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Resilient Controller Synthesis Against DoS Attacks for Vehicular Platooning in Spatial Domain

Jian Gong, Carlos Murguia, Anggera Bayuwindra, Jinde Cao

TL;DR

This work tackles resilient vehicular platooning under Denial-of-Service (DoS) attacks by formulating the problem in the spatial domain and introducing a robust controller synthesis framework. It leverages polytopic overapproximation of space-delay dynamics induced by DoS to convert the uncertain closed-loop model into a finite set of LMIs, enabling joint guarantees of internal stability and $L_2$ string stability under disturbances. The main contributions are (i) a polytopic overapproximation methodology based on real Jordan forms, (ii) LMI-based conditions for global asymptotic stability and string stability with disturbance attenuation, and (iii) demonstrated robustness through simulations showing maintained spacing, velocity tracking, and reduced perturbation amplification in the presence of stochastic space delays. The framework offers a principled, scalable approach to resilient platoon control with potential applicability to broader cyber-physical networked systems.

Abstract

This paper proposes a vehicular platoon control approach under Denial-of-Service (DoS) attacks and external disturbances. DoS attacks increase the service time on the communication network and cause additional transmission delays, which consequently increase the risk of rear-end collisions of vehicles in the platoon. To counter DoS attacks, we propose a resilient control scheme that exploits polytopic overapproximations of the closed-loop dynamics under DoS attacks. This scheme allows synthesizing robust controllers that guarantee tracking of both the desired spacing policy and spatially varying reference velocity for all space-varying DoS attacks satisfying a hard upper bound on the attack duration. In addition, L2 string stability conditions are derived to ensure that external perturbations do not grow as they propagate through the platoon, thus ensuring the string stability. Numerical simulations illustrate the effectiveness of the proposed control method.

Resilient Controller Synthesis Against DoS Attacks for Vehicular Platooning in Spatial Domain

TL;DR

This work tackles resilient vehicular platooning under Denial-of-Service (DoS) attacks by formulating the problem in the spatial domain and introducing a robust controller synthesis framework. It leverages polytopic overapproximation of space-delay dynamics induced by DoS to convert the uncertain closed-loop model into a finite set of LMIs, enabling joint guarantees of internal stability and string stability under disturbances. The main contributions are (i) a polytopic overapproximation methodology based on real Jordan forms, (ii) LMI-based conditions for global asymptotic stability and string stability with disturbance attenuation, and (iii) demonstrated robustness through simulations showing maintained spacing, velocity tracking, and reduced perturbation amplification in the presence of stochastic space delays. The framework offers a principled, scalable approach to resilient platoon control with potential applicability to broader cyber-physical networked systems.

Abstract

This paper proposes a vehicular platoon control approach under Denial-of-Service (DoS) attacks and external disturbances. DoS attacks increase the service time on the communication network and cause additional transmission delays, which consequently increase the risk of rear-end collisions of vehicles in the platoon. To counter DoS attacks, we propose a resilient control scheme that exploits polytopic overapproximations of the closed-loop dynamics under DoS attacks. This scheme allows synthesizing robust controllers that guarantee tracking of both the desired spacing policy and spatially varying reference velocity for all space-varying DoS attacks satisfying a hard upper bound on the attack duration. In addition, L2 string stability conditions are derived to ensure that external perturbations do not grow as they propagate through the platoon, thus ensuring the string stability. Numerical simulations illustrate the effectiveness of the proposed control method.
Paper Structure (16 sections, 4 theorems, 84 equations, 15 figures, 3 tables)

This paper contains 16 sections, 4 theorems, 84 equations, 15 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Delay-based Spacing Policy
  4. Vehicle Longitudinal Dynamics
  5. Longitudinal Platoon Modeling
  6. DoS Attacks Model
  7. Control Synthesis Objective
  8. Distributed Platoon Controller Design
  9. Polytopic Overappromaximation
  10. Internal Stability
  11. Controller Synthesis for String Stability
  12. Simulation results
  13. Conclusion
  14. Proof of Lemma 2
  15. Proof of Theorem 1
  16. ...and 1 more sections

Key Result

Lemma 1

cloosterman2009stability Consider the uncertain closed-loop system $\mathcal{X}_{i,k+1}=(\bar{A}(\bar{\tau}_{i,k})-\bar{B}(\bar{\tau}_{i,k})\bar{K})\mathcal{X}_{i,k}$ in augumentplatoonmodel. There exists a common quadratic Lyapunov function $V(\mathcal{X}_{i,k})=\mathcal{X}_{i,k}^TP\mathcal{X}_{i,k

Figures (15)

  • Figure 1: A scenario of a vehicular platoon driving on a straight lane subject to DoS attacks.
  • Figure 2: Time-space trajectories of the lead vehicle (yellow), vehicle $i-1$ (green), and vehicle $i$ (red) in the platoon. Time-coordinate indicates time $t$(s) as a function of space $s$.
  • Figure 3: A scenario of vehicle information transmission from vehicle $i-1$ to vehicle $i$ with spatial delays under DoS attacks. Vehicle $i-1$ samples its information at space $s=s_1$, and transmits to vehicle $i$ (top row). Vehicle $i$ receives the sampled information of vehicle $i-1$ at space $s=s_2$, where two cases are included: 1) Case 1: $s_2 \leq s_1$ (middle row); 2) Case 2: $s_2 > s_1$ (bottom row).
  • Figure 4: Polytopic overapproximation.
  • Figure 5: Profile of the stochastic delays $\bar{\tau}_{i,k}$ induced by DoS attacks.
  • ...and 10 more figures

Theorems & Definitions (11)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Definition 1
  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Theorem 2
  • ...and 1 more