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Volume 11 Issue 4
Apr.  2024

IEEE/CAA Journal of Automatica Sinica

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Article Contents
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
Citation: 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

Quantization and Event-Triggered Policy Design for Encrypted Networked Control

doi: 10.1109/JAS.2023.124101
Funds:  This work was partly supported by the Research Grants Council of Hong Kong (CityU 21208921) and the Chow Sang Sang Group Research Fund Sponsored by Chow Sang Sang Holdings International Ltd
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  • This paper proposes a novel event-driven encrypted control framework for linear networked control systems (NCSs), which relies on two modified uniform quantization policies, the Paillier cryptosystem, and an event-triggered strategy. Due to the fact that only integers can work in the Pailler cryptosystem, both the real-valued control gain and system state need to be first quantized before encryption. This is dramatically different from the existing quantized control methods, where only the quantization of a single value, e.g., the control input or the system state, is considered. To handle this issue, static and dynamic quantization policies are presented, which achieve the desired integer conversions and guarantee asymptotic convergence of the quantized system state to the equilibrium. Then, the quantized system state is encrypted and sent to the controller when the triggering condition, specified by a state-based event-triggered strategy, is satisfied. By doing so, not only the security and confidentiality of data transmitted over the communication network are protected, but also the ciphertext expansion phenomenon can be relieved. Additionally, by tactfully designing the quantization sensitivities and triggering error, the proposed event-driven encrypted control framework ensures the asymptotic stability of the overall closed-loop system. Finally, a simulation example of the secure motion control for an inverted pendulum cart system is presented to evaluate the effectiveness of the theoretical results.


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    • An event-driven encrypted control framework is proposed using the Paillier cryptosystem, modified static and dynamic quantization policies, and the quantization-related event-triggered strategy
    • A novel dynamic quantization policy with a state-dependent sensitivity is presented, which ensures the asymptotic convergence of the system state
    • By defining a quantization-related measurement error, the adverse effect of quantization errors is implicitly considered in the event-triggered strategy, which contributes to a rigorous analysis of the inter-event time interval


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