The Controllability And Optimal Topological Structure Of A Class Of Multi-agent Network Systems Under Symbolic Directed Graphs

With the rapid development of engineering application technology in the field of modern network control,the system becomes more and more large-scale,the complexity increases,the target task is complicated,and the wide popularization of distributed multi-agent network system has become the mainstream choice of the development trend of science and technology.The controllability method is the key technology to decide whether the distributed multi-agent network system can be successfully applied in the project.The discussion of optimal topological structure is an important direction to solve the cost of industrial application.This paper deals with the controllability algebraic criteria of a class of multi-agent network systems under signed digraph and the optimal structure of the corresponding topological graphs under the given system cost function.In the controllability part of the system,the Laplacian matrix of the system is transformed into the Jordan standard matrix by the linear transformation which does not change the controllability of the multi agent network system.For Jordan standard matrix with controllability equivalence,the concept of Jordan block controllability and the minimum number of external inputs are defined respectively.Based on the fixed minimum external coupling inputs,the constraints of controllability on topology communication are discussed.Based on the fixed topological properties,the influence of the number of external coupling inputs on the controllability of the system is investigated.Theoretical results show that the realization of perfect controllability is a more complex representation of the constraints of topological rules among agents.In addition,this paper extends the problem of perfect controllability to the more general case of multiple external inputs,it is defined as a general perfect controllability problem.In the part of optimal topological structure,the cooperative-competitive directed network system is transformed into cooperative directed network system analysis by using the method of canonical transformation.Combined with the knowledge of LQR theory and Graph theory,this paper discusses how to achieve the bipartite consensus of a given cost function with minimum energy consumption.Based on the coupling between control energy and information interaction between agents in the system,the connection characteristics of the optimal topology corresponding to single-leader case and multileader case in the first-order,second-order and general linear systems are presented.In the simulation part of the conclusion,abundant examples and simulation results are used to provide sufficient reliability support for the research content.The formulation of controllability criteria,especially the theoretical results of general perfect controllable topology,is of great commercial significance to accelerate the application process of distributed multi-agent network system.Based on the analysis of the topological structure of the system energy cost,the paper optimizes the energy usage caused by the communication characteristic and the communication mode of the agent on the basis of realizing the bipartite consensus,which has an important practical influence on the conversion of the industrial production.