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Characterization of full-scale denial-of-service

Anindya Basu, Indrani Kar

TL;DR

This work addresses resilience of cyber-physical systems with multiple sensors under denial-of-service attacks on both sensor-to-controller and controller-to-actuator links. It advances the theory by simultaneously characterizing Full-Scale DoS (FSDoS) and Multi-Channel DoS (MCDoS) while designing an observer-based dynamic event-triggered control scheme that preserves Input-to-State Stability (ISS). The key contributions include a switched Luenberger observer with an event-triggered mechanism, LMIs that certify ISS under MCDoS, FSDoS frequency/duration bounds that guarantee stability, and a resilient control logic that avoids Zeno behavior. The results offer robust, provably stable guidance for networked CPS under adversarial communications, with practical implications for critical applications such as power systems and smart infrastructures.

Abstract

This article investigates the resilient control problem for Cyber-Physical Systems (CPSs) with multiple sensors, where both sides of the communication channels are affected by Denial-of-Service (DoS) attacks. While previous work focused on characterizing Multi-Channel DoS (MCDoS), this study emphasizes the characterization of Full-Scale DoS (FSDoS). First, a partial observer technique is proposed to address the MCDoS condition. Then, an event-triggered control strategy is designed to handle FSDoS. Finally, the frequency and duration of FSDoS are analyzed to ensure the Input-to-State Stability (ISS) of the closed-loop system.

Characterization of full-scale denial-of-service

TL;DR

This work addresses resilience of cyber-physical systems with multiple sensors under denial-of-service attacks on both sensor-to-controller and controller-to-actuator links. It advances the theory by simultaneously characterizing Full-Scale DoS (FSDoS) and Multi-Channel DoS (MCDoS) while designing an observer-based dynamic event-triggered control scheme that preserves Input-to-State Stability (ISS). The key contributions include a switched Luenberger observer with an event-triggered mechanism, LMIs that certify ISS under MCDoS, FSDoS frequency/duration bounds that guarantee stability, and a resilient control logic that avoids Zeno behavior. The results offer robust, provably stable guidance for networked CPS under adversarial communications, with practical implications for critical applications such as power systems and smart infrastructures.

Abstract

This article investigates the resilient control problem for Cyber-Physical Systems (CPSs) with multiple sensors, where both sides of the communication channels are affected by Denial-of-Service (DoS) attacks. While previous work focused on characterizing Multi-Channel DoS (MCDoS), this study emphasizes the characterization of Full-Scale DoS (FSDoS). First, a partial observer technique is proposed to address the MCDoS condition. Then, an event-triggered control strategy is designed to handle FSDoS. Finally, the frequency and duration of FSDoS are analyzed to ensure the Input-to-State Stability (ISS) of the closed-loop system.
Paper Structure (17 sections, 10 theorems, 143 equations, 2 figures)

This paper contains 17 sections, 10 theorems, 143 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. System description
  4. Multi-Channel DoS and Full-Scale DoS
  5. Stabilizing control update policy
  6. Control architecture
  7. Switching mode analysis
  8. Assumption: time constrained MCDoS
  9. Control Objectives
  10. Stability analysis of observer-based ETM under MCDoS
  11. ISS for ETM under MCDoS
  12. Minimum inter-execution time
  13. Input-to-State Stability under Full Scale Denial-of-Service
  14. Assumptions
  15. ISS under FSDoS
  16. ...and 2 more sections

Key Result

Lemma 3.4

basu2024characterization If $\frac{d}{dt}V_\sigma(x(t)) \leq -x^\top(t)\Gamma_{1_\sigma} x(t)+(\varepsilon_{1_\sigma}+ \varepsilon_{2_\sigma} + \psi_1)f^2(t)$ exists where $\Gamma_{1_\sigma}>0, \forall \sigma \in \{1, \cdots, n_s\},$ and $\{\varepsilon_{1_\sigma}, \varepsilon_{2_\sigma}, \psi_1\} \in \mathbb{R}_{>0}$, then $\forall t\in \mathbb{R}_{\geq 0}$ we have where $\iota_0=0,$ and

Figures (2)

  • Figure 1: Time axis from $0$ to $t$ where red lines represent jump points, green lines represent the starting points of the interval $W_m,m \in \mathbb{N}$ where \ref{['eq:update_rule_1']} may not hold, and blue lines represent the ending point of the interval $W_m, m \in \mathbb{N}$. Green lines are not jump points, but some blue lines may be jump points. This blue line and the next red line will be considered a single point in that scenario. For example, if $\varphi_1 + v_1$ is a jump point then $\varphi_1 + v_1 = \iota_{q_0+1}$.
  • Figure 2: Time axis from $0$ to $t$ where $W_{m(t)-(p+1)}, Y_{m(t)-(p+1)}, W_{m(t)-p},$ and $Y_{m(t)-p}$ sections are highlighted and red lines represent jump points, green lines represent the starting points of the interval $W_m,m \in \mathbb{N}$ where \ref{['eq:update_rule_1']} may not hold, and blue lines represent the ending point of the interval $W_m, m \in \mathbb{N}$.

Theorems & Definitions (17)

  • Definition 3.2
  • Definition 3.3
  • Lemma 3.4
  • Lemma 3.5
  • Theorem 4.1
  • proof
  • Lemma 4.2
  • proof
  • Remark 1
  • Lemma 5.3
  • ...and 7 more