Non-Negative Scaled Edge-Consensus Of Multi-agent Systems With Input Saturation

Multi-agent systems fulfill complex tasks through communication and collaboration between agents.It has the advantages of robustness,reliability,and flexibility,and has aroused many attentions from researchers in many areas.This paper focuses on the multi-agent systems,based on given nodal network,the corresponding edge network is established,and the edge model of positive systems with input saturation is established.Then with the help of the ARE-based low-gain feedback technique,graph theory,matrix theory,positive system theory,and the relationships between the node network and edge network,non-negative scaled edge-consensus problems of linear continues-time systems and linear discrete-time systems with non-negative constraints and input saturation are solved respectively,which enriches the existing results of consensus problems.The main achievements are given as follows:The semi-global scaled edge-consensus problems of linear continuous-time multi-agent systems on both undirected networks and directed networks is researched.By utilizing the ARE-based low-gain feedback method,graph theory,matrix theory and positive system theory,the distributed edge-consensus protocols for both undirected and directed networks are established.Then the feedback gain matrix is designed to guarantee the non-negative scaled edge-consensus with input saturation and non-negative constraint.Finally,some sufficient conditions are obtained to guarantee the non-negative edge states and avoid the input saturation,which only need the edge number and the nodal number.The semi-global scaled edge-consensus problems of linear discrete-time multi-agent systems on both undirected networks and directed networks is researched.By utilizing the modified algebraic Riccati equation(MARE)-based low-gain feedback method,the graph theory,the matrix theory and the positive system theory,the distributed edge-consensus protocols for both undirected and directed networks are established.Then given suitable low-gain feedback parameters can solve the non-negative edge-consensus problem with input saturation and non-negative constraint.Finally,some sufficient conditions are obtained to guarantee the non-negative edge states and avoid the input saturation,which only need the edge number and the nodal number.The semi-global scaled edge-consensus problems of linear discrete-time multi-agent systems on undirected networks is researched.By utilizing the MARE(modified algebraic Riccati equation)-based low-gain feedback method,the graph theory,the matrix theory and the positive system theory,the distributed edge-consensus protocols for undirected networks are established.After finding suitable low-gain feedback parameters,the observer matrix and the feedback gain matrix for undirected networks are designed to guarantee the non-negative scaled edge-consensus with input saturation and non-negative constraint.Finally,some sufficient conditions are obtained to guarantee the non-negative edge states and avoid the input saturation,which only need the edge number and the nodal number.Besides,the sufficient conditions of the edge-consensus protocols are also proved to guarantee the non-negative edge-states and the bounded control input.