Distributed $H_\infty$ Secure Fusion Estimation for Energy-Constrained Multi-Sensor Systems Under Hybrid Attacks

This paper investigates the distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> secure fusion estimation problem for energy-constrained multi-sensor systems subject to hybrid attacks. Given the limited energy supply, sensor nodes operate in two modes: high-energy mode, which ensures robust security during information transmission, and low-energy mode, which makes transmissions more vulnerable to hybrid attacks. The phenomenon of hybrid attacks is described as the stochastic occurrence of false data injection (FDI) and denial-of-service (DoS) attacks in the communication channels from sensors to local estimators. To handle these challenges, we propose a novel distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> secure fusion estimation model designed specifically for energy-constrained multi-sensor systems under hybrid attacks scenarios. Subsequently, sufficient conditions are derived to ensure that the secure fusion estimation error system achieves exponential mean-square stability and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance level. Additionally, the design of optimal fusion weight matrices is addressed. Finally, the effectiveness of the proposed distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> secure fusion estimation method is demonstrated through an illustrative example.