Group Consensus Analysis And Design Of Multi-agent Systems

In the past decade,more and more scholars pay attention to the theoretical research and practical application on the coordination control of multi-agent systems.The key problem is to design suitable control protocols or algorithms finally to make some key quantity of multi-agent systems achieve consensus,according to different allocation of tasks and performance requirements.Because the multi-agent systems can achieve coordinated control of the whole system through the local information exchange,the coorperation control has been found many application such as cooperative control for unmanned aerial vehicle,target tracking of sensor network and congestion control in communication network.So far,many results have been derived for the consensus problem of multi-agent systems,while there are few results on the group consensus of multi-agent systems.Hence,in the thesis we study the group consensus problem and H_?group consensus problem of multi-agent systems based on the theory of nonnegative matrix,algebraic graph theory and Lyapunov stability theory.The main contributions are as follows:1.A balanced graph is one of conditions to guarantee individual states achieve consensus,in addition,a group balanced graph is one of conditions to make individual state in the same group achieve consensus.For weighted directed/ undirected graphs which have two subgraphs,we design two different group-balance algorithms respectively.Firstly,we study the group balance of weighted directed graphs containing two subgraphs and relize the balance for individuals in the same group by changing some of the edge weights.Then,for weighted undirected graphs including two subgraphs,we dicuss the group balanced agorithms for two cases: i)group balance the weighted undirected graphs containing two subgraphs connected each other;ii)group balance the weighted undirected graphs containing two subgraphs which have s(s?1)connected components.Two balanced agorithms are apparented to realize the group balance in finite steps.Finally,the effectiveness of theoritical results is verified by some example simulations.2.Three cases of H_? group consensus issues are considered for the first-order continuous-time multi-agent systems: i)fixed topology without communication time delay;ii)switching topology without communication time delay;iii)fixed topology with single communication time delay.For the three cases,we convert the original systems into reduced order systems,use Lyapunov stability theory to study the stability of reduced order systems,and obtain sufficient conditions in the form of linear matrix inequalities(LMIs)to solve the H_? group consensus problems of multi-agent systems.Finally,we verify the effectiveness of theoritical results through numerical example simulations.