Adaptive neural network predictive control for nonlinear pure feedback systems with input delay
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This paper simultaneously considers the influence of both backlash-like hysteresis and input delay in nonstrict-feedback nonlinear systems.
“Unlike studies such as [16,17], which focus solely on backlash hysteresis, or [31,32], which primarily address input delay, this paper simultaneously considers the influence of both backlash-like hysteresis and input delay in nonstrict-feedback nonlinear systems.”
From Fixed-Time Adaptive Control for Nonstrict-Feedback Nonlinear Systems with Input Delay and Unknown Backlash-Like Hysteresis (2025) · cites this paper as [32]
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Self-citationInput Delay Estimation for Input-Affine Dynamical Systems Based on Taylor Expansion
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“The units and values of the parameters are shown in Table I [4], [26].”
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“[4] where an adaptive NNobserver was designed for nonlinear systems.”
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“Therefore, [36] designed an observer-based NN adaptive control schemes for the uncertain nonlinear systems.”
BackgroundNetworked Predictive Control: A Survey
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Tensor Product-Based Model Transformation Technique Applied to Modeling Vertical Three Tank Systems
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“Several control structures for the level control in the V3TS include neural networks [10], fuzzy control [11], and switched model predictive control [12].”
MethodA survey on hyper basis function neural networks
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“Some representative results on adaptive MPC include adaptive single-loop MPC [14], adaptive MPC with comparison model [15], [16], adaptive persistently-excited MPC [17], adaptive MPC with neural networks [18], and nonlinear adaptive MPC [19].”
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“Thus, system (20) is an asymptotically stable system under the supervision controller.”
BackgroundRobust Predictive Discrete-Time Controller in Constrained Systems With Uncertain and Delayed Terms
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“Utilizing a neural network, a predictive scheme is adaptively suggested for delayed models with nonlinearity [7].”
MethodTensor product-based model transformation for level control of vertical three tank systems
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“Several control structures for the level control in the V3TS include neural networks [17], [18], IFT–based linear and fuzzy control [19], [20], and switched model predictive control [21].”
MethodControl Solutions for Vertical Three-Tank Systems
Bojan‐Dragos, C., Szedlak-Stinean, A.-I., Precup, R., Gurgui, L., Hedrea, E., & Mituleţu, I.-C. (2018) · IEEE International Symposium on Applied Computational Intelligence and Informatics (SACI) · doi:10.1109/saci.2018.8440939 · Cited by 6 · see citing works
“Several control structures for the level control in the three-tank systems include the popular Proportional-IntegralDerivative (PID) control [1], neural networks [2], [3], IFT–based linear and fuzzy control [4], [5], switched model predictive control [6], robust and fuzzy predictive control [7], gain-scheduling contro…”
MethodZhang, G., & Zhang, X. (2016) · International Journal of Control Automation and Systems · doi:10.1007/s12555-015-0054-7 · Cited by 6 · see citing works
“Nonlinearly parameterized and periodically time-varying disturbances often exist in many industrial processes such as marine control system, industrial robots and other industrial systems depending on the frequency of the power supply [1, 2].”
BackgroundAdaptive Control for Pure-Feedback Nonlinear Systems Preceded by Asymmetric Hysteresis
Lai, X., Pan, H., & Zhao, X. (2019) · Energies · doi:10.3390/en12244675 · Cited by 6 · see citing works
Kharrat, M., & Alhazmi, H. (2025) · Neural Processing Letters · doi:10.1007/s11063-025-11749-7 · Cited by 5 · see citing works
“Additionally, a method using adaptive neural network predictive control has been applied to pure feedback nonlinear systems with input delays [32].”
