Study On Group Consensus Of Multi-agent Systems

Because of the wide applications in military and civilian problems, the dis-tributed control of multi-agent systems has been an active research field andattracted many researchers from mathematics, physics, biology, control science,computer science, etc. Consensus is the base to develop other coordinated con-trol problems. This dissertation studies group consensus problems of multi-agentsystems and our main results and contributions are as follows.1. For first-order multi-agent system with periodic sampled-data control, weestablish its group consensus criteria. By algebraic graph theory, matrix theory,it is proved that the group consensus can be reached if and only if the Laplacianmatrix has exactly0eigenvalue of multiplicity two, all the other eigenvalues havepositive real parts and the sample period h satisfies some conditions. Whether thegraph has a directed spanning tree has no inevitable relation to group consensus.2. A rotation matrix is introduced to an existing consensus algorithm forsingle-integrator dynamics. Based on algebraic matrix theories, graph theoriesand the properties of Kronecker product, some necessary and sufcient criteriafor the group consensus are derived, where we show that both the eigenvaluedistribution of the Laplacian matrix and the Euler angle of the rotation matrixplay an important role in achieving group consensus.3. For second-order multi-agent systems, by augmented system method, themulti-agent system is equivalently transformed into a discrete-time system, whichreduces the difculty of our research in a sense. By algebraic graph theory andmatrix theory, some necessary and sufcient conditions of the group consensusare derived.