Adaptive Encoding-Decoding Protocol to SMC for Multiple-Rate Stochastic Systems With Optimized Dynamic Quantization

Jianlin Bai; Jun Cheng; Huaicheng Yan; Michael V. Basin; Leszek Rutkowski

doi:10.1109/JAS.2026.125969

Volume 13 Issue 10

Oct. 2026

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 18.3, Top 1 (SCI Q1)

CiteScore: 28.2, Top 1% (Q1)
Google Scholar h5-index: 95， TOP 5

Turn off MathJax

Article Contents

Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2026 > 13(10): 2367-2377

J. Bai, J. Cheng, H. Yan, M. V. Basin, and L. Rutkowski, “Adaptive encoding-decoding protocol to SMC for multiple-rate stochastic systems with optimized dynamic quantization,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 10, pp. 2367–2377, Oct. 2026. doi: 10.1109/JAS.2026.125969

Citation:

J. Bai, J. Cheng, H. Yan, M. V. Basin, and L. Rutkowski, “Adaptive encoding-decoding protocol to SMC for multiple-rate stochastic systems with optimized dynamic quantization,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 10, pp. 2367–2377, Oct. 2026. doi: 10.1109/JAS.2026.125969

Citation:

J. Bai, J. Cheng, H. Yan, M. V. Basin, and L. Rutkowski, “Adaptive encoding-decoding protocol to SMC for multiple-rate stochastic systems with optimized dynamic quantization,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 10, pp. 2367–2377, Oct. 2026. doi: 10.1109/JAS.2026.125969

PDF( 1679 KB)

Adaptive Encoding-Decoding Protocol to SMC for Multiple-Rate Stochastic Systems With Optimized Dynamic Quantization

doi: 10.1109/JAS.2026.125969

Funds: This work was supported by the National Natural Science Foundation of China (62173100) and the Key Laboratory of Interdisciplinary Research for Data Science (Guangxi Normal University), Education Department of Guangxi Zhuang Autonomous Region

More Information

Author Bio:
Jianlin Bai received the B.S. degree in mathematics from Guangxi Normal University in 2023, and the M.S. degree in applied mathematics from Guangxi Normal University in 2026. His research interests include networked control systems

Jun Cheng (Senior Member, IEEE) received the B.S. degree in mathematics and applied mathematics from Hubei University for Nationalities in 2010, and the Ph.D. degree from the University of Electronic Science and Technology of China in 2015. From 2015 to 2019, he was a Staff with the Hubei University for Nationalities. He was a Visiting Scholar with the Department of Electrical and Computer Engineering, National University of Singapore, Singapore, from 2013 to 2014, and the Department of Electrical Engineering, Yeungnam University, Gyeongsan, South Korea, in 2016 and 2018. Since 2019, he has been with Guangxi Normal University. His current research interests include analysis and synthesis for networked control systems and multi-agent systems. Dr. Cheng has been a recipient of the Highly Cited Researcher Award listed by Clarivate Analytics in 2019−2022. He has served as an Associate Editor for several international journals, including IEEE Transactions on Fuzzy Systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, IEEE Transactions on Industrial Cyber-Physical Systems, International Journal of Control, Automation, and Systems, and Franklin Open

Huaicheng Yan received the B.Sc. degree in automatic control from Wuhan University of Technology in 2001, and the Ph.D. degree in control theory and control engineering from Huazhong University of Science and Technology in 2007. He is currently a Professor with the School of Information Science and Engineering, East China University of Science and Technology. His research interests include networked control systems, multiagent systems, and robotics. Dr. Yan is an Associate Editor for IEEE Transactions on Neural Networks and Learning Systems, IEEE Transactions on Fuzzy Systems, and International Journal of Robotics and Automation

Michael V. Basin (Fellow, IEEE) received the Ph.D. degree in physical and mathematical sciences with a major in automatic control and system analysis from Moscow Aviation University (MAI), Moscow, Russia, in 1992. He is currently a Full Professor with the Autonomous University of Nuevo Leon, San Nicolas’de los Garza, Mexico, and a Distinguished Professor with Ningbo University of Technology. Since 1992, he has published more than 400 research articles in international refereed journals and conference proceedings. He is the author of the monograph New Trends in Optimal Filtering and Control for Polynomial and Time-Delay Systems (Springer). His works are cited more than 10k times (H-index = 53). He has supervised 17 doctoral and 11 master’s theses. His research interests include variable structure systems and sliding mode control, fully actuated systems, nonlinear and robust control, stochastic systems, applications to mechatronic, robotic, aerospace, and transportation systems

