Explicit Solution for Improvement of Real-time Performance of Model Predictive Control in Intelligent Vehicle Stability

doi:10.3901/JME.2025.10.263

Abstract

Abstract: Model predictive control(MPC) has many advantages. However, the complexity of the optimization algorithm arises due to the multi-constraints and nonlinear character of its dynamic model when applied to yaw stability control in intelligent vehicles, making it challenging to achieve sufficiently short control cycle time and step. Therefore, an online explicit solution method for intelligent vehicle yaw stability control based MPC is proposed. It uses Taylor expansion to convert nonlinear model predictive control(NMPC) to linear time-varying model predictive control(LTV-MPC), and then designs a rolling adjustment weight coefficient to convert inequality constrained optimization to unconstrained optimization that can be directly and explicitly solved, so as to avoid multi-step iterative optimization and speed up computation time of MPC. The simulation results indicate that the proposed explicit solution can increase the solving speed of MPC by 3-4 times while ensuring the same control effectiveness, which can significantly improve the real-time performance of MPC in vehicle yaw stability.

Key words: vehicle yaw stability, model predictive control, real-time, penalty function, explicit solution

CLC Number:

TP273

JIAO Hengchao, SHU Ran, ZENG Zhaofeng, TANG Xiaolin, SHU Hongyu. Explicit Solution for Improvement of Real-time Performance of Model Predictive Control in Intelligent Vehicle Stability[J]. Journal of Mechanical Engineering, 2025, 61(10): 263-275.

