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State and Fault Estimation for Uncertain Complex Networks Using Binary Encoding Schemes Under Switching Couplings and

Nan Hou^1,2,3,4,5, Mengdi Chang^2,4,6, Hongyu Gao^1,2,3,4,6

¹Sanya Offshore Oil & Gas Research Institute of Northeast Petroleum University, Sanya 572025, China.

Sensors (Basel, Switzerland)

|January 10, 2026

Summary

This summary is machine-generated.

This study introduces a novel state and fault estimator for nonlinear complex networks, incorporating binary encoding to manage uncertainties and attacks. The approach ensures estimation error is bounded, minimizing the upper bound for robust performance.

Keywords:

binary encoding schemes complex networks deception attacks randomly switching couplings state and fault estimation

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Area of Science:

Control Systems Engineering
Network Science
Information Theory

Background:

Complex networks are susceptible to parameter uncertainties, switching couplings, deception attacks, and noise.
Existing estimation methods may not adequately address these combined challenges in nonlinear systems.

Purpose of the Study:

To design a state and fault estimator for nonlinear complex networks.
To ensure the estimation error dynamic system is exponentially ultimately bounded in mean square.
To minimize the ultimate upper bound of the estimation error.

Main Methods:

Utilizing a Markov chain for random switching phenomena.
Employing binary encoding for measurement signal transmission via a binary symmetric channel.
Viewing random bit flipping as equivalent stochastic noise.
Applying statistical property analysis, Lyapunov stability theory, and matrix inequality techniques.
Solving an optimization problem for estimator gain parameters using MATLAB.

Main Results:

A state and fault estimator is designed for nonlinear complex networks under various uncertainties and attacks.
Sufficient conditions for the existence of the estimator are established.
The estimation error dynamic system is proven to be exponentially ultimately bounded in mean square.
Simulation examples validate the effectiveness of the proposed approach.

Conclusions:

The developed state and fault estimator effectively handles nonlinear complex networks with parameter uncertainties, switching couplings, deception attacks, and stochastic noises.
The method provides theoretical guidance for engineering applications in complex network estimation.
The approach enriches the research landscape of estimation for complex networks.