Fault-Tolerant Control of Unmanned Surface Vehicle with Input and State Quantization
Ning, J., Cui, R., Li, T., & Liu, L. (2025) · Nonlinear Dynamics · doi:10.1007/s11071-025-10921-x · Cited by 5 · see citing works
Deep representation-based packetized predictive compensation for networked nonlinear systems
Chen, S., Cao, Y. H., Kang, Y., Sun, B., & Wang, X. (2020) · Neural Computing and Applications · doi:10.1007/s00521-020-05346-z · Cited by 4 · see citing works
RBF Neural Control Design for SISO Nonaffine Nonlinear Systems
Kumar, P., Kumar, N., & Panwar, V. S. (2018) · Procedia Computer Science · doi:10.1016/j.procs.2017.12.006 · Cited by 4 · see citing works
Adaptive Parameter Estimation and Velocity Control of UAV Systems
Gui, H., Sun, R., & Chen, J. (2018) · Chinese Control Conference (CCC) · doi:10.23919/chicc.2018.8483199 · Cited by 4 · see citing works
“At present, the research focus on the parameter identification method of nonlinear aerodynamic parameters and nonlinear closed-loop system([9,10,11,12]).”
BackgroundWang, R., Yu, F., & Wang, J. (2014) · Asian Journal of Control · doi:10.1002/asjc.1028 · Cited by 4 · see citing works
“As mentioned in [15], Ge first proposed a novel technique for a pure-feedback system that was not based on the backstepping scheme.”
MethodArtificial Neural Network Control of Chemical Processes
Ahmed, D. F. (2014) · Engineering and Technology Journal · doi:10.30684/etj.32.1a.14 · Cited by 4 · see citing works
Wang, R., Yu, F., Liu, Y., Wang, J., Yu, L. Z., & Zhao, L. (2018) · Nonlinear Analysis Hybrid Systems · doi:10.1016/j.nahs.2018.07.001 · Cited by 4 · see citing works
Dias, C. G., Librantz, A. F. H., & dos Santos, F. C. R. (2020) · Engenharia Sanitaria e Ambiental · doi:10.1590/s1413-41522020173961 · Cited by 3 · see citing works
Mohammadzaheri, M., & Ghodsi, M. (2023) · International Conference on Automation and Computing (ICAC) · doi:10.1109/icac57885.2023.10275221 · Cited by 3 · see citing works
“In fact, (12) is the combination of a single-delay two-output model presented in [18] and a double-input model of [19]; it also includes all possible delays, neglected in previous research.”
BackgroundInfluentialCascade Control Solutions for Level Control of Vertical Three Tank Systems
Hedrea, E., Precup, R., Bojan‐Dragos, C., Hedrea, C., Ples, D., & Popovici, D. (2019) · IEEE International Symposium on Applied Computational Intelligence and Informatics (SACI) · doi:10.1109/saci46893.2019.9111542 · Cited by 3 · see citing works
“An overview of some recent control structures for the level control in the three-tank systems includes: the popular Proportional–Integral– Derivative (PID) control [1], neural networks [2], [3], IFT– based linear and fuzzy control [4], [5], switched model predictive control [6], robust and fuzzy predictive control [7]…”
MethodNeural Network-Based Robust Adaptive Output Feedback Control for MIMO Time-Varying Delay Systems
Zouari, F., & Mahmud, M. (2025) · Communications in computer and information science · doi:10.1007/978-3-031-98498-3_5 · Cited by 2 · see citing works
Adaptive neural network control with predictive compensation for uncertain nonlinear systems
Niu, L. (2012) · International Conference on Advanced Computational Intelligence (ICACI) · doi:10.1109/icaci.2012.6463221 · Cited by 2 · see citing works
Wu, Y., Zhuang, G., Jiang, M., & Wang, Y. (2024) · Applied Mathematics and Computation · doi:10.1016/j.amc.2024.129158 · Cited by 1 · see citing works
Li, X., He, D., Zhang, Q., & Liu, H. (2025) · Nonlinear Dynamics · doi:10.1007/s11071-025-11385-9 · Cited by 1 · see citing works
“In order to address the effects of input delay, an adaptive predictor combined with high-order NNs observer has been proposed to overcome input delay in [18].”
