Quantization and Event-Triggered Policy Design for Encrypted Networked Control

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 closedloop 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.

Secure motion control of micro-spacecraft using semi-homomorphic encryption

This paper studies the secure motion control problem for micro-spacecraft systems.A novel semi-homomorphic encrypted control framework,consisting of a logarithmic quantizer,two uniform quantizers,and an encrypted control law based on the Paillier cryptosystem is developed.More specifically,a logarithmic quantizer is adopted as a digitizer to convert the continuous relative motion information to digital signals.Two uniform quantizers with different quantization sensitivities are designed to encode the control gain matrix and digitized motion information to integer values.Then,we develop an encrypted state-feedback control law based on the Paillier cryptosystem,which allows the controller to compute the control input using only encrypted data.Using the Lyapunov stability theory and the homomorphic property of the Paillier cryptosystem,we prove that all signals in the closed-loop system are uniformly ultimately bounded.Different from the traditional motion control laws of spacecraft,the proposed encrypted control framework ensures the security of the exchanged data over the communication network of the spacecraft,even when communication channels are eavesdropped by malicious adversaries.Finally,we verify the effectiveness of the proposed encrypted control framework using numerical simulations.