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

A state and fault estimator is designed in this paper for nonlinear complex networks using binary encoding schemes subject to parameter uncertainties, randomly switching couplings, randomly occurring deception attacks and bounded stochastic noises. A Markov chain is employed to reflect the randomly switching phenomena of topological structures (or outer coupling strengths) and internal coupling strengths in complex networks. Binary encoding scheme is utilized to adjust the measurement signal transmission, where the signal is quantized and encoded into a binary bit string which is transmitted via a binary symmetric channel. Random bit flipping resulted from channel noises and randomly occurring deception attacks launched by hacker may take place inevitably during the network transmission process, whose occurrences are represented by two sequences of Bernoulli distributed random variables. The influence of random bit flipping is viewed as an equivalent stochastic noise, which facilitates the estimator design afterwards. The malicious signal is characterized by a nonlinear function satisfying an inequality constraint condition. The received binary bit string is decoded and used for estimating the system state and the fault. This paper aims to design a state and fault estimator such that the estimation error dynamic system is exponentially ultimately bounded in mean square, and the ultimate upper bound is minimized. A sufficient condition is put forth that ensures the existence of the expected state and fault estimator via adopting statistical property analysis, Lyapunov stability theory and matrix inequality technique. An exponentially ultimately bounded state and fault estimator in mean square is designed for such a kind of complex networks using the matrix inequality method. The estimator gain parameter is readily obtained by tackling an optimization issue subject to matrix inequalities constraints using Matlab software. Finally, two simulation examples are carried on which validate the effectiveness of the proposed state and fault estimation approach. The work in this paper plays a role in enriching the research system of estimation for complex network, and providing theoretical guidance for engineering applications.