Robust data-driven control for set-point tracking of linear discrete-time systems with time delays

Chengyan Wang; Xingren Chen; Shi Li; Chengyan Wang; Xingren Chen; Shi Li

doi:10.3934/era.2026281

Electronic Research Archive

2026, Volume 34, Issue 9: 6432-6447. doi: 10.3934/era.2026281

Previous Article Next Article

Research article Special Issues

Robust data-driven control for set-point tracking of linear discrete-time systems with time delays

School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210046, China

Received: 06 May 2026 Revised: 25 June 2026 Accepted: 07 July 2026 Published: 20 July 2026

This paper focused on the direct data-driven set-point tracking control problem of linear discrete-time systems with input time-delay. First, a tracking error was introduced by constructing an extended state vector through state reconstruction to generate a data-driven model. Second, a data-based tracking controller was designed with the objective of minimizing the $ L_2 $ gain from disturbances to the performance output through $ H_{ \infty} $ control, thereby reducing the impact of input delay and disturbance and ensuring asymptotic tracking stability. Finally, to validate the effectiveness and practicality of the proposed method, this paper took an autonomous direct current (DC) micro-grid with two distributed generation units as the research object. Through simulation results, the effectiveness of the data-driven method in addressing set-point tracking control issues for time-delay systems was demonstrated.
- data-driven control,
- set-point tracking,
- input time-delay,
- $ H_{ \infty} $ control
Citation: Chengyan Wang, Xingren Chen, Shi Li. Robust data-driven control for set-point tracking of linear discrete-time systems with time delays[J]. Electronic Research Archive, 2026, 34(9): 6432-6447. doi: 10.3934/era.2026281

Related Papers:

Abstract

This paper focused on the direct data-driven set-point tracking control problem of linear discrete-time systems with input time-delay. First, a tracking error was introduced by constructing an extended state vector through state reconstruction to generate a data-driven model. Second, a data-based tracking controller was designed with the objective of minimizing the $ L_2 $ gain from disturbances to the performance output through $ H_{ \infty} $ control, thereby reducing the impact of input delay and disturbance and ensuring asymptotic tracking stability. Finally, to validate the effectiveness and practicality of the proposed method, this paper took an autonomous direct current (DC) micro-grid with two distributed generation units as the research object. Through simulation results, the effectiveness of the data-driven method in addressing set-point tracking control issues for time-delay systems was demonstrated.

