Bioinspired Nonlinear Dynamics-Based Adaptive Neural Network Control for Vehicle Suspension Systems With Uncertain/Unknown Dynamics and Input Delay
Abstract
A unique adaptive neural network control scheme is proposed for active suspension systems by employing bioinspired nonlinear dynamics, so as to address several critical engineering issues including energy efficiency, input delay, and unknown/uncertain dynamics simultaneously. A novel constructive predictor is firstly designed to solve the effect of input delay. Neural networks are then adopted to approximate the uncertain/unknown dynamics, and importantly, a unique finite-time adaptive control is established which can not only online update the input and output weights of the neural networks but also intentionally introduce beneficial nonlinear dynamics to vibration control. The significant difference from most existing controllers lies in that the designed controller can effectively utilize beneficial nonlinear stiffness and damping characteristics of a novel bioinspired reference model and, thus, purposely achieve superior vibration suppression and obvious energy-saving performance simultaneously. Theoretical analysis and experimental results vindicate that the proposed controller can effectively suppress vibration with much more improved control performance and considerably reduced control energy consumption more than 44%. This should be for the first time to reveal both in theory and experiments that a superior suspension performance is achieved simultaneously with an obvious control energy saving, by employing beneficial bioinspired nonlinear dynamics, compared to most traditional control methods.
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Recent research has introduced several adaptive control approaches tailored for nonlinear systems with input delays.
“Recent research has introduced several adaptive control approaches tailored for nonlinear systems with input delays [29,30].”
From Fixed-Time Adaptive Control for Nonstrict-Feedback Nonlinear Systems with Input Delay and Unknown Backlash-Like Hysteresis (2025) · cites this paper as [29]
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Liu, W., Gong, M., Xu, X., Ji, C., Zhao, D., & Chen, H. (2025) · Applied Mathematical Modelling · doi:10.1016/j.apm.2025.116314 · Cited by 3 · see citing works
Adaptive Control for Active Suspension System Based on the High-order Fully Actuated System Theory
Zhao, H., Zhang, Y., & Jiao, X. (2024) · Conference on Fully Actuated System Theory and Applications (FASTA) · doi:10.1109/fasta61401.2024.10595334 · Cited by 3 · see citing works
Energy-saving robust control of active suspension system based on bioinspired reference model
Liu, W., Gong, M., Zhao, D., Chen, H., & Zhao, D. (2024) · Proceedings of the Institution of Mechanical Engineers Part D Journal of Automobile Engineering · doi:10.1177/09544070241233841 · Cited by 3 · see citing works
“29 Afterward, Zhang et al. then put forward a sliding mode control theory using a biomimetic reference model, which does not involve approximate function 30,31 to solve the unknown dynamics of suspension.”
Li, M., & Jing, X. (2021) · Lecture notes in electrical engineering · doi:10.1007/978-981-16-5912-6_6 · Cited by 3 · see citing works
Self-citationPD sliding mode control of active suspension based on adaptive disturbance observer
sun, Z., Shao, S., Zhang, Z., Liu, J., Tang, H., Li, L., & Yuan, S. (2025) · Measurement Science and Technology · doi:10.1088/1361-6501/adead2 · Cited by 2 · see citing works
“In recent years, various represent active control methods have been proposed by scholars to address nonlinearities and parameter uncertainties in active suspension systems, including robust control [7, 8], fuzzy control [9, 10], neural network control [11], and sliding mode control [12, 13].”
Wang, W., Liu, S., Zhao, D., & Zhang, C. (2025) · ISA Transactions · doi:10.1016/j.isatra.2025.08.024 · Cited by 2 · see citing works
Gu, S., Liu, S., Yan, M., & Zhao, D. (2026) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2025.3647879 · Cited by 2 · see citing works
“However, nonlinear disturbances such as unmodeled dynamics, varying road conditions, and external forces significantly affect the suspension performance and degrade trajectory tracking control accuracy [28].”
