State Consensus Of Heterogeneous And Interconnected Multi-Agent Systems Based On Linear Transformation

The cooperative control of multi-agent systems is now a research hotspot in a lot of application fields such as robot formation,UAV formation,intelligent transportation network and military exploration technology.The fundamental problem of multi-agent systems is consensus control problem,which has become the most important and basic research wind vane in the research of cooperative control of multi-agent systems.However,in practical engineering systems,due to the influence of external uncertainties and various constraints,the more common model of agents is heterogeneous,that is,the dynamic models of agents in the multi-agent system are different from each other.Therefore,the consensus of heterogeneous multi-agent systems with the same structure but different parameters are studied.The theoretical study of consensus problem of the heterogeneous multi-agent system can be used as a theoretical basis for vehicle networking and system formation,for example,the formation of vehicles composed of different types of networked vehicles or vehicles with different sizes and weights can reduce the distance between vehicles when they pass on the expressway,thus increasing the expressway traffic volume.At the same time,in real life,many multi-agent systems are interconnected,that is,there are inherent connections between the agents themselves,and this type of multi-agent systems is called as the interconnected multiagent systems.It can be used as the technical support of power grid system,heavy-haul train,traffic flow network and energy network.Therefore,through induction and analysis of scientific research results on existing consensus control problems,the consensus problem of heterogeneous and interconnected multi-agent systems is studied in depth.The main research contents and analysis ideas are shown below:Firstly,the leader-following state consensus of heterogeneous multi-agent systems under fixed directed communication topology is studied,and the research objects include high-order systems and second-order systems.The research ideas of this problem are as follows.First,for the general parameter heterogeneous model of multiagent systems,under the condition of directed communication topology with general matrix-type communication weights,a consensus protocol consisting of four parts is proposed.At the same time,the state linear transformation is adopted to equivalently transform the state consensus problem into a partial variable stability problem with rich research results.Then,based on the partial variable stability theory,some consensus criteria and analytical expressions expressed by the Hurwitz stability of real matrices are deduced,which are necessary and sufficient conditions.Finally,the gain matrices of the protocol are obtained by solving the bilinear matrix inequality by using the homotopy iterative algorithm,so as to verify the validity and feasibility of the proposed protocol design method by six groups of simulation examples.Secondly,the leaderless state consensus problem of second-order heterogeneous linear multi-agent systems under general fixed directed communication topology is explored.The analysis process is as follows.First,a general consensus protocol with different gain matrices and matrix-type communication weights is proposed,and the state linear transformation method is used to transform the consensus problem into the partial variable stability problem of the corresponding auxiliary system,so as to reduce the computational complexity.Then,for general form and special form of second-order leaderless heterogeneous multi-agent systems,sufficient and necessary consensus convergence criteria are deduced from Hurwitz stability,and based on bilinear matrix inequality,the homotopy algorithm is used to solve the gain matrices in the protocol.Finally,the accuracy of the derived uniform convergence criteria are proved by providing simulation examples of the leaderless heterogeneous multi-agent system in general and special cases.Thirdly,based on a general directed communication topology,the leader-following state consensus problem of high-order linear interconnected multi-agent systems is studied.The core line of research is as follows.First,a consensus protocol,which is more comprehensive than the control protocols used in the current interconnected multi-agent systems,is proposed consisting of leader input,state feedback of the agent itself,feedback of the relative state between the agent and its neighbors,and feedback of the relative state between the agent and the leader.Besides,different agents in the protocol can have different gain matrices and matrix-type communication weights.Then by using the method of state linear transformation,the leader-following state consensus problem of the interconnected multi-agent system is equivalently transformed into a fully studied partial variable stability problem,and a sufficient and necessary consensus convergence criterion expressed by the Hurwitz stability of real matrices is derived.Then,an iterative algorithm is used to design the gain matrices in the consensus protocol by solving bilinear matrix inequalities.Finally,the operability of the derived conclusion is illustrated by providing simulation examples of high-order leader-following linear interconnected multi-agent systems in two cases(the leader’s control signal is a constant vector and the leader’s control signal is zero).