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A Data-Driven Approach To Preserve Safety and Reference Tracking for Constrained Cyber-Physical Systems Under Network Attacks

Mehran Attar, Walter Lucia

TL;DR

A data-driven robust anomaly detector is designed to detect cyber-attack occurrences and an add-on tracking supervisor module allows safe open-loop tracking control operations in case of unreliable measurements.

Abstract

This paper proposes a worst-case data-driven control architecture capable of ensuring the safety of constrained Cyber-Physical Systems under cyber-attacks while minimizing, whenever possible, potential degradation in tracking performance. To this end, a data-driven robust anomaly detector is designed to detect cyber-attack occurrences. Moreover, an add-on tracking supervisor module allows safe open-loop tracking control operations in case of unreliable measurements. On the plant side, a safety verification module and a local emergency controller are designed to manage severe attack scenarios that cannot be handled on the controller's side. These two modules resort to worst-case reachability and controllability data-driven arguments to detect potential unsafe scenarios and replace, whenever strictly needed, the tracking controller with emergency actions whose objective is to steer the plant's state trajectory in a predefined set of admissible and safe robust control invariant region until an attack-free scenario is restored. The effectiveness of the proposed solution has been shown through a simulation example.

A Data-Driven Approach To Preserve Safety and Reference Tracking for Constrained Cyber-Physical Systems Under Network Attacks

TL;DR

A data-driven robust anomaly detector is designed to detect cyber-attack occurrences and an add-on tracking supervisor module allows safe open-loop tracking control operations in case of unreliable measurements.

Abstract

This paper proposes a worst-case data-driven control architecture capable of ensuring the safety of constrained Cyber-Physical Systems under cyber-attacks while minimizing, whenever possible, potential degradation in tracking performance. To this end, a data-driven robust anomaly detector is designed to detect cyber-attack occurrences. Moreover, an add-on tracking supervisor module allows safe open-loop tracking control operations in case of unreliable measurements. On the plant side, a safety verification module and a local emergency controller are designed to manage severe attack scenarios that cannot be handled on the controller's side. These two modules resort to worst-case reachability and controllability data-driven arguments to detect potential unsafe scenarios and replace, whenever strictly needed, the tracking controller with emergency actions whose objective is to steer the plant's state trajectory in a predefined set of admissible and safe robust control invariant region until an attack-free scenario is restored. The effectiveness of the proposed solution has been shown through a simulation example.
Paper Structure (15 sections, 5 theorems, 29 equations, 3 figures, 1 table, 2 algorithms)

This paper contains 15 sections, 5 theorems, 29 equations, 3 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Contributions
  3. Preliminaries and problem formulation
  4. Plant model and safety constraints
  5. Tracking controller
  6. Networked cyber-attacks
  7. Anomaly detector
  8. Problem Formulation
  9. Proposed Solution
  10. Safety Verification Module
  11. Emergency Controller Module
  12. Tracking Supervisor Module (TS)
  13. Tracking Performance Evaluation
  14. Simulation
  15. Conclusions

Key Result

Lemma 1

alanwar2021data Let $T = \sum_{i=1}^{N_t} N^{(i)}_s$ and consider the following concatenation of multiple noise zonotopes where $C_w\in \mathop{{\rm I} {\rm R}}\nolimits^{n\times (n+m)}=[c_{w},\ldots,\,c_w]$, and $G_{M_w}\in \mathop{{\rm I} {\rm R}}\nolimits^{n\times T(n+m)}$ is built $\forall\,i \in \{ 1, \ldots, q\},\, \forall\, j \in \{2, \ldots, T-1\}$ as Then, the matrix zonotope where $\l

Figures (3)

  • Figure 1: Proposed Control Architecture
  • Figure 2: State trajectory: proposed solution with attacks (blue solid line) vs trajectory in attack-free scenario (purple dashed line).
  • Figure 3: State evolution: no attack, proposed approach, attar2024safety.

Theorems & Definitions (13)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Remark 1
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Proposition 1
  • Remark 2
  • ...and 3 more