Research On Consensus Of Multi-agent Systems With A Saturation Constraint

In recent years,the distributed control for multi-agent systems is a new and emerging scientific discipline that has attracted extensive and in-depth investigations by scientist from various fields including biology,mathematical and physical science,computer science,mechanics and control theory.This is mainly attributed to the vast practical applications in such fields as spacecraft formation control,distributed sensor networks,congestion control in communication networks,parallel computing as an interdiscipline.Consensus problem is one of the fundamental problems arise in multi-agent systems.The objective of consensus is to design appropriate and effective distributed protocols for each agent so that the states such as voltage,position,velocity,etc.,of all agents in the system can reach a consensus as time goes by.The consensus protocols is rules of information exchange between the agents themselves and their neighbors.Based on the present research,taking advantage of algebraic graph theory,matrix theory and stability theory,this thesis mainly studies the more generalized consensus problems,group consensus,as well as the consensus problem under the saturation constraint.Firstly,some preliminaries such as algebraic graph theory,matrix theory and stability theory are introduced.The consensus for multi-agent systems under continuous and discrete time are introduced and verified.Secondly,the consensus for continuous-time multi-agent systems is investigated based on current work in continuous-time multi-agent systems with single-integrator dynamics.For continuous-time multi-agent systems with double-integrator dynamics,we design a group consensus protocol containing a couple coefficient ?.The sufficient conditions of group consensus under the directed communication topology are obtained.We also discuss the influence to the convergence speed of the system by the couple coefficient ?.For continuous-time multi-agent systems with double-integrator dynamics under the connected bipartite graph,the group consensus protocol based on competition is designed for the multi-agent systems,while the sufficient conditions of group consensus and the consensus equilibriums of each subgroups are obtained based on the algebraic graph theory and the matrix theory.Thirdly,the consensus for discrete-time multi-agent systems is investigated.For discrete-time multi-agent systems with single-integrator dynamics,a protocol design method without the in-degree balanced assumption is presented.a group consensus protocol for first-order discrete-time multi-agent systems is designed,while the sufficient and necessary conditions of group consensus for the systems are obtained.In contrast to the existing results,the conclusions we have obtained are more general for they don't rely on the in-degree balanced assumptions and special topology.Lastly,for continuous-time multi-agent systems with single-integrator dynamics under the saturation constraint,we design a consensus protocol with a bounded control input.The sufficient and necessary conditions of consensus for multi-agent systems under the undirected topology are obtained by The characteristics of hyperbolic function and Lyapunov control approach.