Leszek Rutkowski (Life Fellow, IEEE) received the M.Sc., Ph.D., and D.Sc. degrees from Wrocław University of Technology, Wrocław, Poland, in 1977, 1980, and 1986, respectively, and the Honoris Causa degree from the AGH University of Krakow, Krakow, Poland, in 2014. From 1987 to 1990, he was a Visiting Professor at Oklahoma State University, Stillwater, OK, USA. He is currently a Professor with the Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland, and AGH University of Krakow. He has published over 400 papers, including more than 70 in IEEE Transactions journals and leading AI conferences such as ICDM, AAAI, ICML, and ICLR. His research interests include machine learning, data mining, large language models (LLMs), agent systems, and stochastic modeling and control. Dr. Rutkowski was a Member of Academia Europaea in 2022 and European Academy of Sciences and Arts in 2023 and a Full Member of the Polish Academy of Sciences in 2016. He received the IEEE Transactions on Neural Networks Outstanding Paper Award. He is the Founder and the President of the Polish Neural Networks Society and the General Chair of the International Conference on Artificial Intelligence and Soft Computing (ICAISC) from 1994 to 2025. He is also the Editor-in-Chief of Journal of Artificial Intelligence and Soft Computing Research
Corresponding author: Jun Cheng, e-mail: jcheng@gxnu.edu.cn; Michael V. Basin, e-mail: mbasin@nbut.edu.cn
Received Date: 2025-12-22
Accepted Date: 2026-02-26

Abstract

Abstract

This study presents an adaptive encoding-decoding protocol to sliding mode control for multiple-rate stochastic systems employing optimized dynamic quantization. To facilitate tractable analysis without resorting to lifting techniques, a unified stochastic modeling framework is adopted, in which a non-homogeneous Markov process is employed to characterize the interaction between multi-rate sampling, zero-order hold behavior, and controller switching. A measurement-output-driven dynamic encoding-decoding protocol is then constructed, where both the quantized measurement and its associated quantization parameter are jointly transmitted, enabling accurate reconstruction and explicit characterization of decoding errors. By incorporating the resulting error bounds into a Lyapunov-based analysis, sufficient conditions are derived to guarantee mean-square exponential ultimate boundedness and sliding surface reachability. Furthermore, a co-design optimization framework based on a differential evolution algorithm is developed to jointly determine controller parameters and performance indices. Simulation results on a direct-current (DC) motor system demonstrate the effectiveness of the proposed approach.
- Differential evolution algorithm (DEA),
- dynamic quantization,
- encoding-decoding protocol (EDP),
- multi-rate systems,
- sliding mode control (SMC)

FullText(HTML)

References(30)

