and Roy, A. (2011). Signal and Data Processing of Small Targets 2011, SPIE."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"109083","DOI":"10.1016\/j.ymssp.2022.109083","article-title":"Constraint performance pressure tracking control with asymmetric continuous friction compensation for booster based brake-by-wire system","volume":"174","author":"Ji","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1254","DOI":"10.1109\/TAC.2009.2019800","article-title":"Cubature Kalman Filters","volume":"54","author":"Arasaratnam","year":"2009","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"112890","DOI":"10.1016\/j.oceaneng.2022.112890","article-title":"A modified adaptive Kalman filtering method for maneuvering target tracking of unmanned surface vehicles","volume":"266","author":"Fan","year":"2022","journal-title":"Ocean. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1017\/S0373463307004316","article-title":"Improving Adaptive Kalman Estimation in GPS\/INS Integration","volume":"60","author":"Ding","year":"2007","journal-title":"J. Navig."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"106831","DOI":"10.1016\/j.est.2023.106831","article-title":"A hierarchical adaptive extended Kalman filter algorithm for lithium-ion battery state of charge estimation","volume":"62","author":"Wang","year":"2023","journal-title":"J. Energy Storage"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"106936","DOI":"10.1016\/j.infsof.2022.106936","article-title":"A search-based framework for automatic generation of testing environments for cyber\u2013physical systems","volume":"149","author":"Humeniuk","year":"2022","journal-title":"Inf. Softw. Technol."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Riccio, V., and Tonella, P. (2020, January 8\u201313). Model-based exploration of the frontier of behaviours for deep learning system testing. Proceedings of the 28th ACM Joint Meeting on European Software Engineering Conference and Symposium on the Foundations of Software Engineering, Virtual Event, USA.","DOI":"10.1145\/3368089.3409730"},{"key":"ref_36","unstructured":"State Administration for Market Regulation, and Standardization Administration of China (2019). China Automotive Test Cycle Part 1: Light-Duty Vehicles: GB\/T 38146.1-2019, Standards Press of China."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.jprocont.2022.11.009","article-title":"Enhanced MPC based on unknown state estimation and control compensation","volume":"121","author":"Sun","year":"2023","journal-title":"J. Process Control"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/9\/4568\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:31:34Z","timestamp":1760124694000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/9\/4568"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,8]]},"references-count":37,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["s23094568"],"URL":"https:\/\/doi.org\/10.3390\/s23094568","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,8]]}}}