Cost Function Reduction Using Stability-Informed Bayesian Optimization for the Model Predictive Control of a Semi-Active Suspension System
Received: 3 July 2025 | Revised: 28 July 2025 and 16 August 2025 | Accepted: 20 August 2025 | Online: 6 October 2025
Corresponding author: S. N. Prasad
Abstract
Traditional Model Predictive Control (MPC) performance is very sensitive to the state-weighting matrix and the control-weighting , resulting in time-consuming and suboptimal results. This work introduces a smart control approach for semi-active suspension systems that combines MPC with Stability-informed Bayesian Optimization (SiBO). The Bayesian framework uses a neural network surrogate model to approximate the cost function, significantly reducing the number of iterations required for optimization. Using a quarter-car model with a Magnetorheological (MR) damper, the method tackles the challenge of non-linear damping by linearizing it and directly integrating it into the MPC cost function. This reduces the computational load and makes the control more suitable for real-time use. The proposed strategy optimizes the damping coefficient to balance ride comfort and stability. Compared to traditional methods, it delivers clear improvements. The system showed a 15% reduction in Root Mean Square (RMS) body acceleration and a 12% improvement in suspension travel over standard Proportional–Integral–Derivative (PID)-tuned damping. It also achieved faster convergence, reaching optimal performance in just 10 iterations. In contrast, Particle Swarm Optimization (PSO) and Genetic Algorithms (GAs) required more than 50 iterations to reach such results.
Keywords:
semi-active suspension, Model Predictive Control (MPC), cost function reduction, Bayesian Optimization (BO), ride comfort, vehicle stabilityDownloads
References
I. T. Jiregna and G. Sirata, "A review of the vehicle suspension system," Journal of Mechanical and Energy Engineering, vol. 4, no. 2, pp. 109–114, Nov. 2020.
G. Ji et al., "Research on variable universe fuzzy PID control for semi-active suspension with CDC dampers based on dynamic adjustment functions," Scientific Reports, vol. 14, no. 1, Feb. 2024, Art. no. 3442.
D. Karnopp, M. J. Crosby, and R. A. Harwood, "Vibration Control Using Semi-Active Force Generators," Journal of Engineering for Industry, vol. 96, no. 2, pp. 619–626, May 1974.
S.-B. Choi, H.-S. Lee, and Y.-P. Park, "H8 Control Performance of a Full-Vehicle Suspension Featuring Magnetorheological Dampers," Vehicle System Dynamics, vol. 38, no. 5, pp. 341–360, Oct. 2002.
M. M. ElMadany and Z. S. Abduljabbar, "Linear Quadratic Gaussian Control of a Quarter-Car Suspension," Vehicle System Dynamics, vol. 32, no. 6, pp. 479–497, Dec. 1999.
Y. Shen, "Vehicle Suspension Vibration Control with Magnetorheological Dampers," Ph.D. dissertation, University of Waterloo, Waterloo, Canada, 2006.
Y. Tsai, K. Mai, and K. Shyu, "Sliding mode control for unmatched uncertain systems with totally invariant property and exponential stability," Journal of the Chinese Institute of Engineers, vol. 29, no. 1, pp. 179–183, Jan. 2006.
A. J. Barr and J. I. Ray, "Control of an active suspension using fuzzy logic," in Proceedings of IEEE 5th International Fuzzy Systems, New Orleans, LA, USA, 1996, pp. 42–48 vol.1.
N. Al-Holou, D. S. Joo, and A. Shaout, "The development of fuzzy logic based controller for semi-active suspension system," in Proceedings of 1994 37th Midwest Symposium on Circuits and Systems, Lafayette, LA, USA, 1994, pp. 1373–1376 vol.2.
P. Gandhi, S. Adarsh, and K. I. Ramachandran, "Performance Analysis of Half Car Suspension Model with 4 DOF using PID, LQR, FUZZY and ANFIS Controllers," Procedia Computer Science, vol. 115, pp. 2–13, Jan. 2017.
