With the increased risk of targeted cyber-attacks, it has become essential to incorporate cyber-secure approaches into physical networked control systems to ensure safe and secure operations. The use of unsecure networks to facilitate communication between various components of networked control systems, along with computations involving sensitive data on outsourced platforms, can result in the risk of data manipulation and interception. Several approaches have been used to ensure cyber-security in networked control systems, some of which include machine-learning based detectors for advanced threat detection [1], design of two-tier controllers [2] and encrypted control systems [3]. In our previous work [4], we developed a Lyapunov-based encrypted Model Predictive Control (MPC) scheme for nonlinear systems, which involved establishing secure communication in the sensor-controller and controller-actuator links. Due to the nature of cryptosystems, real valued signals have to be mapped to a set of positive integers, on which the encryption-decryption operations are carried out. This mapping results in quantization errors, and, in our previous work, we analyzed the effect of these quantization errors on closed-loop stability of the nonlinear system.

In this work, we use the previously developed encrypted Lyapunov-based MPC scheme to control a chemical process simulated using the well-known high-fidelity process simulator, Aspen Plus Dynamics. As the model predictive controller uses a first-principles model of the process, there is a model mismatch between the model used in the controller and the Aspen model. Specifically, we analyze the combined and relative effects of the quantization errors, arising due to the encryption operations, and the error due to the plant-model mismatch on closed-loop stability of the nonlinear system.

References:

[1] Omar S, Ngadi A, Jebur HH. Machine learning techniques for anomaly detection: an overview. International Journal of Computer Applications. 2013;79:33–41.

[2] Chen S, Wu Z, Christofides PD. A cyber-secure control-detector architecture for nonlinear processes. AIChE Journal. 2020;66:e16907.

[3] Darup MS, Redder A, Shames I, Farokhi F, Quevedo D. Towards encrypted MPC for linear constrained systems. IEEE Control Systems Letters. 2017;2:195–200.

[4] Suryavanshi A., Alnajdi A, Alhajeri M, Abdullah F, Christofides PD (in press). Encrypted Model Predictive Control Design for Security to Cyber-Attacks. AIChE Journal.