On Reaching Weighted Consensus Of Second-order Multi-agent Systems With Time-Delay

The consensus of the multi-agent system means that any node in the cluster does not utilize the central controller or global communication signals.They only communicate and share resources with their neighbors,so that the states of all the agents in the cluster convergence to the same value.This complex behavior of cooperation effectively improve the ability of individuals to complete complex tasks in engineering applications.Being affected by external factors such as delay,noise,and communication topology,there will be variety of consensus states in the multi-agent system.However,in real applications,it is usually required to control the multi-agent system reaching a specific final state.The weighted consensus method can effectively achieve this goal.Therefore,the research on the weighted consensus of multi-agent systems is more practical.In this paper,algebraic graph theory,matrix theory,frequency domain control theory and stability theory are used to analyze and discuss the weighted consensus problems of second-order continuous-time multi-agent systems without time-delay,the weighted consensus of continuous-time multi-agent systems with time delay and the weighted consensus of second-order discrete-time multi-agent systems with time delay.The contents of this article can be summarized as follows:The weighted consensus problem of second-order continuous-time multi-agent systems without time delay and under directed equilibrium graph is studied.Based on the cooperative relationship between agents,a novel weighted consensus control protocol for second-order continuous-time multi-agent system was first proposed.The algebraic condition criterion for the system to achieve weighted consensus is obtained,and the correctness and validity of the obtained conclusion are further verified by numerical simulation experiments.The weighted consensus problem of second-order continuous-time multi-agent systems with time-delay under directed equilibrium graph is discussed.Due to the limitations of communication channel bandwidth and information transmission speed,various types of delays may occur in the transmission and reception of information between agents.In order to get closer to the actual application requirements,this paper discusses the system's weighted consensus problems with time-delay and then obtains the algebraic condition criterion for the system's asymptotic convergence.Based on the cooperative relationship between agents,a novel weighted consensus control protocol with delay is proposed.The correctness of the protocol is verified by mathematical proofs.At the same time,the conditions of algebraic conditions for asymptotic convergence of the system are obtained.Finally,simulation experiments verified the correctness of the theoretical results.Moreover,through theoretical analysis and simulation experiments,it can be concluded that within the scope of algebraic conditions,the specific convergence state of the system has nothing to do with time delay,coupling weight,and coupling strength,but only with the node weight and the initial state of each agent.The weighted consensus problem of the second-order discrete-time multi-agent systems with time-delay under the directed equilibrium graph is analyzed.Due to the limitation of various factors,there are often discrete-time systems in practical engineering applications.Inspired by this,the weighted consensus of the second-order discrete systems based on equilibrium graphs are discussed,and the influence of delay on the consensus problems is also discussed.A novel second-order system weighted consensus control protocol is proposed,and the algebraic condition criterion for ensuring weighted consensus is obtained.Through theoretical analysis and simulation experiments,it can be concluded that the weighted consensus of the multi-agent systems is only related to the node weight and the initialization state of each agent.