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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Encrypted Networked Control with Quantization and Event-Triggered Mechanism

Journal of Applied Nonlinear Dynamics 15(2) (2026) 491--501 | DOI:10.5890/JAND.2026.06.015

Mingqi Liu$^1$, Guopeng Zhou$^{1,2}$, Peng Jin$^1$, Yangxizi Liu$^1$

$^1$ School of Electronic and Electrical Engineering, Wuhan Textile University, Wuhan, 430200, China

$^2$ Department of Research and Development, Hubei Xiangcheng Intelligent Electromechanical Industry Technology Research Institute Co., Ltd., Xianning, 437100, China

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Abstract

This paper addresses the security and resource efficiency challenges in networked control systems (NCSs)—specifically, the integer-only operation limitation of homomorphic encryption (HE), ciphertext expansion-induced communication overload, quantization nonlinearities that degrade stability or limit convergence, and the lack of a unified solution integrating security and efficiency. To resolve these issues, a unified encrypted control framework is proposed. For HE's integer constraint, static quantization is designed for control gains and dynamic quantization for system states (adjusting sensitivity by state magnitude to ensure asymptotic convergence of quantized states to equilibrium, overcoming fixed-sensitivity quantizers' bounded stability limitation). Different from traditional encryption control, a quantization-aware dynamic event-triggered mechanism (DETM) is developed to reduce communication load and relieve ciphertext expansion, incorporating quantization-related errors into its triggering condition to transmit encrypted data only when necessary and guarantee Zeno-free operation. Finally, simulation results further prove the proposed method is effective.

Acknowledgments

This work was supported by the 2025 Technology Talent Service Enterprise Project (Grant 2025DJB06); the 2024 Provincial Science and Technology Plan Project (First Batch) - ``Top Talent Recruitment" Project (Grant 2024BEB029); the 2023 Hubei Province `Chutian Talents Program' Science and Technology Innovation Team Project; and the Central Government-Guided Local Science and Technology Development Special Project of Hubei Province (Grant 2025EIA044).

References

  1. [1]  Li, Y., Li, Y.X., and Tong, S. (2022), Event-based finite-time control for nonlinear multiagent systems with asymptotic tracking, IEEE Transactions on Automatic Control, 68(6), 3790--3797.
  2. [2]  Rojas, A.J. and Garcés, H.O. (2025), Power-constrained networked process control system design, Systems and Control Letters, 205, 106231.
  3. [3]  Zhang, X.M., Han, Q.L., Ge, X., Ding, D., Ding, L., Yue, D., and Peng, C. (2019), Networked control systems: a survey of trends and techniques, IEEE/CAA Journal of Automatica Sinica, 7(1), 1--17.
  4. [4]  Duo, W., Zhou, M., and Abusorrah, A. (2022), A survey of cyber attacks on cyber physical systems: recent advances and challenges, IEEE/CAA Journal of Automatica Sinica, 9(5), 784--800.
  5. [5]  Acar, A., Aksu, H., Uluagac, A.S., and Conti, M. (2018), A survey on homomorphic encryption schemes: theory and implementation, ACM Computing Surveys, 51(4), 1--35.
  6. [6]  Zhang, Z., Cheng, P., Wu, J., and Chen, J. (2020), Secure state estimation using hybrid homomorphic encryption scheme, IEEE Transactions on Control Systems Technology, 29(4), 1704--1720.
  7. [7]  Marcantoni, M., Jayawardhana, B., Chaher, M.P., and Bunte, K. (2022), Secure formation control via edge computing enabled by fully homomorphic encryption and mixed uniform-logarithmic quantization, IEEE Control Systems Letters, 7, 395--400.
  8. [8]  Ruan, M., Gao, H., and Wang, Y. (2019), Secure and privacy-preserving consensus, IEEE Transactions on Automatic Control, 64(10), 4035--4049.
  9. [9]  Alexandru, A.B., Gatsis, K., Shoukry, Y., Seshia, S.A., Tabuada, P., and Pappas, G.J. (2020), Cloud-based quadratic optimization with partially homomorphic encryption, IEEE Transactions on Automatic Control, 66(5), 2357--2364.
  10. [10]  Cheon, J.H., Han, K., Kim, H., Kim, J., and Shim, H. (2018), Need for controllers having integer coefficients in homomorphically encrypted dynamic system, In Proc. IEEE 58th Conference on Decision and Control, 5020--5025.
  11. [11]  Schlüter, N. and Darup, M.S. (2021), On the stability of linear dynamic controllers with integer coefficients, IEEE Transactions on Automatic Control, 67(10), 5610--5613.
  12. [12]  Kim, J., Shim, H., and Han, K. (2022), Dynamic controller that operates over homomorphically encrypted data for infinite time horizon, IEEE Transactions on Automatic Control, 68(2), 660--672.
  13. [13]  Teranishi, K., Shimada, N., and Kogiso, K. (2019), Stability analysis and dynamic quantizer for controller encryption, In Proc. IEEE 58th Conference on Decision and Control, 7184--7189.
  14. [14]  Teranishi, K., Shimada, N., and Kogiso, K. (2020), Stability‐guaranteed dynamic ElGamal cryptosystem for encrypted control systems, IET Control Theory and Applications, 14(16), 2242--2252.
  15. [15]  Zhang, Z., Zhang, L., Hao, F., and Wang, L. (2016), Leader-following consensus for linear and Lipschitz nonlinear multiagent systems with quantized communication, IEEE Transactions on Cybernetics, 47(8), 1970--1982.
  16. [16]  Wu, Z.G., Xu, Y., Pan, Y.J., Su, H., and Tang, Y. (2018), Event-triggered control for consensus problem in multi-agent systems with quantized relative state measurements and external disturbance, IEEE Transactions on Circuits and Systems I: Regular Papers, 65(7), 2232--2242.
  17. [17]  Xu, T., Duan, Z., Sun, Z., and Chen, G. (2022), A unified control method for consensus with various quantizers, Automatica, 136, 110090.
  18. [18]  Liu, T., Zhang, P., and Jiang, Z.P. (2019), Event-triggered input-to-state stabilization of nonlinear systems subject to disturbances and dynamic uncertainties, Automatica, 108, 108488.
  19. [19]  Zhang, Z., Wen, C., Xing, L., and Song, Y. (2021), Adaptive event-triggered control of uncertain nonlinear systems using intermittent output only, IEEE Transactions on Automatic Control, 67(8), 4218--4225.
  20. [20]  Shu, F. and Zhai, J. (2023), Event-triggered prescribed-time tracking control for nonlinear systems with asynchronous switching, IEEE Transactions on Circuits and Systems I: Regular Papers, 70(10), 4159--4168.
  21. [21]  Li, X. and Li, P. (2021), Input-to-state stability of nonlinear systems: event-triggered impulsive control, IEEE Transactions on Automatic Control, 67(3), 1460--1465.
  22. [22]  Girard, A. (2015), Dynamic triggering mechanisms for event-triggered control, IEEE Transactions on Automatic Control, 60(7), 1992--1997.
  23. [23]  Rikos, A.I., Charalambous, T., Johansson, K.H., and Hadjicostis, C.N. (2022), Distributed event-triggered algorithms for finite-time privacy-preserving quantized average consensus, IEEE Transactions on Control of Network Systems, 10(1), 38--50.
  24. [24]  Murguia, C., Farokhi, F., and Shames, I. (2020), Secure and private implementation of dynamic controllers using semihomomorphic encryption, IEEE Transactions on Automatic Control, 65(9), 3950--3957.

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