Resilient Distributed Control for Uncertain Nonlinear Interconnected Systems under Network Anomaly

TL;DR

This paper proposes a distributed adaptive control method for nonlinear interconnected systems that maintains stability despite network anomalies by deriving bounds on anomaly duration and resting time, supported by simulations.

Contribution

It introduces a novel distributed adaptive control approach that ensures stability under network anomalies by quantifying resilience through bounds on anomaly duration and frequency.

Findings

System remains asymptotically stable if anomaly duration is below a certain bound.

All signals stay bounded if resting time exceeds a specific threshold.

Simulation results confirm theoretical resilience conditions.

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.