Cooperative $\mathcal{H}_\infty$ Fault-Tolerant Tracking with ISS Guarantees for Networked Systems with Sensor Faults

TL;DR

This paper presents a scalable cooperative fault-tolerant control framework for networked linear systems with sensor faults, ensuring robust state estimation, disturbance rejection, and consensus tracking.

Contribution

It introduces an augmented $ ext{H}_ ext{infty}$ observer and a convex LMI-based controller synthesis for resilient cooperative tracking under sensor faults and disturbances.

Findings

Accurate state and fault estimation demonstrated in numerical studies.

Robust cooperative tracking achieved despite disturbances and sensor faults.

Network-wide consensus tracking guaranteed with ISS properties.

Abstract

This paper develops a cooperative fault-tolerant tracking framework for heterogeneous networked linear systems subject to sensor faults and external disturbances. Each unit employs an augmented $\mathcal{H}_\infty$ observer that jointly reconstructs the system state and unknown sensor fault, providing disturbance-attenuated estimation guarantees. An inner state-feedback gain is synthesized through convex $\mathcal{H}_\infty$ Linear Matrix Inequalities (LMIs) to ensure robust closed-loop stabilization and disturbance rejection, while an outer distributed integral action eliminates steady-state tracking offsets and enables cooperative tracking of a setpoint source. The resulting cooperative error dynamics are shown to satisfy an Input-to-State Stability (ISS) property with respect to disturbances and residual estimation uncertainty, and converge exponentially to zero in the disturbance-free case. Furthermore, vanishing cooperative error guarantees network-wide consensus tracking of the desired setpoint. Numerical studies on heterogeneous DC-motor networks with star, cyclic, and path communication topologies demonstrate accurate state and fault estimation, robust cooperative tracking, and resilience against disturbances and time-varying sensor faults. The proposed framework provides a scalable and robust coordination strategy for interconnected systems operating under sensing imperfections and uncertain environments.