Couple-Group Consensus For Delayed Discrete-Time Heterogeneous Multi-Agent Systems

Complex systems and collaborative control are an important branch of distributed artificial intelligence.They are widely used in many fields such as computer science,automation control,communication engineering and bionics.The group consensus problem of multi-agent systems are the premise and foundation of collaborative control of complex systems,and it is also a frontier and hot spot.At present,the research related to the group consensus problem mostly is based on the homogeneous system,that is,the whole system is composed of agents with the same dynamics.However,due to environmental constraints and actual demand,there are usually differences in the agents.Therefore,it is particularly necessary to study the group consensus problem of heterogeneous systems.It not only increases the flexibility of system construction,but also makes full use of resources to save control costs.Meanwhile,most of the current control protocols of group consensus have strict restrictions on the system topology,such as the in-degree balance.In addition,the communication delay and input delay may occur due to insufficient communication and computing capabilities in the actual operation,time delay is an important factor that affects or even destroys the stability of complex systems.However,most of the current research work does not consider or only consider one of them.Based on the existing work,using complex network theory,system stability theory and distributed computing theory,the group consensus problem of two kinds of discrete-time heterogeneous multi-agent systems affected by communication and input time delay is discussed.The specific contents are as follows:The dynamics model of discrete-time heterogeneous systems composed of firstorder and second-order agents are constructed,which are affected by communication and input delays.On this basis,unlike the common cooperative-based consensus strategies,we design novel protocols by using the feature of the bipartite graph and the competitive relationship between agents.In this way,making the system topology not need to meet the strict in-degree balance condition existing in the cooperative-based system.For the system with time delays,using the frequency domain method and the Gerschgorin theorem,the sufficient conditions for the heterogeneous system to achieve group consensus are obtained.The theoretical results show that the decisive factors for achieving consensus are system control parameters,network coupling weights and the input delay of each node,while the communication delays among agents do not determine the consensus.Simulation experiments verify the correctness of the theories and the effectiveness of the group control protocol.In addition,the experiments also show that the communication delay does not affect the convergence of the heterogeneous system,but it will interfere with the convergence speed of the system.Based on the study above,in the purpose of releasing more constraints,the group consensus of heterogeneous multi-agent system where cooperation and competition coexist is discussed.Novel group consensus protocols are designed to make nodes in the same group to cooperate to converge but nodes in the different groups to compete to disperse.In this way,the system topology does not need to meet the in-degree balance condition neither to be the bipartite graph.The algebraic conditions for ensuring consensus are obtained through theoretical analysis.The theoretical results show that the system control parameters,network coupling weights and input delays determine whether the system can achieve group consensus.The simulations verify the correctness of the theoretical results and the validity of the group consensus control protocol.