Output Feedback-Based Direct Yaw Control System and Finite-Time Robust Dynamic Control Allocation for Unknown Road Conditions

Abstract

This paper presents a three-layer control architecture designed to enhance vehicle lateral stability under uncertain and varying road conditions. The system utilizes output-feedback-based finite-time controllers to track the desired yaw rate and longitudinal slip in the upper and lower layers, respectively. The middle layer incorporates a finite-time robust dynamic control allocation to distribute longitudinal slips among the tires. This approach effectively handles uncertainties and changing road conditions without the need for direct estimation of unmeasurable variables such as tire-road friction and sideslip angle. The proposed output feedback control law consists of a stabilizer component to ensure finite-time stability, a compensator to eliminate the unknown function in the upper and lower layers, and an auxiliary tracking term. Key advantages of the proposed framework include: no requirement for additional sensors, finite-time convergence, reduced computational complexity compared to optimization-based methods, and the ability to perform finite-time stability analysis for the integrated closed-loop system. The system performance is evaluated using a validated 10-degree-of-freedom vehicle dynamics model and CarSim simulations during a double-lane change maneuver. Simulation results demonstrate the superiority of the proposed control structure over sliding mode control, offering improved tracking accuracy and robust performance under varying road conditions.

Keywords

dynamic control allocation / finite-time stability / output feedback control / vehicle lateral stability

References

[1] M. Mirzaei, A. R. Vali, F. Allahverdizadeh, and V. Behnamgol, “Fixed-Time Dynamic Control Allocation for the Distribution of Braking Forces in a Vehicle ESC System,” Nonlinear Dynamics 112, no. 24 (2024): 22009–22037.

[2] N. Ahmadian, A. Khosravi, and P. Sarhadi, “Driver Assistant Yaw Stability Control via Integration of AFS and DYC,” Vehicle System Dynamics 60, no. 5 (2022): 1742–1762.

[3] H. Liu, L. Zhang, P. Wang, and H. Chen, “A Real-Time NMPC Strategy for Electric Vehicle Stability Improvement Combining Torque Vectoring With Rear-Wheel Steering,” IEEE Transactions on Transportation Electrification 8, no. 3 (2022): 3825–3835.

[4] A. Goodarzi and E. Esmailzadeh, “Design of a VDC System for All-Wheel Independent Drive Vehicles,” IEEE/ASME Transactions on Mechatronics 12, no. 6 (2007): 632–639.

[5] A. Medina, G. Bistue, and A. Rubio, “Comparison of Typical Controllers for Direct Yaw Moment Control Applied on an Electric Race Car,” Vehicles 3, no. 1 (2021): 127–144.

[6] E. Muhammad, A. Vali, A. Kashaninia, and V. Bahnamgol, “Stability Enhancement of Hybrid Electric Vehicles Using Optimal Fuzzy Logic,” International Journal of Dynamics and Control 12, no. 4 (2024): 1130–1145.

[7] F. Alfatti, M. Montani, T. Favilli, et al., “Implementation and Performances Evaluation of Advanced Automotive Lateral Stability Controls on a Real-Time Hardware in the Loop Driving Simulator,” Applied Sciences 13, no. 11 (2023): 6592.

[8] Z. R. Magalhaes Junior, A. Murilo, and R. V. Lopes, “Vehicle Stability Upper-Level Controller Based on Parameterized Model Predictive Control,” IEEE Access 10 (2022): 21048–21065.

[9] H. Zhang, R. Wang, and J. Wang, “Robust H∞ Output-Feedback Yaw Control for In-Wheel Motor-Driven Electric Vehicles With Differential Steering,” Neurocomputing 173, no. 3 (2023): 131–152.

[10] H. Atoui, O. Sename, V. Milanes, and J. J. Martinez, “LPV-Based Autonomous Vehicle Lateral Controllers: A Comparative Analysis,” IEEE Transactions on Intelligent Transportation Systems 23, no. 8 (2022): 13570–13581.

