Dynamic event-triggered mean-square consensus of positive multi-agent systems via impulsive control under false data injection attacks

Abstract

This paper investigates the mean-square impulsive consensus problem of positive multi-agent systems (MASs) under stochastic sensor false data injection attacks (FDIA). False data injection attacks are mortal to a positive system since the system positivity could be destroyed with ease (by tampering with the sampled positive state value to a negative one, for instance). To deal with this issue, a data compensator is proposed which preprocesses deliberately distorted state values to reduce their adverse impacts on the positivity of the positive MASs. On the other hand, a novel sampled-data-based dynamic event-triggered mechanism (SDB-DETM) is tailored to generate impulsive control time sequences, save control costs, and promise a desired control performance. A maximum event-trigger time interval is introduced as a substitute for the assumption of the average time interval when considering the randomness of FDIA. Furthermore, the dynamics of the auxiliary dynamic variable are improved to adapt the novel SDB-DETM with mixed signals. A sufficient and necessary condition of the positivity of the positive MASs under FDIA is presented. The commonly used positive constraints on the error system are removed. By constructing a quadratic Lyapunov function, a sufficient condition of the mean-square consensus of the positive MASs is derived. Two numerical examples are provided to illustrate the effectiveness of theoretical results.