Liu, K., Yang, X., Lyu, S., Wang, R., Gao, C., & Liu, Y. (2025) · IEEE Access · doi:10.1109/access.2025.3609753 · Cited by 1 · see citing works
“…problems, advanced control techniques, including sliding mode control [5], [6], [7], [8], adaptive neural network (NN) control [9], [10], [11], [12], [13], and feedback linearization [14], [15], have been widely The associate editor coordinating the review of this manuscript and approving it…”
Kharrat, M., Alhazmi, H., Mhemdi, A., & Gargouri, A. (2026) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.70036 · Cited by 1 · see citing works
Cognitive Control for Decision and Human-Robot Collaboration
Pulgarín, E. J. L., Leonards, U., & Herrmann, G. (2022) · The MIT Press eBooks · doi:10.7551/mitpress/13780.003.0023 · Cited by 1 · see citing works
Research on Neural Network Model for Greenhouse Temperature Predictive Control
Qi, K. C., Chen, Y., Liu, B., & Du, S. (2013) · Lecture notes in electrical engineering · doi:10.1007/978-3-642-38524-7_60 · Cited by 1 · see citing works
“Model predictive control is an algorithm that has been widely applied to industrial field [7].”
MethodAdaptive Neural Network Control for Uncertain Nonlinear Systems with Asymptotic Stability Guarantees
Niu, L. (2013) · International Conference on Intelligent Human-Machine Systems and Cybernetics · doi:10.1109/ihmsc.2013.278 · Cited by 1 · see citing works
New 5-Step Discrete-Time Zeroing Neuronet for Time-Dependent Matrix Square Root Finding
Liu, X., Hu, C., Kang, X., Mao, M., Zhang, Y., & Qiu, B. (2019) · International Conference on Systems and Informatics (ICSAI) · doi:10.1109/icsai48974.2019.9010145 · Cited by 1 · see citing works
“On account of the in-depth investigation of neuronets [11], as one of the important approaches, recurrent neuronent can handle various scientific and engineering problems [12]– [14].”
BackgroundLi, X., Zhang, Q., & He, D. (2020) · Complexity · doi:10.1155/2020/8859328 · Cited by 1 · see citing works
“mentioning that an adaptive predictor incorporated with a high-order neural network observer was proposed to obtain the predictions of the future system states in pure-feedback systems in [28], which were applied in the control design to avoid the input delay and nonlinearities.”
MethodCastamann, G., Veit, M. T., Colombo, W. L. R., Palácio, S. M., Gonçalves, G. D. C., & Zanette, J. C. (2022) · Research Society and Development · doi:10.33448/rsd-v11i11.33976 · Cited by 1 · see citing works
Data-driven performance improvement of control systems for three-tank systems
Precup, R., Rădac, M., Petriu, E. M., Bojan‐Dragos, C., Preitl, Ș., & Szedlak-Stinean, A.-I. (2013) · Conference on Human System Interactions · doi:10.1109/hsi.2013.6577840
Wang, R., Lin, S., Wen, L., & Yu, L. (2016) · Chinese Control and Decision Conference (CCDC) · doi:10.1109/ccdc.2016.7530947
“So, we adopt non-backstepping technique to construct controller directly; In addition, different from using FLSs or NN as approximation to model unknown functions [20-23], we adopt VUFC scheme to construct controller.”
MethodFeasibility Study of Fast Output Sampling based State Estimation Technique
Patel, S. B., Mukhopadhyay, S., & Tiwari, A. P. (2019) · IEEE International Conference for Convergence in Technology (I2CT) · doi:10.1109/i2ct45611.2019.9033811
“Considering the state vector, x = [CA(t) T (t)] the linearized model at the steady state operating point can be represented in the standard state space form as follows: TABLE I NOMINAL OPERATING POINTS [8]”
BackgroundAn Associatively Recursive Dynamic Backstepping Control Design for Pure-Feedback Nonlinear Systems
Zhang, S., Du, X., Hu, F., & Huang, J. (2021) · Chinese Control Conference (CCC) · doi:10.23919/ccc52363.2021.9550542
“[13] resorted to the mean-value theorem to obtain the affine form for the backstepping controller design.”
