(206b) Framework to Guarantee Stability, Feasibility and Profitability of Nonlinear Systems Characterized By Evolving Dynamics and Vulnerable to Cyberattacks on Control Elements

The adoption of cyber-physical systems (CPS) in chemical and manufacturing industries has enhanced process efficiency and transparency. However, this integration also exposes these systems to cyberattacks that can jeopardize process safety, stability, and economic performance^[1]. Existing cyberattack detection strategies often compare model-based predictions of process states with sensor measurements to identify anomalies^[2]. However, most of these methods assume that process dynamics remain time-invariant, a condition rarely met in real-world chemical processes where fouling, catalyst degradation, or environmental changes introduce time-varying nonlinear dynamics. Consequently, model mismatch arising from unaccounted dynamics can lead to false alarms or miss detecting an attack.

This work proposes a two-tier detection strategy designed for closed-loop nonlinear systems with time-varying dynamics. The approach provides rigorous guarantees of stability and recursive feasibility, even in the presence of process disturbances and undetected cyberattacks on control elements such as sensors and/or actuators. The proposed strategy is a hybrid detection framework developed by integrating passive^[3,4] and active^[5,6] detection strategies within a Lyapunov-based Economic Model Predictive Control (LEMPC) framework^[7] to detect for either a change in the process dynamics or the presence of an attack. The key idea of the strategy is to not distinguish between a change in process dynamics or a cyberattack, but to focus on their impact and the passive component of the detection strategy addresses this.

The passive detection component, implemented in the top tier, compares model-based state estimates with sensor measurements and employs a two-tier threshold approach. Breach of the lower threshold triggers model re-identification to adapt to changing dynamics, while a breach of the upper threshold activates emergency control actions ^[8]. In parallel, the active detection component introduces small, systematic perturbations to the control inputs using a modified LEMPC formulation. The active component consists of redundant controllers (top tier) that update predicted process states and set a limit on process economics, and an 'actual' controller (bottom tier) continuously probes for actuator attacks while preserving system stability by constraining the Lyapunov function to decrease at every sampling time. The active component of the detection strategy forces a deviation from the optimal operation of the process, impacting process economics. Hence, this work also incorporates a prior framework^[9] to quantify and set theoretical bounds on the associated process economic loss. The proposed framework is demonstrated on a continuous stirred tank reactor (CSTR), a representative nonlinear process system, to highlight its characteristics. This work contributes a systematic and theoretically grounded approach to resilient model predictive control that guarantees process stability and quantifies the impact on profitability under the dual challenges of cyberattacks and dynamic process variability.

References:

[1] Cárdenas AA, Amin S, Lin ZS, Huang YL, Huang CY, Sastry S. Attacks against process control systems: risk assessment, detection, and response. In Proceedings of the 6th ACM symposium on information, computer and communications security, 355-366 (2011).

[2] Oyama, H. and H. Durand. Integrated Cyberattack Detection and Resilient Control Strategies Using Lyapunov-Based Economic Model Predictive Control, AIChE Journal, 66 ("Futures" issue), ee17084 (2020).

[3] Liu, S., Wei, G., Song, Y., Liu, Y. Extended kalman filtering for stochastic nonlinear systems with randomly occurring cyber attacks. Neurocomputing, 207, 708-716 (2016).

[4] Parker, S., Wu, Z., & Christofides, P.D. Cybersecurity in process control, operations, and supply chain. Computers & Chemical Engineering, 171, 108169 (2023).

[5] Li, Y., Voos, H., Rosich, A., Darouach, M. A stochastic cyber-attack detection scheme for stochastic control systems based on frequency-domain transformation technique, in: International Conference on Network and System Security, Springer, 209-222 (2015).

[6] Narasimhan, S., El-Farra, N. H., & Ellis, M. J. Active multiplicative cyberattack detection utilizing controller switching for process systems. Journal of Process Control, 116, 64-79 (2022).

[7] Heidarinejad, M., Liu, J., & Christofides, P. D. Economic model predictive control of nonlinear process systems using Lyapunov techniques. AIChE Journal, 58(3), 855-870 (2012).

[8] Rangan, K. K., Oyama, H., & Durand, H. Integrated Cyberattack Detection and Handling for Nonlinear Systems with Evolving Process Dynamics under Lyapunov-based Economic Model Predictive Control. Chemical Engineering Research and Design (2021).

[9] Rangan, K. K., & Durand, H. Profit Considerations For Nonlinear Control-Integrated Cyberattack Detection On Process Actuators. IFAC-PapersOnLine, 58(14), 592-597 (2024).