D. Savaresi, F. Favalli, S. Formentin, and S. M. Savaresi, "On-line Damping Estimation in Road Vehicle Semi-active Suspension Systems," IFAC-PapersOnLine, vol. 52, no. 5, pp. 679–684, Jan. 2019.
J. Guanetti and F. Borrelli, "Stochastic MPC for cloud-aided suspension control," in 2017 IEEE 56th Annual Conference on Decision and Control, Melbourne, Australia, 2017, pp. 238–243.
O. A. Dahunsi and J. O. Pedro, "Neural Network-Based Identification and Approximate Predictive Control of a Servo-Hydraulic Vehicle Suspension System," Engineering Letters, vol. 18, no. 4, Nov. 2010, Art. no. EL_18_4_5.
M. A. Sehr and R. R. Bitmead, "Stochastic output-feedback model predictive control," Automatica, vol. 94, pp. 315–323, Aug. 2018.
B. K. Cho, "Active suspension controller design using MPC with preview information," KSME International Journal, vol. 13, no. 2, pp. 168–174, Feb. 1999.
K. Çalışkan, R. Henze, and F. Küçükay, "Potential of Road Preview for Suspension Control under Transient Road Inputs," IFAC-PapersOnLine, vol. 49, no. 3, pp. 117–122, Jan. 2016.
N. Giorgetti, A. Bemporad, H. E. Tseng, and D. Hrovat, "Hybrid Model Predictive Control Application Towards Optimal Semi-Active Suspension," in Proceedings of the IEEE International Symposium on Industrial Electronics, 2005, Dubrovnik, Croatia, 2005, vol. 1, pp. 391–398.
M. M. Morato, O. Sename, and L. Dugard, "LPV-MPC Fault Tolerant Control of Automotive Suspension Dampers," IFAC-PapersOnLine, vol. 51, no. 26, pp. 31–36, Jan. 2018.
J. Hou, X. Cao, and C. Zhan, "Symmetry Control of Comfortable Vehicle Suspension Based on H∞," Symmetry, vol. 14, no. 1, Jan. 2022, Art. no. 171.
G. Guastadisegni et al., "Ride analysis tools for passenger cars: objective and subjective evaluation techniques and correlation processes – a review," Vehicle System Dynamics, vol. 62, no. 7, pp. 1876–1902, Jul. 2024.
C. Göhrle, A. Schindler, A. Wagner, and O. Sawodny, "Model Predictive Control of semi-active and active suspension systems with available road preview," in 2013 European Control Conference, Zurich, Switzerland, 2013, pp. 1499–1504.
M. Ghoniem, T. Awad, and O. Mokhiamar, "Control of a new low-cost semi-active vehicle suspension system using artificial neural networks," Alexandria Engineering Journal, vol. 59, no. 5, pp. 4013–4025, Oct. 2020.
A. Khadr, A. Houidi, and L. Romdhane, "Design and optimization of a semi-active suspension system for a two-wheeled vehicle using a full multibody model," Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, vol. 231, no. 4, pp. 630–646, Dec. 2017.
M. J. Mahmoodabadi, A. A. Safaie, A. Bagheri, and N. Nariman-zadeh, "A novel combination of Particle Swarm Optimization and Genetic Algorithm for Pareto optimal design of a five-degree of freedom vehicle vibration model," Applied Soft Computing, vol. 13, no. 5, pp. 2577–2591, May 2013.
Q. Liu et al., "A Fractional-Order Model Predictive Control Strategy with Takagi–Sugeno Fuzzy Optimization for Vehicle Active Suspension System," Fractal and Fractional, vol. 8, no. 10, Oct. 2024, Art. no. 610.
H. V. Nguyen, F. Deng, and T.-D. Nguyen, "Optimal FLC-Sugeno Controller based on PSO for an Active Damping System," Engineering, Technology & Applied Science Research, vol. 14, no. 1, pp. 12769–12774, Feb. 2024.
S. Hirt, M. Pfefferkorn, A. Mesbah, and R. Findeisen, "Stability-informed Bayesian Optimization for MPC Cost Function Learning," IFAC-PapersOnLine, vol. 58, no. 18, pp. 208–213, Jan. 2024.
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