Research On Consensus Problems Of Multi-Agent Systems Under Replay Attacks

Distributed cooperative control of multi-agent systems has attracted mounting attention in recent years.In this research field,security of multi-agent systems has become hot issues gradually.Among them,research on security issues has gradually become an emerging research direction in the field of control.In practical application,there are often many malicious attacks during the process of information transmission among agents.Replay attacks are common attack methods of computer hackers since stealthiness often brings great harm to the system.Since it is hard to predict when and where these attacks will take place,it is important to provide resilient solutions to mitigate the effects of replay attacks such that multi-agent systems can complete the task under malicious attacks.In addition,with the widespread application of digital sensors and controllers,information transmission between agents is usually periodic.Therefore,it is of great theoretical significance to study the secure consensus of discrete time multi-agent systems under replay attack.Based on the model predictive control,this paper studies the secure consensus problem of discrete time multi-agent systems under replay attack for three different multi-agent systems models.The main contributions of this paper are as follows:(1)The secure consensus problem of first-order multi-agent systems under replay attack is studied.The communication topology of the system is assumed to be fixed topology and switching topology respectively,by the model predictive control algorithm,secure consensus control protocol and state information sequence are obtained.Thereby the problem that the state information of the agent is not available under replay attack is effectively solved.Firstly,considering the existence of replay attack,by applying algebraic graph theory,the original system is turned into an equivalent one whose system matrix is stochastic.Sufficient conditions under which first-order multi-agent systems reach consensus asymptotically under replay attack are obtained by applying the properties of nonnegative matrix.Furthermore,the effectiveness of the proposed control scheme is verified by numerical simulation.(2)The secure consensus problem of second-order multi-agent systems under replay attack is studied.Rewrite the second-order system into a compact form when the network topology of the system is strongly connected.Consider the irregularity of replay attacks,by the model predictive control algorithm,secure consensus control protocol and state information sequence are obtained.Thereby the problem that the state information of the agent is not available under replay attack is effectively solved.Firstly,by model transformations and applying the related algebraic graph theory,the original system is turned into an equivalent one whose system matrix is stochastic.Then,based on this obtained equivalent system,sufficient conditions under which second-order multi-agent systems reach consensus asymptotically under replay attack are obtained by apply the properties of nonnegative matrix.Furthermore,the effectiveness of the proposed control scheme is verified by numerical simulation.(3)The secure consensus problem of second-order multi-agent systems with switching topologies under replay attack is studied.When the network topology of the system is directed,distributed consensus algorithm against replay attacks is designed by applying the model predictive control methodology.Thereby the harm of replay attacks is mitigated.Firstly,by model transformations and applying the related algebraic graph theory,the original system is turned into an equivalent one whose system matrix is stochastic.Then,based on this obtained equivalent system,sufficient conditions under which second-order multi-agent systems with switching topologies reach consensus asymptotically under replay attack are obtained by apply the properties of nonnegative matrix.Furthermore,the effectiveness of the proposed control scheme is verified by numerical simulation.