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Cooperative Observer-Based $\mathcal{H}_\infty$ Fault-Tolerant Tracking Control for Networked Processes with Sensor Faults

Moh Kamalul Wafi, Yurid E. Nugraha, Bambang L. Widjiantoro, Katherin Indriawati

Abstract

This paper develops a cooperative fault-tolerant control framework for heterogeneous networked linear systems subject to sensor degradation and external disturbances. Each unit employs an augmented $\mathcal{H}_\infty$ observer that jointly reconstructs its state and sensor fault, providing disturbance-attenuated estimation guarantees. An inner state-feedback gain is then synthesized via convex $\mathcal{H}_\infty$ LMIs to ensure robust closed-loop stabilization, while an outer distributed integral action drives all units to track a constant setpoint source. The resulting network error dynamics satisfy an input-to-state stability condition with respect to disturbances and estimation imperfections, and converge to zero in their absence. Simulations on star, cyclic, and path topologies with heterogeneous agents confirm reliable tracking despite abrupt sensor faults and bounded disturbances, demonstrating a scalable and resilient coordination strategy for multi-agent systems with sensing imperfections.

Cooperative Observer-Based $\mathcal{H}_\infty$ Fault-Tolerant Tracking Control for Networked Processes with Sensor Faults

Abstract

This paper develops a cooperative fault-tolerant control framework for heterogeneous networked linear systems subject to sensor degradation and external disturbances. Each unit employs an augmented observer that jointly reconstructs its state and sensor fault, providing disturbance-attenuated estimation guarantees. An inner state-feedback gain is then synthesized via convex LMIs to ensure robust closed-loop stabilization, while an outer distributed integral action drives all units to track a constant setpoint source. The resulting network error dynamics satisfy an input-to-state stability condition with respect to disturbances and estimation imperfections, and converge to zero in their absence. Simulations on star, cyclic, and path topologies with heterogeneous agents confirm reliable tracking despite abrupt sensor faults and bounded disturbances, demonstrating a scalable and resilient coordination strategy for multi-agent systems with sensing imperfections.

Paper Structure

This paper contains 6 sections, 5 theorems, 39 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Communication Network
  3. Problem Formulation
  4. Cooperative Fault--Tolerant Control
  5. Numerical Results
  6. Conclusion

Key Result

Proposition 1

Assume that Remark rem:threshold holds such that the Laplacian $\mathbb{L}$ is positive stable and the weights $w_{ij}, w_{i0}\ge 0$ satisfy $(\mathbb{A}_m+\mathbb{A}_0)\mathbf{1}_m=\mathbf{1}_m$. Therefore $\bar{e} = 0$ if and only if $\hat{y}_i = \hat{y}_j$ for all $i,j\in\{1,\dots,m\}$ and $\hat{

Figures (3)

  • Figure 1: Example of a graph $\mathcal{G}$ with $m=5$, unit-to-unit subgraph $\mathcal{G}_m$, and source-to-unit subgraph $\mathcal{G}_0$, showing the decoupling and assignment of $w_{ij}$.
  • Figure 2: Three network topologies $(\mathcal{G}_{\mathrm{s}}, \mathcal{G}_{\mathrm{c}}, \mathcal{G}_{\mathrm{p}})$ with weights used in the simulations.
  • Figure 3: Trajectories of $m = 4$ sensing nodes for three topologies, along with corresponding error norms.

Theorems & Definitions (14)

  • Remark 1
  • Definition 1
  • Proposition 1
  • Theorem 1
  • Theorem 2
  • Remark 2
  • Theorem 3
  • Remark 3
  • Corollary 1
  • Proof 1: Proof of Proposition \ref{['prop:e-zero-implies-consensus']}
  • ...and 4 more