Encrypted Model Predictive Control of Nonlinear Systems

Abstract

In recent years, cyber-security of networked control systems has become crucial, as these systems are vulnerable to targeted cyber-attacks that compromise the stability, integrity and safety of these systems. In this work, secure and private communication links are established between sensor-controller and controller-actuator elements using semi-homomorphic encryption to ensure cyber-security in Model Predictive Control (MPC) of nonlinear systems. Specifically, Paillier Cryptosystem is implemented for encryption-decryption operations in the communication links. Cryptosystems, in general, work on a subset of integers. As a direct consequence of this nature of encryption algorithms, quantization errors arise in the closed-loop MPC of non-linear systems. Thus, the closed-loop encrypted MPC is designed with a certain degree of robustness to the quantization errors. Furthermore, the trade-off between the accuracy of the encrypted MPC and the computational cost is discussed. Finally, a multi-input multi-output continuous stirred tank reactor (CSTR) example is presented to demonstrate the implementation of the proposed encrypted MPC design.