Delay-resilient robust control of automobile active suspensions via deep reinforcement learning
Zhao, R., & Yang, S. (2026) · Results in Engineering · doi:10.1016/j.rineng.2026.109381 · Cited by 2 · see citing works
Li, W., Liang, L., Xie, Z., Wong, P. K., & Zhao, J. (2026) · Chinese Journal of Mechanical Engineering · doi:10.1016/j.cjme.2025.100137 · Cited by 2 · see citing works
Lai, H., Hu, J., Xia, K., & Yao, B. (2025) · IEEE/ASME Transactions on Mechatronics · doi:10.1109/tmech.2025.3570498 · Cited by 2 · see citing works
“I NPUT delay widely exists in electromechanical systems, chemical processes, communication networks and various scenarios [1], [2], [3], [4], which could result in poor performance and even instability if disregarded in control.”
Zhang, C., Liu, S., Zhao, D., & Wei, Y.-Q. (2025) · Vehicle System Dynamics · doi:10.1080/00423114.2025.2526068 · Cited by 1 · see citing works
“A novel bioinspired non-linear dynamics reference proposed in [13,14] can effectively harness the advantageous nonlinear stiffness and damping characteristics, leading to superior vibration suppression and significant energy-saving performance simultaneously.”
Liu, W., Gong, M., Chen, H., & Zhao, D. (2025) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2025.3621676 · Cited by 1 · see citing works
“After that, some researchers use the quasi-zero stiffness characteristics of bionic structures to design reference models for active suspension control and achieve ideal control effects [34], [35], [36].”
Wang, G., Deng, J., & Duan, D. (2025) · Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science · doi:10.1177/09544062251406280 · Cited by 1 · see citing works
Self-citationWang, G., Duan, D., & Zhou, T. (2026) · Journal of the Brazilian Society of Mechanical Sciences and Engineering · doi:10.1007/s40430-026-06392-9 · Cited by 1 · see citing works
Self-citationLi, H., Fu, S., Li, A., Du, J., Liang, X., Yu, D., & Ding, Q. (2026) · Journal of Vibration Engineering & Technologies · doi:10.1007/s42417-026-02451-6 · Cited by 1 · see citing works
“These include fuzzy logic control [25, 26], neural network approaches [27, 28], genetic algorithms [29, 30], support vector machines [31, 32], and Monte Carlo simulations [33].”
Biologically inspired novel design strategy for integrated regenerative shock absorbers: a review
Song, J., Zhang, K., Chen, Z., Li, Y., Hu, C., Zhao, X., An, T., Qi, L., & Zhang, Z. (2026) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2026.114588 · Cited by 1 · see citing works
Zhang, B.-Y., Gao, Y., Huang, T., Qin, Y., Lai, K., Li, J. Q., & Zhang, X. (2026) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2026.114562 · Cited by 1 · see citing works
Dai, Y., & Lee, K. (2022) · Measurement and Control · doi:10.1177/00202940221100517 · Cited by 1 · see citing works
“After processing LiDAR data as (5) and (6), LiDAR data is transferred to camera pixel and printed in the image as (15).”
MethodX-Shaped Structure-Based Modeling and Control for a Stable Platform with a Series Elastic Actuator
Ai, T., Wu, Q., Yang, T., Sun, L., & Sun, N. (2022) · Machines · doi:10.3390/machines10060430 · Cited by 1 · see citing works
“A new compensation mechanism is introduced to solve the problem of the input hysteresis [18].”
BackgroundHu, X., Wen, G., Yin, S., Tan, Z., & Pan, Z. (2022) · Research Square · doi:10.21203/rs.3.rs-1562013/v1 · Cited by 1 · see citing works
Qiang, H., Li, W., & Sun, Y. (2021) · Lecture notes in electrical engineering · doi:10.1007/978-981-16-5912-6_71
Identification of Stiffness Force in Nonlinear Piezoelectric Structures Based on Hilbert Transform
Liu, Q., Cao, J., Hou, Z., Zhang, Y., & Jing, X. (2021) · Lecture notes in electrical engineering · doi:10.1007/978-981-16-5912-6_43
Self-citationZhang, M., Jing, X., Zhu, Z., Li, P., & Chen, L. (2021) · Lecture notes in electrical engineering · doi:10.1007/978-981-16-5912-6_5
Self-citationMoin, H., Shah, U. H., Jawad, M., & Sajid, H. (2023) · SSRN Electronic Journal · doi:10.2139/ssrn.4354052
Road-classification-based sprung-mass adaptive suspension control system
Wu, X., Shi, W., Chen, Z., & Xuan, S. (2024) · Journal of Vibration and Control · doi:10.1177/10775463241296612
“All state parameters of the suspension system can be measured by high-precision encoders (Zhang et al., 2021).”
