(194f) Economic Optimization with Encrypted Control for Cyber-Resilient Operation of Nonlinear Processes

Networked control systems offer numerous advantages, streamlining operations and enhancing efficiency [1]. However, they also introduce vulnerabilities to cyber threats, emphasizing the urgent need for robust cybersecurity protocols. Recent cyberattacks underscore the importance of cybersecurity in networked cyber-physical systems, highlighting the potential consequences of breaches or compromises [2]. Encrypted control systems have been proposed to address this challenge [3]. Traditional process control frameworks combine model predictive control (MPC) with a real-time optimizer (RTO) for steady-state tracking. However, economic model predictive control (EMPC) has emerged to dynamically optimize economic cost functions while maintaining stability constraints [4]. Integrating fluctuations in real-world economics into process control can further maximize economic benefits and maintain profitability in highly competitive markets [5]. However, the integration of encrypted control with dynamic economic optimization remains unexplored, motivating us to propose a novel control framework.

We introduce a two-layer encrypted control system designed to optimize economic performance, address fluctuations in economics, and bolster cyberattack resilience by utilizing encrypted communication and computations at different layers of the control architecture. The upper layer employs a Lyapunov-based economic model predictive control (LEMPC) scheme, receiving updated economic information for each operating period through updated weights in the objective function. The upper layer computes the set points to be tracked by the lower layer via nonlinear optimization and encrypts them before transmission to the lower layer. Consequently, the lower layer utilizes an encrypted linear feedback control system employing encrypted state feedback to track the economically optimal dynamic operating trajectory in an encrypted space, without decryption, ensuring complete confidentiality at the lower layer. To address the cyber vulnerability of the upper layer, a logic-based cyberattack detector utilizing sensor-derived data for attack detection is integrated into the control framework. Simulation results of a nonlinear chemical process demonstrate the economic advantages and cyber resilience of the encrypted two-layer control framework.

References:

[1] Bemporad, A., Heemels, M. and Johansson, M., 2010. Networked control systems (Vol. 406). London: Springer.

[2] Tsvetanov, T. Slaria, S., 2021. The effect of the colonial pipeline shutdown on gasoline prices. Economics Letters, 209, 110122.

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

[4] Amrit, R., Rawlings, J. B., Angeli, D., 2011. Economic optimization using model predictive control with a terminal cost. Annual Reviews in Control, 35, 178–186.

[5] Ellis, M. Christofides, P. D., 2014. Integrating dynamic economic optimization and model predictive control for optimal operation of nonlinear process systems. Control Engineering Practice, 22, 242–251.