Research On Structural Controllability Of Networked Multi-agent Systems With Time-delays

The controllability of networked multi-agent systems has become a hot issue and has certain theoretical value and practical significance.On the basis of previous achievements.Through graph theory,control theory,matrix theory and corresponding mathematical software,this paper mainly studies the complete controllability and structural controllability of multi-agent systems with single time-delays model and multiple time-delays model from the perspectives of algebra and graphics.There are three main aspects as follows:1.The complete controllability and structural controllability of discrete-time multi-agent systems based on absolute protocol with time-delays are studied.We establish a single time-delays model and multiple time-delays model respectively,and transform them into an equivalent augmented system without time-delays,and prove that the augmented system of high dimension without time-delays is equivalent to a subsystem of low dimension,thus some new sufficient and necessary conditions of algebraic and graphical are obtained for complete controllability and structural controllability of the corresponding systems,which also verifies the complete controllability and structural controllability of the original system.At the same time,the numerical examples are given and the corresponding results are verified by simulation.2.The controllability of multi-agent systems of some special topologies based on relative protocols with time-delays is studied.The necessary and sufficient conditions for the controllability of some special topologies are established.By studying the relationship between controllability conditions and special topologies,an applicable controllability algorithm of multi-agent systems is proposed,which is used to test the controllability of these special topologies,and the conclusions of controllability under different topologies are obtained.3.The structural controllability of discrete-time multi-agent systems based on relative protocol is studied.The single time-delays model and multiple time-delays model under relative protocol are established.And an equivalent augmented system without time-delays is obtained,which is transformed into a system of lower dimension.And this system is equivalent to the original system.On this basis,the structural controllability of the system is discussed.The corresponding numerical examples are used to verify the theoretical results.