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Bilateral Cognitive Security Games in Networked Control Systems under Stealthy Injection Attacks

Anh Tung Nguyen, Quanyan Zhu, André Teixeira

TL;DR

This work addresses securing networked control systems (NCSs) against stealthy false data injection by modeling defender-adversary interactions as a bilateral cognitive security game with asymmetric cognitive hierarchies. It integrates cognitive hierarchy reasoning with Stackelberg prediction games and develops semidefinite programming (SDP) methods to compute CH-$k$ defender and CH-$k$ adversary policies under finite-depth reasoning, including a mixed-integer SDP for defense monitoring. A convergence condition is established showing that increasing cognitive depth beyond a threshold does not alter the optimal policies, with numerical simulations on a 10-node network demonstrating convergence and resilience under mismatched and resonant reasoning. The approach provides a practically robust framework for security design in NCSs by accounting for bounded rationality and depth-limited strategic thinking in both defenders and attackers.

Abstract

This paper studies a strategic security problem in networked control systems under stealthy false data injection attacks. The security problem is modeled as a bilateral cognitive security game between a defender and an adversary, each possessing cognitive reasoning abilities. The adversary with an adversarial cognitive ability strategically attacks some interconnections of the system with the aim of disrupting the network performance while remaining stealthy to the defender. Meanwhile, the defender with a defense cognitive ability strategically monitors some nodes to impose the stealthiness constraint with the purpose of minimizing the worst-case disruption caused by the adversary. Within the proposed bilateral cognitive security framework, the preferred cognitive levels of the two strategic agents are formulated in terms of two newly proposed concepts, cognitive mismatch and cognitive resonance. Moreover, we propose a method to compute the policies for the defender and the adversary with arbitrary cognitive abilities. A sufficient condition is established under which an increase in cognitive levels does not alter the policies for the defender and the adversary, ensuring convergence. The obtained results are validated through numerical simulations.

Bilateral Cognitive Security Games in Networked Control Systems under Stealthy Injection Attacks

TL;DR

This work addresses securing networked control systems (NCSs) against stealthy false data injection by modeling defender-adversary interactions as a bilateral cognitive security game with asymmetric cognitive hierarchies. It integrates cognitive hierarchy reasoning with Stackelberg prediction games and develops semidefinite programming (SDP) methods to compute CH- defender and CH- adversary policies under finite-depth reasoning, including a mixed-integer SDP for defense monitoring. A convergence condition is established showing that increasing cognitive depth beyond a threshold does not alter the optimal policies, with numerical simulations on a 10-node network demonstrating convergence and resilience under mismatched and resonant reasoning. The approach provides a practically robust framework for security design in NCSs by accounting for bounded rationality and depth-limited strategic thinking in both defenders and attackers.

Abstract

This paper studies a strategic security problem in networked control systems under stealthy false data injection attacks. The security problem is modeled as a bilateral cognitive security game between a defender and an adversary, each possessing cognitive reasoning abilities. The adversary with an adversarial cognitive ability strategically attacks some interconnections of the system with the aim of disrupting the network performance while remaining stealthy to the defender. Meanwhile, the defender with a defense cognitive ability strategically monitors some nodes to impose the stealthiness constraint with the purpose of minimizing the worst-case disruption caused by the adversary. Within the proposed bilateral cognitive security framework, the preferred cognitive levels of the two strategic agents are formulated in terms of two newly proposed concepts, cognitive mismatch and cognitive resonance. Moreover, we propose a method to compute the policies for the defender and the adversary with arbitrary cognitive abilities. A sufficient condition is established under which an increase in cognitive levels does not alter the policies for the defender and the adversary, ensuring convergence. The obtained results are validated through numerical simulations.
Paper Structure (20 sections, 5 theorems, 36 equations, 2 figures, 1 table, 1 algorithm)

This paper contains 20 sections, 5 theorems, 36 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. PROBLEM DESCRIPTION
  3. Networked control systems under attacks
  4. Networked control systems without attacks
  5. Defense resources
  6. Adversary resources
  7. Networked control systems under stealthy attacks
  8. Bilateral Cognitive Security
  9. BILATERAL COGNITIVE SECURITY GAME
  10. CH-$0$ defender
  11. CH-$k$ adversary ($k \geq 0$)
  12. CH-$k$ defender ($k \geq 1$)
  13. COGNITIVE HIERARCHY POLICY COMPUTATION
  14. CH-$k$ adversary policy
  15. CH-$k$ defender policy
  16. ...and 5 more sections

Key Result

Proposition 1

Let ${\mathcal{M}}_k$ be a fixed CH-$k$ monitoring policy. Suppose the attacker at CH-$\ell$ chooses their policy defined in def_Ak. The CH-$(k,\ell)$ reasoning outcome $({\mathcal{M}}_k, {\mathcal{A}}_\ell, Q({\mathcal{M}}_k, {\mathcal{A}}_\ell))$ gains no benefit for the adversary if there is a co

Figures (2)

  • Figure 1: A networked control system under stealthy injection attacks. An adversary injects attack signals into the information sent from orange nodes to their neighbors while a defender monitors the outputs of blue nodes.
  • Figure 2: The horizontal axis represents the cognitive reasoning employed by the adversary while the vertical axis indicates the reasoning outcome. The reasoning resonance, represented by red asterisks, yields better reasoning outcomes for the adversary.

Theorems & Definitions (17)

  • Definition 1: Stealthy injection attacks
  • Definition 2: Asymmetric CH-$k$ reasoning
  • Definition 3: CH-$(k,\ell)$ reasoning outcome
  • Definition 4: Cognitive mismatch
  • Definition 5: Cognitive resonance
  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Remark 1
  • ...and 7 more