References

[1] 李子先，潘世举，徐友春. 分布式电驱动车辆底盘稳定性协同控制研究综述[J]. 汽车技术，2022，564(9)：1-14.LI Zixian，PAN Shiju，XU Youchun. Review on cooperative control of chassis stability for distributed electric vehicles[J]. Automobile Technology，2022，564(9)：1-14.
[2] JING C Q，SHU H Y，SONG Y T. Model predictive control for integrated lateral stability and rollover prevention based on a multi-actuator control system[J]. International Journal of Control Automation and Systems，2023，21(5)：1518-1537.
[3] 李聪，景晖，黄好，等. 基于MPC的独立驱动电动汽车稳定性集成控制[J]. 汽车工程学报，2022，12(6)：759-772.LI Cong，JING Hiu，HUANG Hao，et al. Integrated stability control of independent drive electric vehicles based on MPC[J]. Chinese Journal of Automotive Engineering，2022，12(6)：759-772.
[4] ZHANG L，CHEN H，HUANG Y J et al. Model predictive control for integrated longitudinal and lateral stability of electric vehicles with in-wheel motors[J]. IET Control Theory and Applications，2020，14(18)：2741-2751.
[5] JING C Q，SHU H Y，SHU R，et al. Integrated control of electric vehicles based on active front steering and model predictive control[J]. Control Engineering Practice，2022，121：105066.
[6] 陈杰，李亮，宋健. 基于LTV-MPC的车辆稳定性控制研究[J]. 汽车工程，2016，38(3)：308-316.CHEN Jie，LI Liang，SONG Jian. A study on vehicle stability control based on LTV-MPC[J]. Automotive Engineering，2016，38(3)：308-316.
[7] ZHANG L，JIANG L B，LIU H H，et al. Coordinated longitudinal and stability improvement for electric vehicles based on a real-time NMPC strategy[J]. IEEE Transactions on Intelligent Transportation Systems，2023，24(5)：5337-5349.
[8] SHI K，YUAN X F，HUANG G M，et al. DLMPCS-based improved yaw stability control strategy for DDEV[J]. IET Intelligent Transport Systems，2019，13(9)：1329-1339.
[9] ELSISI M，EBRAHIM M A. Optimal design of low computational burden model predictive control based on SSDA towards autonomous vehicle under vision dynamics[J]. International Journal of Intelligent Systems，2021，36(11)：6968-6987.
[10] GUO N Y，LENZO B，ZHANG X D，et al. A real-time nonlinear model predictive controller for yaw motion optimization of distributed drive electric vehicles[J]. IEEE Transactions on Vehicular Technology，2020，69(5)：4935-4946.
[11] POURJAFARI E，MOJALLALI H. Predictive control for voltage collapse avoidance using a modified discrete multi-valued PSO algorithm[J]. ISA Transactions，2011，50(2)：195-200.
[12] MAGALHAES Z R，MURILO A M，LOPES R V. Vehicle stability upper-level-controller based on parameterized model predictive control[J]. IEEE Access，2022，10：21048-21065.
[13] ZHENG Y G，SHYRIJAY B. A real-time nolinear MPC for extreme lateral stabilization of passenger vehicles[C]// IEEE International Conference on Mechatronics，New York：IEEE，2019：519-524.
[14] 刘凯，陈慧岩，龚建伟，等. 高速无人驾驶车辆的操控稳定性研究[J]. 汽车工程，2019，41(5)：514-521.LIU Kai，CHEN Huiyan，GONG Jianwei，et al. A research on handling stability of high-speed unmanned vehicles[J]. Automotive Engineering，2019，41(5)：514-521.
[15] 许芳，郭中一，于树友，等. 四轮驱动电动汽车稳定性预测控制器快速实现[J]. 控制理论与应用，2022，39(5)：777-787.XU Fang，GUO Zhongyi，YU Shuyou，et al. Fast realization of stability prediction controller for four-wheel drive electric vehicles[J]. Control Theory and Applications，2022，39(5)：777-787.
[16] BEMPORAD A，MORARI M，DUA V，et al. The explicit linear quadratic regulator for constrained systems[J]. Automatica，2003，39(10)：1845-1864.
[17] GEYER T，TOBIAS F D，MORARI M. Optimal complexity reduction of polyhedral piecewise affine systems[J]. Automatica，2008，44(7)：1728-1740.
[18] KVASNICA M，FIKAR M. Clipping-based complexity reduction in explicit MPC[J]. IEEE Transactions on Automatic Control，2012，57(7)：1878-1883.
[19] NGUYEN N A，GULAN M，OLARU S et al. Convex lifting：Theory and control applications[J]. IEEE Transactions on Automatic Control，2018，63(5)：1243-1258.
[20] GALCIKOVA L，ORAVEC J. Fixed complexity solution of partial explicit MPC[J]. Computers and Chemical Engineering，2022，157：1-8.
[21] PACEJKA H. Tire and vehicle dynamics[M]. Amsterdam：Elsevier，2005.
[22] SONG Y T，SHU H Y，CHEN X B. Chassis integrated control for 4WIS distributed drive EVs with model predictive control based on the UKF observer[J]. Science China-technological Sciences，2022，63(3)：397-409.
[23] 王悦，李春明，肖磊. 基于转矩优化分配的分布式电动车辆横摆力矩研究[J]. 车辆与动力技术，2019，153(1)：16-22.WANG Yue，LI Chunming，XIAO Lei. Research on yaw moment of distributed electric vehicle based on optimal allocation[J]. Vehicle and Power Technology，2019，153(1)：16-22.
[24] WANG Y，BOYD S. Fast model predictive control using online optimization[J]. IEEE Transactions on Control systems Technology，2010，18(2)：267-278.
[25] DIXIT S，MONTANARO，U，DIANATI，M，et al. Trajectory planning for autonomous high-speed overtaking in structured environments using robust MPC[J]. IEEE Transactions on Intelligent Transportation Systems，2020，21(6)：2310-2323.
[26] 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.
[27] EL M，GUENNOUN Z A，BOUALI S，et al. Interior-point methods for linear optimization based on a kernel function with a trigonometric barrier term[J]. Journal of Computational and Applied Mathematics，2012，236(15)：3616-3623.
[28] 李绍松，郭孔辉，仇韬，等. 极限工况下主动前轮转向汽车稳定性控制[J]. 汽车工程，2020，42(2)：191-198.LI Shaosong，GUO Konghui，QIU Tao，et al. Stability control of vehicle with active front steering under extreme conditions[J]. Automotive Engineering，2020，42(2)：191-198.