Secure Adaptive Control of Linear Networked Systems Using Paillier Encryption

This paper addresses the secure control problem of uncertain networked control systems (NCSs) with an untrusted controller, such as a cloud-based controller. Using the Paillier cryptosystem, we propose a model-based adaptive encrypted networked control framework that incorporates joint static and dynamic quantization policies, and an encrypted controller. Within this framework, a novel adaptive updating law is designed to compensate for the nonlinearities caused by quantization and parameter estimation, contributing to the asymptotic convergence of the system state. Moreover, since no raw information is transmitted over the communication network or utilized inside the controller device, the security of NCSs is effectively ensured. Further, to tackle the issue of ciphertext expansion, we develop an event-based adaptive encrypted control scheme. This scheme employs two distinct triggering functions, which significantly reduces frequent information transmission and skillfully eliminates the comprehensive nonlinearities arising from quantization, estimation, and triggering. It is worth noting that, due to the integer-based nature of the Paillier cryptosystem, both the system state and the estimated controller gain should be quantized. This differs significantly from existing works on quantized-based adaptive control methods, where only a single variable, either the system state or the control input, is quantized. Finally, simulation results validate the effectiveness of the proposed encrypted control frameworks.