Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Resilient Distributed Control for Uncertain Nonlinear Interconnected Systems under Network Anomaly

Youqing Wang, Ying Li, Thomas Parisini, Dong Zhao

TL;DR

This paper tackles resilient distributed control for uncertain nonlinear interconnected systems subjected to network anomalies. It develops a backstepping-based distributed adaptive controller with neural network approximations for uncertainty, and derives quantitative resilience conditions that bound anomaly duration and resting time to ensure stability or boundedness. The main contributions are a rigorous Lyapunov-based analysis yielding explicit bounds and a comprehensive simulation with four interconnected subsystems validating robustness to anomaly propagation. The results advance resilience quantification in cyber-physical systems by incorporating both local anomalies and their propagation through interconnections, without requiring precise anomaly detection. The framework offers practical guidelines for maintaining stable operation under stealthy network disturbances in large-scale CPS.

Abstract

We address a distributed adaptive control methodology for nonlinear interconnected systems possibly affected by network anomalies. In the framework of adaptive approximation, the distributed controller and parameter estimator are designed by exploiting a backstepping approach. The stability of the distributed control system under anomalies is analyzed, where both local and neighboring anomaly effects are considered. To quantify the resilience of the interconnected system under the action of network anomalies, we derive bounds on the duration of each anomaly and the resting time between two consecutive anomalies. Specifically, when each anomaly duration is smaller than our designed upper bound, the interconnected system controlled by the distributed approximation-based controller remains asymptotically stable. Moreover, if the resting time between two consecutive anomalies is larger than the proposed bound, then all signals of the control system are guaranteed to be bounded. In the paper, we show that under the action of the proposed distributed adaptive controller, the interconnected system remains stable in the presence of network anomalies, with both the qualitative and quantitative resilient conditions. Extensive simulation results show the effectiveness of our theoretical results.

Resilient Distributed Control for Uncertain Nonlinear Interconnected Systems under Network Anomaly

TL;DR

This paper tackles resilient distributed control for uncertain nonlinear interconnected systems subjected to network anomalies. It develops a backstepping-based distributed adaptive controller with neural network approximations for uncertainty, and derives quantitative resilience conditions that bound anomaly duration and resting time to ensure stability or boundedness. The main contributions are a rigorous Lyapunov-based analysis yielding explicit bounds and a comprehensive simulation with four interconnected subsystems validating robustness to anomaly propagation. The results advance resilience quantification in cyber-physical systems by incorporating both local anomalies and their propagation through interconnections, without requiring precise anomaly detection. The framework offers practical guidelines for maintaining stable operation under stealthy network disturbances in large-scale CPS.

Abstract

We address a distributed adaptive control methodology for nonlinear interconnected systems possibly affected by network anomalies. In the framework of adaptive approximation, the distributed controller and parameter estimator are designed by exploiting a backstepping approach. The stability of the distributed control system under anomalies is analyzed, where both local and neighboring anomaly effects are considered. To quantify the resilience of the interconnected system under the action of network anomalies, we derive bounds on the duration of each anomaly and the resting time between two consecutive anomalies. Specifically, when each anomaly duration is smaller than our designed upper bound, the interconnected system controlled by the distributed approximation-based controller remains asymptotically stable. Moreover, if the resting time between two consecutive anomalies is larger than the proposed bound, then all signals of the control system are guaranteed to be bounded. In the paper, we show that under the action of the proposed distributed adaptive controller, the interconnected system remains stable in the presence of network anomalies, with both the qualitative and quantitative resilient conditions. Extensive simulation results show the effectiveness of our theoretical results.
Paper Structure (16 sections, 2 theorems, 114 equations, 11 figures, 2 tables)

This paper contains 16 sections, 2 theorems, 114 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. A glimpse of the state of the art
  3. Objectives and Contributions
  4. Assumptions and Problem Formulation
  5. Model description
  6. Network anomaly
  7. Adaptive approximation
  8. Problem statement
  9. Dessign of the distributed adaptive controller
  10. Resilience quantification with network anomalies
  11. The time duration of each anomaly
  12. Resting time between two consecutive anomalies
  13. Simulation
  14. Simulation of the time duration of each anomaly
  15. Simulation of the resting time between two consecutive anomalies
  16. ...and 1 more sections

Key Result

Theorem 1

Under Assumptions 1-4 and $\gamma>1$, the uncertain nonlinear interconnected system given by (1) and controlled by (17) is asymptotically stable, if the duration of each network anomaly satisfies where $n _m=\max \left\{n_i :i=\left\{ 1,...,M \right\} \right\}$, and

Figures (11)

  • Figure 1: Time series of network anomaly
  • Figure 2: The control structure of the interconnected system
  • Figure 3: The received states for the distributed controllers of the nonlinear interconnected system under multiple network anomalies. (The pale orange color represents the historical state that has been altered due to the network anomaly, while the pale green color indicates a secure state.)
  • Figure 4: Anomaly time intervals. $J\left( t \right)=1$: anomalous; $J\left( t \right)=0$: normal.
  • Figure 5: Trajectory of system states $x_{i,j}$ with long anomaly time
  • ...and 6 more figures

Theorems & Definitions (8)

  • Remark 1
  • Remark 2
  • Theorem 1
  • Remark 3
  • Theorem 2
  • Remark 4
  • Remark 5
  • Remark 6