References

[1]	L. Zou, Z. Wang, B. Shen, and H. Dong, “Encryption-decryption-based state estimation with multirate measurements against eavesdroppers: A recursive minimum-variance approach,” IEEE Trans. Autom. Control, vol. 68, no. 12, pp. 8111–8118, Dec. 2023. doi: 10.1109/TAC.2023.3288624
[2]	Y. Wu, J. Cheng, and Z.-G. Wu, “Fuzzy-affine-model-based filtering design with memory-based dynamic event-triggered protocol,” IEEE Trans. Fuzzy Syst., vol. 31, no. 4, pp. 1340–1351, Apr. 2023. doi: 10.1109/TFUZZ.2022.3199822
[3]	L. Zhang, L. Xie, W. Dai, S. Lu, and H. Su, “Operational optimal tracking control for industrial multirate systems subject to unknown disturbances,” IEEE Trans. Syst. Man Cybern. Syst., vol. 54, no. 1, pp. 180–192, Jan. 2024. doi: 10.1109/TSMC.2023.3305245
[4]	K. Feng and C. Liu, “Multi-rate sampling control design and stability analysis for frequency and voltage regulation in islanded microgrids,” IEEE Trans. Sustain. Energy, vol. 14, no. 1, pp. 704–716, Jan. 2023. doi: 10.1109/TSTE.2022.3225081
[5]	D. Zheng, L. Zhou, and Z. Song, “Kernel generalization of multi-rate probabilistic principal component analysis for fault detection in nonlinear process,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 8, pp. 1465–1476, Aug. 2021. doi: 10.1109/JAS.2021.1004090
[6]	J. Cheng, H. Pang, H. Yan, and D. Zhang, “Protocol-based PID control of switched systems with DoS attacks,” IEEE Trans. Inform. Forensics Sec., vol. 20, pp. 8059–8068, Aug. 2025. doi: 10.1109/TIFS.2025.3594552
[7]	X. Wang, S. Zhao, M. Yang, X. Wang, and X. Wu, “Neural network-based state estimation for nonlinear systems with denial-of-service attack under try-once-discard protocol,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 10, pp. 2182–2184, Oct. 2024. doi: 10.1109/JAS.2023.123690
[8]	Y. Ju, Y. Chen, D. Ding, G. Wei, and Y. Sun, “Neural-network-based distributed state estimation under encoding-decoding schemes: Probabilistic-constrained cases,” IEEE Trans. Syst. Man Cybern. Syst., vol. 55, no. 8, pp. 5332–5344, Aug. 2025. doi: 10.1109/TSMC.2025.3571783
[9]	J. Hu, S. Fan, C. Chen, H. Liu, and X. Yi, “Encoding-decoding-based distributed fusion filtering for multi-rate nonlinear systems with sensor resolutions,” IEEE Trans. Signal Inform. Proc. Netw., vol. 9, pp. 811–822, Nov. 2023.
[10]	H. Wang, Y. Peng, and Y. Wang, “Quantized communications in target enclosing of autonomous surface vehicles with prescribed performance control: Theory and experiment,” IEEE Trans. Veh. Technol., vol. 74, no. 10, pp. 15040–15049, Oct. 2025. doi: 10.1109/TVT.2025.3568016
[11]	Z. Chen, P. Yi, L. Li, and Y. Hong, “Distributed time-varying convex optimization with dynamic quantization,” IEEE Trans. Cybern., vol. 53, no. 2, pp. 1078–1092, Feb. 2023. doi: 10.1109/TCYB.2021.3099905
[12]	M. Li, J. Liang, and J. Qiu, “Set-membership filtering for 2-D systems under uniform quantization and weighted try-once-discard protocol,” IEEE Trans. Circ. Syst. II Express Briefs, vol. 70, no. 9, pp. 3474–3478, Sep. 2023. doi: 10.1201/9781003189497-5
[13]	T. Liu, D. Shen, and J. Wang, “Adaptive quantized iterative learning control using encoding-decoding strategy,” IEEE Trans. Cybern., vol. 55, no. 3, pp. 1359–1371, Mar. 2025. doi: 10.1109/TCYB.2024.3524240
[14]	D. Liberzon, “Hybrid feedback stabilization of systems with quantized signals,” Automatica, vol. 39, no. 9, pp. 1543–1554, Sep. 2003. doi: 10.1016/S0005-1098(03)00151-1
[15]	J. Li, Y. Niu, and D. W. C. Ho, “Dynamic coding-based control scheme under Lossy digital network: An optimized time-varying packet length approach,” IEEE Trans. Cybern., vol. 54, no. 5, pp. 2955–2965, May 2024. doi: 10.1109/TCYB.2022.3232529
[16]	X. Zhang, S. He, Y. Tan, and W. Zhang, “Sliding mode control of Markov jump systems: Multi-processor based observer approach,” Automatica, vol. 174, Art. no. Art. no. 112132, Apr. 2025. doi: 10.1016/j.automatica.2025.112132