References

[1]	Z. S. Hou, Z. Wang, From model-based control to data-driven control: Survey, classification and perspective, Inf. Sci., 235 (2013), 3–35. https://doi.org/10.1016/j.ins.2012.07.014 doi: 10.1016/j.ins.2012.07.014
[2]	Z. S. Hou, S. T. Jin, Data-driven model-free adaptive control for a class of MIMO nonlinear discrete-time systems, IEEE Trans. Neural Networks, 22 (2011), 2173–2188. https://doi.org/10.1109/TNN.2011.2176141 doi: 10.1109/TNN.2011.2176141
[3]	Y. Wang, K. Zhao, J. L. G. Guirao, K. Pan, H. Chen, Online intelligent maneuvering penetration methods of missile with respect to unknown intercepting strategies based on reinforcement learning, Electron. Res. Arch., 30 (2022), 4366–4381. https://doi.org/10.3934/era.2022221 doi: 10.3934/era.2022221
[4]	L. Zhang, Vibration analysis and multi-state feedback control of maglev vehicle-guideway coupling system, Electron. Res. Arch., 30 (2022), 3887–3901. https://doi.org/10.3934/era.2022198 doi: 10.3934/era.2022198
[5]	J. Berberich, J. Köhler, M. A. Müller, F. Allgöwer, Data-driven model predictive control with stability and robustness guarantees, IEEE Trans. Autom. Control, 66 (2021), 1702–1717. https://doi.org/10.1109/TAC.2020.3000182 doi: 10.1109/TAC.2020.3000182
[6]	P. Yu, S. Tan, J. Guo, Y. Song, Data-driven optimal controller design for sub-satellite deployment of tethered satellite system, Electron. Res. Arch., 32 (2024), 505–522. https://doi.org/10.3934/era.2024025 doi: 10.3934/era.2024025
[7]	L. Huang, J. Zhen, J. Lygeros, F. Dörfler, Robust data-enabled predictive control: Tractable formulations and performance guarantees, IEEE Trans. Autom. Control, 68 (2023), 3163–3170. https://doi.org/10.1109/TAC.2023.3241282 doi: 10.1109/TAC.2023.3241282
[8]	M. Wang, J. Qiu, H. Yan, Y. Tian, Z. Li, Data-driven control for discrete-time piecewise affine systems, Automatica, 155 (2023), 111168. https://doi.org/10.1016/j.automatica.2023.111168 doi: 10.1016/j.automatica.2023.111168
[9]	J. G. Rueda-Escobedo, E. Fridman, J. Schiffer, Data-driven control for linear discrete-time delay systems, IEEE Trans. Autom. Control, 67 (2022), 3321–3336. https://doi.org/10.1109/TAC.2021.3096896 doi: 10.1109/TAC.2021.3096896
[10]	X. Y. Wang, G. D. Wang, S. H. Li, Distributed finite-time optimization for disturbed second-order multiagent systems, IEEE Trans. Cybern., 51 (2021), 4634–4647. https://doi.org/10.1109/TCYB.2020.2988490 doi: 10.1109/TCYB.2020.2988490
[11]	H. Modares, F. L. Lewis, Z. P. Jiang, $H_\infty$ tracking control of completely unknown continuous-time systems via off-policy reinforcement learning, IEEE Trans. Neural Networks Learn. Syst., 26 (2015), 2550–2562. https://doi.org/10.1109/TNNLS.2015.2441749 doi: 10.1109/TNNLS.2015.2441749
[12]	M. Rotulo, C. De Persis, P. Tesi, Online learning of data-driven controllers for unknown switched linear systems, Automatica, 145 (2022), 110519. https://doi.org/10.1016/j.automatica.2022.110519 doi: 10.1016/j.automatica.2022.110519
[13]	T. Hu, X. Xu, T. M. Nguyen, F. Liu, S. Yuan, L. Xie, Tire wear aware trajectory tracking control for multi-axle swerve-drive autonomous mobile robots, J. Autom. Intell., 4 (2025), 243–253. https://doi.org/10.1016/j.jai.2025.05.003 doi: 10.1016/j.jai.2025.05.003
[14]	J. X. Zhang, T. Chai, Fault-tolerant control of wheeled mobile robots with prescribed trajectory tracking performance, J. Autom. Intell., 4 (2025), 73–81. https://doi.org/10.1016/j.jai.2025.03.003 doi: 10.1016/j.jai.2025.03.003
[15]	A. S. Bazanella, L. Campestrini, D. Eckhard, The data-driven approach to classical control theory, Annu. Rev. Control, 56 (2023), 100906. https://doi.org/10.1016/j.arcontrol.2023.100906 doi: 10.1016/j.arcontrol.2023.100906
[16]	K. J. Åström, P. R. Kumar, Control: A perspective, Automatica, 50 (2014), 3–43. https://doi.org/10.1016/j.automatica.2013.10.012 doi: 10.1016/j.automatica.2013.10.012
[17]	Z. Bubnicki, Modern Control Theory, Springer Science & Business Media, Berlin, 2005. https://doi.org/10.1007/3-540-28087-1
[18]	P. J. Antsaklis, A. N. Michel, Linear Systems, Birkhäuser, Boston, 2006. https://doi.org/10.1007/0-8176-4435-0
[19]	Y. Xu, L. Zhou, J. Zhao, L. Ma, C. Yang, Direct data-driven optimal set-point tracking control of linear discrete-time systems, IEEE Trans. Circuits Syst. II Express Briefs, 71 (2024), 3795–3799. https://doi.org/10.1109/TCSII.2024.3368271 doi: 10.1109/TCSII.2024.3368271
[20]	F. Yang, J. He, D. Wang, New stability criteria of delayed load frequency control systems via infinite-series-based inequality, IEEE Trans. Ind. Inf., 14 (2018), 231–240. https://doi.org/10.1109/TII.2017.2751510 doi: 10.1109/TII.2017.2751510
[21]	Z. Jia, X. Li, Q. Cui, L. Li, Asymptotical stability of stochastic delayed time-varying systems with stochastic delayed impulses, Int. J. Syst. Sci., 56 (2025), 1662–1674. https://doi.org/10.1080/00207721.2024.2429024 doi: 10.1080/00207721.2024.2429024
[22]	Y. Liu, H. Zhang, R. Yu, Q. Qu, Data-driven optimal tracking control for discrete-time systems with delays using adaptive dynamic programming, J. Franklin Inst., 355 (2018), 5649–5666. https://doi.org/10.1016/j.jfranklin.2018.06.013 doi: 10.1016/j.jfranklin.2018.06.013
[23]	L. Cui, B. Pang, M. Krstić, Z. Jiang, Learning-based adaptive optimal control of linear time-delay systems: A value iteration approach, Automatica, 171 (2025), 111944. https://doi.org/10.1016/j.automatica.2024.111944 doi: 10.1016/j.automatica.2024.111944
[24]	K. Gu, V. L. Kharitonov, J. Chen, Introduction to Time-Delay Systems: Analysis and Control, Springer, Boston, 2014.
[25]	C. De Persis, P. Tesi, Formulas for data-driven control: Stabilization, optimality, and robustness, IEEE Trans. Automat. Control, 65 (2020), 909–924. https://doi.org/10.1109/TAC.2019.2959924 doi: 10.1109/TAC.2019.2959924
[26]	S. Derakhshan, M. Shafiee-Rad, Q. Shafiee, M. R. Jahed-Motlagh, S. Sahoo, F. Blaabjerg, Decentralized voltage control of autonomous dc microgrids with robust performance approach, IEEE J. Emerging Sel. Top. Power Electron., 9 (2021), 5508–5520. https://doi.org/10.1109/JESTPE.2021.3054723 doi: 10.1109/JESTPE.2021.3054723
[27]	V. Venkatasubramanian, H. Schattler, J. Zaborszky, Fast time-varying phasor analysis in the balanced three-phase large electric power system, IEEE Trans. Autom. Control, 40 (1995), 1975–1982. https://doi.org/10.1109/9.471228 doi: 10.1109/9.471228

Reader Comments

Your name:*

Email:*
© 2026 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)