(420d) Evaluating Implementation Feasibility of Cyberattack Detection Strategies Based on Lyapunov-Based Economic Model Predictive Control

Recent works from our group have explored cyberattack resilient Lyapunov-based economic model predictive control (LEMPC) frameworks in terms of detection of attacks on controller components, specifically sensors and actuators [3,4,5]. To ensure confidence in cyberattack detection and safety guarantees however, the LEMPC must be designed to meet conditions theoretically guaranteeing feasible control actions and stable operation, subject to assumptions. Though the theoretical conditions are sufficient but not necessary, they are important from a cybersecurity standpoint for guaranteeing that there are not vulnerabilities in integrated control and detection policies which an attacker might exploit. Though there are methods for designing parts of the control strategy including the Lyapunov function [6] and explicit stabilizing controller [2], developing methods for obtaining all of the parameters and functions required for guaranteeing cybersecurity for practical systems remains a challenge.

This talk will discuss various strategies employed to approximate sets of functions and parameters which meet the control theory of LEMPC as a move toward discussing the practicality of the control-theoretic cyberattack detection policies from our prior work, and what it would take to provide these greater practical utility. We first present a discussion of determining LEMPC parameters which meet theoretical guarantees for a chemical process example involving a continuous stirred tank reactor to be placed under LEMPC [1]. We present a series of inequality conditions central to LEMPC theory [1] and select several strictly increasing functions required by the theory. We then perform a "best-case" analysis to find an upper bound on the size of the sampling period of the LEMPC that would be required, in the absence of plant/model mismatch, for the theoretical conditions of LEMPC to be satisfied. We demonstrate that the best case can be quite small, but that it also partially depends on the functions initially selected. For this reason, we then explore simultaneous development of various functions required by the theory using an optimization problem where various functions are suggested to take a certain functional form, and the optimization problem is meant to aid in estimating the coefficients. We discuss the benefits and limitations of these methods, and what they reveal about the use of LEMPC from a practical perspective. Building from this discussion, we next review several cyberattack detection strategies from [3] from the viewpoint of showcasing how the analysis described for LEMPC might be performed for obtaining the control-theoretic parameters for these control designs. We discuss how the added consideration of cybersecurity affects the "best-case" results obtained as the initial approximation of the parameters.

[1] Heidarinejad, Mohsen, Jinfeng Liu, and Panagiotis D. Christofides. "Economic model predictive control of nonlinear process systems using Lyapunov techniques." AIChE Journal 58.3 (2012): 855-870.

[2] Lin, Yuandan, and Eduardo D. Sontag. "A universal formula for stabilization with bounded controls." Systems & Control Letters 16.6 (1991): 393-397.

[3] Oyama, Henrique, and Helen Durand. "Integrated cyberattack detection and resilient control strategies using Lyapunov‐based economic model predictive control." AIChE Journal 66.12 (2020): e17084.

[4] Oyama, Henrique, Keshav Kasturi Rangan, and Helen Durand. "Handling of stealthy sensor and actuator cyberattacks on evolving nonlinear process systems." Journal of Advanced Manufacturing and Processing 3.3 (2021): e10099.

[5] Oyama, Henrique, Dominic Messina, Keshav Kasturi Rangan, and Helen Durand. "Lyapunov-Based Economic Model Predictive Control for Detecting and Handling Actuator and Simultaneous Sensor/Actuator Cyberattacks on Process Control Systems." Frontiers in Chemical Engineering: 11.

[6] Papachristodoulou, Antonis, and Stephen Prajna. "On the construction of Lyapunov functions using the sum of squares decomposition." Proceedings of the 41st IEEE Conference on Decision and Control, 2002. Vol. 3. IEEE, 2002.