[17]	Z. Wu, Y. Zhao, F. Li, T. Yang, Y. Shi, and W. Gui, “Asynchronous learning-based output feedback sliding mode control for semi-Markov jump systems: A descriptor approach,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 6, pp. 1358–1369, Jun. 2024. doi: 10.1109/JAS.2024.124416
[18]	T. Xu, Y. Niu, and Z. Cao, “Attack-tolerant control for Markovian jump systems with stochastic sampling: A sliding mode scheme,” Automatica, vol. 161, Art. no. Art. no. 111496, Mar. 2024. doi: 10.1016/j.automatica.2023.111496
[19]	S. Abrazeh, A. Parvaresh, S.-R. Mohseni, M. J. Zeitouni, M. Gheisarnejad, and M. H. Khooban, “Nonsingular terminal sliding mode control with ultra-local model and single input interval type-2 fuzzy logic control for pitch control of wind turbines,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 3, pp. 690–700, Mar. 2021. doi: 10.1109/JAS.2021.1003889
[20]	X. Qi, L. Zhu, X. Li, and R. Gong, “Observer-based event-triggered sliding mode security control for nonlinear cyber-physical systems under DoS attacks,” IEEE Trans. Autom. Sci. Eng., vol. 21, no. 4, pp. 7480–7493, Oct. 2024. doi: 10.1109/TASE.2023.3343752
[21]	D. Zhao, Z. Wang, L. Wang, and G. Wei, “Proportional-integral observer design for multirate-networked systems under constrained bit rate: An encoding-decoding mechanism,” IEEE Trans. Cybern., vol. 53, no. 7, pp. 4280–4291, Jul. 2023. doi: 10.1109/TCYB.2022.3165041
[22]	N. Huo, D. Shen, and D. W. C. Ho, “Encoding-decoding-based quantized learning control using spherical polar coordinates,” IEEE Trans. Cybern., vol. 55, no. 2, pp. 812–825, Feb. 2025. doi: 10.1109/TCYB.2024.3496794
[23]	Y. Wang, Z. Wang, L. Zou, Q. Ge, and H. Dong, “Observer-based fuzzy PID control for nonlinear systems with degraded measurements: Dealing with randomly perturbed sampling periods,” IEEE Trans. Fuzzy Syst., vol. 32, no. 12, pp. 6848–6862, Dec. 2024. doi: 10.1109/TFUZZ.2024.3466218
[24]	Z. Cao, Z. Wang, Y. Niu, J. Song, and H. Liu, “Sliding mode control for sampled-data systems subject to deception attacks: Handling randomly perturbed sampling periods,” IEEE Trans. Cybern., vol. 53, no. 11, pp. 7034–7047, Nov. 2023. doi: 10.1109/TCYB.2022.3202486
[25]	Y. Sun, L. Li, and D. W. C. Ho, “Quantized synchronization control of networked nonlinear systems: Dynamic quantizer design with event-triggered mechanism,” IEEE Trans. Cybern., vol. 53, no. 1, pp. 184–196, Jan. 2023. doi: 10.1109/TCYB.2021.3090999
[26]	S. Zhou, J. Song, H.-K. Lam, S. He, and Z. Cao, “Coding-decoding-based sliding mode control for Markovian jump systems under constrained bit rate: An adaptive quantizer approach,” IEEE Trans. Control Netw. Syst., vol. 11, no. 1, pp. 257–2703, Mar. 2024. doi: 10.1109/TCNS.2023.3280458
[27]	S. Wang, Z. Wang, H. Dong, B. Shen, and Y. Chen, “Quadratic filtering for discrete time-varying non-Gaussian systems under binary encoding schemes,” Automatica, vol. 158, Art. no. Art. no. 111268, Dec. 2023. doi: 10.1016/j.automatica.2023.111268
[28]	X. Zhao, X. Wang, S. Zhang, and G. Zong, “Adaptive neural backstepping control design for a class of nonsmooth nonlinear systems,” IEEE Trans. Syst. Man Cybern. Syst., vol. 49, no. 9, pp. 1820–1831, Sep. 2019. doi: 10.1109/TSMC.2018.2875947
[29]	H. Guo, Y. Ma, Z. Ma, J. Chen, X. Zhang, Z. Cao, J. Zhang, and Y.-J. Gong, “Deep reinforcement learning for dynamic algorithm selection: A proof-of-principle study on differential evolution,” IEEE Trans. Syst. Man Cybern. Syst., vol. 54, no. 7, pp. 4247–4259, Jul. 2024. doi: 10.1109/TSMC.2024.3374889
[30]	Y. Shi and E. Nekouei, “Quantization and event-triggered policy design for encrypted networked control,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 4, pp. 946–955, Apr. 2024. doi: 10.1109/JAS.2023.124101

Supplements(0)

Cited By

Proportional views

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Figures(9)

Get Citation

PDF

XML

Article Metrics

Article views (16) PDF downloads(1)

Adaptive Encoding-Decoding Protocol to SMC for Multiple-Rate Stochastic Systems With Optimized Dynamic Quantization

doi: 10.1109/JAS.2026.125969

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Export File

Citation

Format

Content