Secure Distributed Finite-Time Filtering for Positive Systems Over Sensor Networks Under Deception Attacks

This paper is concerned with secure ${\ell _{1}}$ -gain performance analysis and distributed finite-time filter design for a positive discrete-time linear system over a sensor network in the presence of deception attacks. A group of intercommunicating sensors is densely deployed to measure, gather, and process the output of the positive system. Each sensor is capable of sharing its measurement with its neighboring sensors in accordance with a prescribed network topology while suffering from random communication link failure. Meanwhile, the aggregated measurement on each sensor during network transmission is corrupted by stochastic deception attacks which compromise the sensor's measurement integrity. First, a unified sensor measurement transmission model is put forward to account for the simultaneous presence of deception attacks and various network-induced constraints. Second, delicate secure distributed filters are constructed by admitting the corrupted sensor measurement. Third, theoretical analysis on finite-time ${\ell _{1}}$ -gain boundedness of the filtering error system and design of desired positive filters are carried out. The solution to the filter gain parameters is characterized by a set of linear programming inequalities. Finally, the effectiveness of the obtained results is verified through the secure monitoring of power distribution in the smart grid.