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Nash Equilibrium Between Consumer Electronic Devices and DoS Attacker for Distributed IoT-enabled RSE Systems

Gengcan Chen, Donghong Cai, Zahid Khan, Jawad Ahmad, Wadii Boulila

TL;DR

This work addresses DoS vulnerabilities in IoT-enabled remote state estimation by formulating the defender-attacker interaction as a Nash equilibrium problem. It integrates a remote joint estimation model with a Kalman filter at the remote estimator to reduce device workload and data leakage, and develops centralized and distributed Minimax-DQN algorithms to compute NE in open-loop and closed-loop settings, including a belief-state formulation for partial observability. The results demonstrate rapid convergence and robust NE solutions, with centralized and distributed Minimax-DQN achieving stable performance improvements over state-of-the-art baselines and showing practical potential for large-scale, resource-constrained IoT deployments. The approach provides a scalable framework for securing real-time monitoring in distributed IoT-enabled RSE systems against DoS attacks, with implications for predictive maintenance and future IoT security research.

Abstract

In electronic consumer Internet of Things (IoT), consumer electronic devices as edge devices require less computational overhead and the remote state estimation (RSE) of consumer electronic devices is always at risk of denial-of-service (DoS) attacks. Therefore, the adversarial strategy between consumer electronic devices and DoS attackers is critical. This paper focuses on the adversarial strategy between consumer electronic devices and DoS attackers in IoT-enabled RSE Systems. We first propose a remote joint estimation model for distributed measurements to effectively reduce consumer electronic device workload and minimize data leakage risks. The Kalman filter is deployed on the remote estimator, and the DoS attacks with open-loop as well as closed-loop are considered. We further introduce advanced reinforcement learning techniques, including centralized and distributed Minimax-DQN, to address high-dimensional decision-making challenges in both open-loop and closed-loop scenarios. Especially, the Q-network instead of the Q-table is used in the proposed approaches, which effectively solves the challenge of Q-learning. Moreover, the proposed distributed Minimax-DQN reduces the action space to expedite the search for Nash Equilibrium (NE). The experimental results validate that the proposed model can expeditiously restore the RSE error covariance to a stable state in the presence of DoS attacks, exhibiting notable attack robustness. The proposed centralized and distributed Minimax-DQN effectively resolves the NE in both open and closed-loop case, showcasing remarkable performance in terms of convergence. It reveals that substantial advantages in both efficiency and stability are achieved compared with the state-of-the-art methods.

Nash Equilibrium Between Consumer Electronic Devices and DoS Attacker for Distributed IoT-enabled RSE Systems

TL;DR

This work addresses DoS vulnerabilities in IoT-enabled remote state estimation by formulating the defender-attacker interaction as a Nash equilibrium problem. It integrates a remote joint estimation model with a Kalman filter at the remote estimator to reduce device workload and data leakage, and develops centralized and distributed Minimax-DQN algorithms to compute NE in open-loop and closed-loop settings, including a belief-state formulation for partial observability. The results demonstrate rapid convergence and robust NE solutions, with centralized and distributed Minimax-DQN achieving stable performance improvements over state-of-the-art baselines and showing practical potential for large-scale, resource-constrained IoT deployments. The approach provides a scalable framework for securing real-time monitoring in distributed IoT-enabled RSE systems against DoS attacks, with implications for predictive maintenance and future IoT security research.

Abstract

In electronic consumer Internet of Things (IoT), consumer electronic devices as edge devices require less computational overhead and the remote state estimation (RSE) of consumer electronic devices is always at risk of denial-of-service (DoS) attacks. Therefore, the adversarial strategy between consumer electronic devices and DoS attackers is critical. This paper focuses on the adversarial strategy between consumer electronic devices and DoS attackers in IoT-enabled RSE Systems. We first propose a remote joint estimation model for distributed measurements to effectively reduce consumer electronic device workload and minimize data leakage risks. The Kalman filter is deployed on the remote estimator, and the DoS attacks with open-loop as well as closed-loop are considered. We further introduce advanced reinforcement learning techniques, including centralized and distributed Minimax-DQN, to address high-dimensional decision-making challenges in both open-loop and closed-loop scenarios. Especially, the Q-network instead of the Q-table is used in the proposed approaches, which effectively solves the challenge of Q-learning. Moreover, the proposed distributed Minimax-DQN reduces the action space to expedite the search for Nash Equilibrium (NE). The experimental results validate that the proposed model can expeditiously restore the RSE error covariance to a stable state in the presence of DoS attacks, exhibiting notable attack robustness. The proposed centralized and distributed Minimax-DQN effectively resolves the NE in both open and closed-loop case, showcasing remarkable performance in terms of convergence. It reveals that substantial advantages in both efficiency and stability are achieved compared with the state-of-the-art methods.

Paper Structure

This paper contains 18 sections, 2 theorems, 50 equations, 8 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model and DoS Attacks
  3. Distributed IoT Model
  4. Remote State Estimation
  5. DoS Attack Model
  6. NE Framework for Distributed IoT Security
  7. Game in Infinite Time Horizon
  8. Nash Equilibrium
  9. Open-Loop Security Strategies
  10. Centralized Minimax-DQN for Infinite Time-Horizon Game
  11. Distributed Minimax-DQN for Infinite Time-Horizon Game
  12. Closed-Loop Security Strategies
  13. Simulation and Analysis
  14. System Parameter Setting
  15. Open-loop Case
  16. ...and 3 more sections

Key Result

Lemma 1

(anderson1979optimal) The innovation $z_{i,k}$ has the following properties:

Figures (8)

  • Figure 1: Remote State Estimation of Distributed IoT with DoS Attacker.
  • Figure 2: Training process of centralized Minimax-DQN.
  • Figure 3: The correctness verification of the designed model.
  • Figure 4: $Q(s,\bm{\alpha},\bm{\beta}|\theta)$ in four state duiring centralized learning under open-loop case, respectively.
  • Figure 5: Q-value of consumer electronic devices and DoS attacker in two states during the distributed learning under open-loop case, respectively.
  • ...and 3 more figures

Theorems & Definitions (8)

  • Lemma 1
  • Remark 1
  • Lemma 2
  • proof
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5