[11] X. Cao, T. Xu, Y. Tian, and X. Ji, “Gain-Scheduling LPV Synthesish∞ Robust Lateral Motion Control for Path Following of Autonomous Vehicle via Coordination of Steering and Braking,” Vehicle System Dynamics 61, no. 4 (2023): 968–991.

[12] B. Mashadi and M. Majidi, “Integrated AFS/DYC Sliding Mode Controller for a Hybrid Electric Vehicle,” International Journal of Vehicle Design 56, no. 1 (2011): 246–269.

[13] M. Mirzaei, A. R. Vali, F. Allahverdizadeh, and V. Behnamgol, “Finite-Time Lateral Stability Control of Vehicles via Longitudinal Tire Slip-Based Dynamic Control Allocation in Limit Handling Manoeuvers,” Vehicle System Dynamics 63 (2025): 1–32.

[14] M. Mirzaei, A. Vali, F. Alahvirdizadeh, and V. Behnamgol, “Robust Vehicle Stability Control Using Smooth Sliding Mode and Tire Slip-Based Dynamic Control Allocation in ESC Systems,” International Journal of Research and Technology in Electrical Industry 3, no. 2 (2024): 371–381.

[15] G. Tagne, R. Talj, and A. Charara, “Higher-Order Sliding Mode Control for Lateral Dynamics of Autonomous Vehicles, With Experimental Validation,” in Proceedings of the IEEE Intelligent Vehicles Symposium (IV) (IEEE, 2013), 678–683.

[16] E. Muhammad, V. Behnamgol, A. Vali, A. Kashaninia, and M. Mirzaei, “Adaptive MIMO Sliding Mode Control for Enhanced Vehicle Stability With Coordinated AFS and DYC Systems,” Asian Journal of Control 27, no. 3 (2025): 1442–1454.

[17] P. Ge, L. Guo, J. Feng, and X. Zhou, “Adaptive Stability Control Based on Sliding Model Control for BEVs Driven by In-Wheel Motors,” Sustainability 15, no. 11 (2023): 8660.

[18] V. Behnamgol, M. Mirzaei, and B. Sohani, “Enhanced Vehicle Lateral Stability Under Unknown Road Conditions Using Finite-Time Smooth Adaptive Sliding Mode Control,” International Journal of Dynamics and Control 13, no. 6 (2025): 221.

[19] J. Zhao, K. Yang, Y. Cao, et al., “Observer-Based Discrete-Time Cascaded Control for Lateral Stabilization of Steer-by-Wire Vehicles With Uncertainties and Disturbances,” IEEE Transactions on Circuits and Systems I: Regular Papers 70, no. 8 (2023): 3347–3358.

[20] A. El Hajjaji, M. Chadli, M. Oudghiri, and O. Pages, “Observer-Based Robust Fuzzy Control for Vehicle Lateral Dynamics,” in Proceedings of the American Control Conference (IEEE, 2006), 6, https://doi.org/10.1109/ACC.2006.1657457.

[21] M. Oudghiri, M. Chadli, and A. E. Hajjaji, “Robust Observer-Based Fault-Tolerant Control for Vehicle Lateral Dynamics,” International Journal of Vehicle Design 48, no. 3–4 (2008): 173–189.

[22] E. Muhammad, V. Bahnamgol, A. Vali, and A. Kashaninia, “Observer-Based Integrated Smooth MIMO Sliding Mode Control for Coordinating AFS and DYC Systems Under Uncertainties,” Journal of the Brazilian Society of Mechanical Sciences and Engineering 47, no. 2 (2025): 56.

[23] J. Hu, K. Zhang, P. Zhang, and F. Yan, “Direct Yaw Moment Control for Distributed Drive Electric Vehicles Based on Hierarchical Optimization Control Framework,” Mathematics 12, no. 11 (2024): 1715.

[24] L. Cai, Z. Liao, S. Wei, and J. Li, “Novel Direct Yaw Moment Control of Multi-Wheel Hub Motor Driven Vehicles for Improving Mobility and Stability,” IEEE Transactions on Industry Applications 59, no. 1 (2023): 591–600.

