Consensus Problems Of Multi-agent Systems

The consensus of multi-agent system is an important problem in the feld of systemsand control, it not only reveals many physical phenomena in nature, but also has a verywide application background. In this paper, by using a new form of variable transfor-mation, the consensus problem of multi-agent system is turned into the known stabilityproblem, through designing diferent consensus protocols, frst-order linear and nonlinearsystems and second-order linear and nonlinear systems are studied respectively, the con-sensus conditions are obtained. The main contents in this paper can be summarized asfollows:The frst section is introduction, in which we introduce research background, purposeand signifcance of consensus problem of multi-agent system, and then give the researchdynamic and direction. Finally the research contents and chapter arrangement of thispaper is also presented.Section2gives some preliminary knowledge. The necessary knowledge to establishmathematical model of multi-agent system which called algebraic graph theory, the basicdefnitions, theorems and some useful math marks are simple introduced in Section2.In Section3, consensus on the frst-order linear multi-agent system is analyzed, theconsensus protocols and the consensus conditions are given. By using a variable transfor-mation which is called star transformation, the consensus problem of multi-agent systemis translated into the simple stability problem. Finally, some numerical simulations aregiven to demonstrate the efectiveness of the results and the feasibility of the methods.The fourth section studies the consensus problem on the frst-order nonlinear multi-agent system and give the consensus protocols and the consensus conditions. Throughusing the same variable transformation as section3, the consensus problem of multi-agentsystem is translated into the simple stability problem. Finally, some numerical simulationsare given to demonstrate the efectiveness of the results and the feasibility of the methods. In Section5, consensus on the second-order linear multi-agent system is analyzed,two diferent consensus protocols and the consensus conditions are given to achieve thesecond-order consensus. By using the same star transformation, the consensus problem ofmulti-agent system is translated into the simple stability problem. Finally, some numericalsimulations are given to demonstrate the efectiveness of the results and the feasibility ofthe methods.The sixth section studied the consensus problem on the second-order nonlinear multi-agent system and give the consensus conditions for achieving the second-order consensus.By using the properties of special functions and Russell invariant principle, the consensusproblem of multi-agent system is translated into the simple stability problem. Finally,some numerical simulations are given to demonstrate the efectiveness of the results andthe feasibility of the methods.