Output Consensus For Multi-Agent Linear Systems With Input Saturation

In recent years,the consensus problem of multi-agent linear systems has attracted compelling attention from many researchers in the field of control.Consensus behavior is a way of life in the process of biological evolution,it can be seen from a lot of phenomena of biological behavior,such as the migration of birds,foraging behavior of fish school,nesting of bee,honey behavior of bee and so on.In the practical study,the researchers in various field abstract the biotic population as the multi-agent systems.The wide attention and research on distributed consensus control will obtain a broadly application in many fields,such as network science,multi-vehicle cooperative control,sensor networks,mobile robot control and so on.This paper has fully insight of the research methods and current research status of multi-agent distributed consensus control problem,which agents are subjected to the external disturbance and input saturation.Consider the perspective of network topology graph,based on low gain technique a distributed algorithm is proposed to solve the output consensus of multi-agent linear systems with external disturbance.The external disturbance can be treated as leader.Then a Lyapunov function based on M matrix theory is proposed.This paper puts forward state feedback law,error feedback law to solve the output consensus of discrete-time system and continuous-time system.A state feedback law is proposed to solve the output consensus problem of discrete-time system.This algorithm can guarantee the output of all agents to reach a same value under a directed topology.In addition,from the perspective of external disturbance,two output consensus models of discrete-time systems are given.The validity of the distributed algorithm can be proved by the Lyapunov stability theory,graph theory,low gain technique.Eventually some numerical simulation examples based on Matlab are given to prove the validity of the theory.Based on the output consensus problem of discrete-time systems,this paper extends the distribute consensus algorithm to figure out the output consensus of continuous-time multi-agent linear systems.Combined with low gain feedback technique,a distributed consensus algorithm based on the error feedback is proposed.This algorithm can make the outputs of all agents are close to the output of external disturbance,the state of observer can approach to the actual state.The input of agents is only correlated with the dynamic of the leader,if these agents have direct communication with leader.Eventually some numerical simulation examples based on Matlab are given to prove the validity of the theory.