Research On Consensus Problems Of Mixed-Order Multi-Agent Systems

In the past decades,multi-agent systems have been paid more and more attention and applied due to their excellent characteristics of distributed control,and the consensus problems are the key to solve the coordination control problems of multiagent systems.In industrial applications,due to various influencing factors or actual task requirements,the dynamic models of individuals in the systems usually take different forms,and because the integrators of the first-order,second-order and thirdorder have definite physical meanings,it is of great application value to study and analyze the consensus problems of the mixed-order multi-agent systems.In this paper,algebraic graph theory,control theory and other relevant knowledge are used to study the consensus problems of mixed-order multi-agent systems as follows.This article firstly to the continuous-time mixed-order to study the consensus problems of multi-agent systems,considering the mixed-order systems of “first-order and second-order”,“second-order and third-order” and “first-order,second-order and third-order” these three kinds of different continuous-time mixed-order systems,according to different systems of second-order agents and third-order agents respectively corresponding linear filters design.Two consensus protocols are designed for each type of systems under the condition that the network topologies are directed and fixed,and the sufficient conditions for the systems to achieve consensus are obtained,and the numerical simulations are carried out.Secondly,the consensus problems of discrete-time mixed-order multi-agent systems are studied,considering the mixed-order systems of “first-order and secondorder”,“second-order and third-order” and “first-order,second-order and third-order”these three kinds of discrete-time mixed-order systems,one higher than the order of the agents for order reduction transformation by analogy the solution of differential equations in continuous-time control systems.Two consensus protocols are designed for each type of systems in undirected fixed topologies respectively,and the sufficient conditions for systems consensus are obtained,and numerical simulations are conducted.Finally,the interface design of all the numerical simulation diagrams in this paper makes the simulation results look more intuitive and more suitable for people’s office needs in the modern information society.