Proportional-Integral State Estimation for a Class of Nonlinear Complex Networks With Uncertain Couplings: Tackling Adversarial Replay Attacks

This paper addresses the proportional-integral state estimation problem for a class of complex networks with uncertain inner couplings under replay attacks. The inner coupling strengths are subject to fluctuations within a specified interval. A replay attack strategy is implemented by the adversary on the communication channel between the network nodes and the state observers, with the intention of replacing the current measurement data with previously recorded measurement data. The dynamic behavior of these replay attacks is characterized by two factors: one dependent on a stochastic variable and the other on a time-varying parameter. A proportional-integral observer (PIO) is developed to handle the challenges posed by uncertain internal couplings and replay attacks. By employing stochastic analysis and matrix inequality techniques, sufficient conditions are obtained to ensure the 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 of the estimation error dynamics. Moreover, the PIO gain parameters are determined through the solution of some matrix inequalities. Finally, numerical simulation results are presented to verify the effectiveness of the developed PIO design algorithm.