Research On Consensus Problems Of Multi-Agent Systems Under False Data Injection Attacks

In the fourth Industrial Revolution,the increasing demand for the "smart factory" makes the distributed cooperative consensus of multi-agent systems attract tremendous attention in recent years.In the study of multi-agent systems,consensus problem is always a hot issue.In past research,researchers would assume that the environments that multi-agent systems stay are safe,which means multi-agent systems will not be influenced by cyber attacks.However,the reliance of multi-agent systems on communication networks exposed them to the threat of cyber attacks.Therefore,it is necessary to take cyber attacks into consideration when designing multi-agent systems.Within the research area of cyber attacks,the stealthy of false data injection attacks makes them more aggressive than other attacks.To mitigate the impact that false data injection attacks imposed on multi-agent systems,researchers have put up many different methods to ensure multi-agent systems can achieve consensus in the presence of false data injection attacks.Under this research background,this paper designed several control schemes for different kinds of false data injection attacks.The main contributions of this paper are as follow(1)For the known-bound false data injection attacks,this paper developed sufficient conditions that ensure consensus of multi-agent systems under known-bounded false data injection attacks in the form of linear matrix inequalities.Based on these conditions,this paper further put up linear matrix inequalities that can be used to calculate the appropriate control gain matrix.In the design of this control scheme,this paper first leaves out the parameter uncertainties to obtain sufficient conditions ensuring consensus of multi-agent systems.Then introduce these parameter uncertainties by applying the Schur complement.Based on these conditions,this paper designed the linear matrix inequalities to obtain the appropriate control gain matrix.Finally,a numeric example is given to validate the feasibility of this scheme.(2)For the unknown-bound false data injection attacks,this paper designed an adaptive fault-tolerant control protocol to ensure the leader-following consensus of multi-agent systems.First,this paper applied radial basis function neural networks to approximate the unknown part of multi-agent systems,then designed the fault-tolerant control protocol to ensure the leaderfollowing consensus of multi-agent systems.After that,the Lyapunov stability theorem is applied to validate the convergence of the proposed control protocol theoretically.Finally,a numerical example is given to validate the feasibility of the proposed control protocol.(3)For the state-based false data injection attacks,this paper designed an adaptive faulttolerant control protocol to ensure the leader-following consensus of multi-agent systems.First,radial basis function neural networks are applied to approximate the unknown part of each agent.Then,new adaptive laws are designed to approximate the parameters of false data injection attacks.Finally,the convergence and feasibility of this adaptive control protocol are proofed by the Lyapunov stability theorem and are validated by numerical examples,respectively.