MethodTensor Product-based and State Feedback Structures for Level Control of Vertical Three Tank Systems
Hedrea, E., Precup, R., Roman, R., Bojan‐Dragos, C., Szedlak-Stinean, A.-I., & Hedrea, C. (2022) · International Conference on System Theory, Control and Computing (ICSTCC) · doi:10.1109/icstcc55426.2022.9931892
“: in [1], a Proportional–Integral–Derivative (PID) controller is given, in [2] and [3] neural networks are used, the IFT–based linear and fuzzy control are given in [4] and [5], switched model predictive control is presented in [6], gain-scheduling control is treated in [7] and [8], sliding mode iterative learning con…”
MethodNon-singular control strategies for a class of strict-feedback nonlinear time-delay systems
Zhao, Y., Liu, X., Liu, C., & Wang, H. (2024) · International Journal of Control · doi:10.1080/00207179.2024.2351054
“As for systems with input time delay, in Li et al. (2017), Na et al. (2012), Niu and Li (2016), Yousef (2014) and C. Wu et al. (2017), neural networks and fuzzy logics were widely applied to deal with the control problems for nonlinear systems with input time delay.”
Zhang, Q., Shao, X., Xu, Y., & Deng, R. (2024) · International Symposium on Intelligent Unmanned Systems and Artificial Intelligence (SIUSAI) · doi:10.1145/3669721.3669972
Adaptive Neural Control of High-Order Nonaffine Systems
Meng, W., & Yang, Q. (2025) · Elsevier eBooks · doi:10.1016/b978-0-443-14081-5.00035-0
Qiu, R., Xia, M., Zhang, J., & Ma, C. (2025) · IEEE Access · doi:10.1109/access.2025.3574842
“Reference [28] proposes a solution for nonlinear pure-feedback systems with input delays by utilizing high-order neural network observers and adaptive predictors to forecast future system states.”
Sampling-Horizon Neural Operator Predictors for Nonlinear Control Under Delayed Inputs
Bhan, L., Quawas, P., Krstic, M., & Shi, Y. (2026) · IEEE Control Systems Letters · doi:10.1109/lcsys.2026.3698435
“However, there are a series of works with finite-dimensional neural network (NN) approximations worth recognizing, including adaptive NN control under unknown delays [1], predictive control for pure-feedback systems with input delay [2], and state-constrained control with input delay [3].”
An Enhanced Smith-Predictor-Based Control Law for a MIMO CSTR with Multiple Time Delays
Mohammadzaheri, M., Al-Humairi, A., Vakili-Nezhaad, G. R., Azizi, A., Ghodsi, M., & Soltani, P. (2026) · Mathematics · doi:10.3390/math14183416
- Authors
- Na, J., Ren, X., Shang, C., & Guo, Y.
- Affiliations
- Kunming University of Science and Technology (CN)
- Beijing Institute of Technology (CN)
- Corresponding author
- Na, Jing
- Venue
- Journal of Process Control
- Publisher
- Elsevier BV
- Published
- 2012-01
- Volume
- 22
- Issue
- 1
- Pages
- 194-206
- ISSN
- 0959-1524 (ISSN-L)
- OpenAlex
- W2038724059
- Cited by
- 101
- References
- 46
- Citations by year
- 2026: 5 · 2025: 7 · 2024: 4 · 2023: 3 · 2022: 5 · 2021: 4 · 2020: 6 · 2019: 11 · 2018: 14 · 2017: 9 · 2016: 7 · 2015: 7 · 2014: 9 · 2013: 8 · 2012: 2
- FWCI
- 9.69
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Process Control (publishedVersion)
- Bristol Research (University of Bristol) (submittedVersion)
- Explore Bristol Research (submittedVersion)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Optimization
- Physical Sciences › Engineering › Control and Systems Engineering › Adaptive Control of Nonlinear Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Keywords
- adaptive neural network control, predictive control, input delay, state prediction, output feedback control, closed-loop stability, continuous stirred tank reactor
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