Jing, X. (2025) · Springer eBooks · doi:10.1007/978-981-96-5769-8_7
Self-citationVibration Suppression in Maglev Systems via Double Time-Delay Feedback ControlPreprint
Zhang, L., Zhang, Z., & Huang, L. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5829995
Adaptive prescribed performance control of nonlinear active suspension based on reference model
Ji, C., Gong, M., Liu, W., & Zhao, D. (2025) · Journal of Vibration and Control · doi:10.1177/10775463251408327
Keerthana, N., Aravinth, N., Sakthivel, R., Kwon, O. M., & Anthoni, S. M. (2026) · Journal of Dynamic Systems Measurement and Control · doi:10.1115/1.4070770
A study on a nonlinear combined dual objective control strategy for active suspension systems
Sun, Z., Yuan, S., Liu, J., Tang, H., Li, L., Zhang, Y., Shao, M., & Shao, S. (2026) · Smart Materials and Structures · doi:10.1088/1361-665x/ae3e46
“For the active suspension system, the unknown disturbance w 3 and w 4 is bounded, which is commonly adopted in [24, 27, 33].”
Liu, N., Xie, X., & Zhang, K. (2026) · IEEE/ASME Transactions on Mechatronics · doi:10.1109/tmech.2026.3656562
“However, in practical applications, suspension systems often face complex dynamic environments and uncertainties, such as changing road conditions, load fluctuations, and system parameter drift [3], [4].”
Lai, G., Zhang, T., Fan, J., Tang, J., Xiao, H., Su, X., & Chen, C. L. P. (2026) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.70566
Jing, X. (2026) · Springer eBooks · doi:10.1007/978-981-95-8295-2_5
Self-citationEvent-Triggered Control with Deferred State Constraints
Cao, L., Pan, Y., Liang, H., & Zhou, Q. (2026) · Intelligent control and learning systems · doi:10.1007/978-981-95-7742-2_7
Pang, H., Lu, Y., Liu, Y., Zhang, M., Huang, T., Zhang, Y., Zhang, Z., & 侯一哲 (2026) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2026.115017
Self-citation
- Authors
- Zhang, M., Jing, X., & Wang, G.
- Affiliations
- Hong Kong Polytechnic University (HK)
- Guizhou Institute of Technology (CN)
- Venue
- IEEE Transactions on Industrial Electronics
- Published
- 2021-12
- Volume
- 68
- Issue
- 12
- Pages
- 12646-12656
- ISSN
- 0278-0046 (ISSN-L)
- 1557-9948
- OpenAlex
- W3109407421
- Cited by
- 89
- References
- 44
- Citations by year
- 2026: 14 · 2025: 20 · 2024: 11 · 2023: 17 · 2022: 16 · 2021: 11
- FWCI
- 6.43
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- IEEE Transactions on Industrial Electronics (publishedVersion)
- Funders
- Innovation and Technology Fund (ITF) Project of HK ITC (Ref. ITP/020/19AP)
- Strategic Research Fund of the Research Institute of Urban Sustainable Development
- HK Polytechnic University
- Project of Strategic Importance of HK PolyU
- General Research Fund of HK RGC (15206717)
- Key Research and Development (Special Public-Funded Projects) of Shandong Province (2019GGX104058)
- National Natural Science Foundation for Young Scientists of China (61903155)
- Topics
- Physical Sciences › Engineering › Civil and Structural Engineering › Vibration Control and Rheological Fluids
- Physical Sciences › Engineering › Control and Systems Engineering › Adaptive Control of Nonlinear Systems
- Physical Sciences › Engineering › Automotive Engineering › Vehicle Dynamics and Control Systems
- Keywords
- active suspension, adaptive neural network control, input delay compensation, unknown dynamics, finite-time adaptive control, vibration suppression, energy efficiency, nonlinear stiffness and damping, vehicle suspension
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