[25] I. G. Jang, S. H. You, S. H. Hwang, and W. Cho, “Lateral Stability Control of a 4-Wheel Independent Drive Electric Vehicle Using the Yaw Moment Contour Line Concept,” IEEE Access 9 (2021): 136892–136904.

[26] R. Rajamani, Vehicle Dynamics and Control (Springer, 2011).

[27] E. Mousavinejad, Q.-L. Han, F. Yang, Y. Zhu, and L. Vlacic, “Integrated Control of Ground Vehicles Dynamics via Advanced Terminal Sliding Mode Control,” Vehicle System Dynamics 55, no. 2 (2017): 268–294.

[28] W. Junmin Wang and R. G. Longoria, “Coordinated and Reconfigurable Vehicle Dynamics Control,” IEEE Transactions on Control Systems Technology 17, no. 3 (2009): 723–732.

[29] X. Zhang, D. Göhlich, and W. Zheng, “Karush–Kuhn–Tuckert Based Global Optimization Algorithm Design for Solving Stability Torque Allocation of Distributed Drive Electric Vehicles,” Journal of the Franklin Institute 354, no. 18 (2017): 8134–8155.

[30] M. Mirzaei, A. Vali, F. Alahvirdizadeh, and V. Behnamgol, “Enhanced Vehicle Stability Control With Smooth Sliding Mode and Tire Slip-Based Allocation in ESC Systems,” in Proceedings of the 10th International Conference on Control, Instrumentation and Automation (ICCIA) (IEEE, 2024), 1–6.

[31] K. Chatrath, Y. Zheng, and B. Shyrokau, “Vehicle Dynamics Control Using Model Predictive Control Allocation Combined With an Adaptive Parameter Estimator,” SAE International Journal of Connected and Automated Vehicles 3 (2020): 103–117.

[32] T. A. Johansen and T. I. Fossen, “Control Allocation—A Survey,” Automatica 49, no. 5 (2013): 1087–1103.

[33] J. V. Alcantar, F. Assadian, and M. Kuang, “Vehicle Dynamics Control of eAWD Hybrid Electric Vehicle Using Slip Ratio Optimization and Allocation,” Journal of Dynamic Systems, Measurement and Control 140, no. 9 (2018): 091010.

[34] Y. Chen and J. Wang, “Adaptive Energy-Efficient Control Allocation for Planar Motion Control of Over-Actuated Electric Ground Vehicles,” IEEE Transactions on Control Systems Technology 22, no. 4 (2013): 1362–1373.

[35] C. Chen, Y. Jia, M. Shu, and Y. Wang, “Hierarchical Adaptive Path-Tracking Control for Autonomous Vehicles,” IEEE Transactions on Intelligent Transportation Systems 16, no. 5 (2015): 2900–2912.

[36] O. Temiz, M. Cakmakci, and Y. Yildiz, “Integrated Vehicle Control Using Adaptive Control Allocation,” International Journal of Adaptive Control and Signal Processing 37, no. 7 (2023): 1803–1826.

[37] V. Behnamgol, A. Vali, A. Mohammadi, and A. Oraee, “Lyapunov-Based Adaptive Smooth Second-Order Sliding Mode Guidance Law With Proven Finite-Time Stability,” Journal of Space Science and Technology 11, no. 2 (2018): 34.

[38] V. Behnamgol, M. Asadi, S. S. Aphale, and B. Sohani, “Recursive PID-NT Estimation-Based Second-Order SMC Strategy for Knee Exoskeleton Robots: A Focus on Uncertainty Mitigation,” Electronics 14, no. 7 (2025): 1455.

[39] B. Kanwar, S. Arat, and S. Taheri, “Literature Review and Fundamental Approaches for Vehicle and Tire State Estimation,” Vehicle System Dynamics 57, no. 11 (2018): 1643–1665.

RIGHTS & PERMISSIONS

2026 The Author(s). International Journal of Mechanical System Dynamics published by John Wiley & Sons Australia, Ltd on behalf of Nanjing University of Science and Technology.