Multi-agent Rendezvous Control Via Internal Model Approach

In recent years,the rendezvous problem of multi-agent system has received more and more attention of the control community.Different from the other cooperative control problems,where the network connectivity is predefined,the rendezvous problem that between requires the connection network among the agents is dynamically changed and the determined by the agents' states them-selves.Therefore,the proposed controller of the rendezvous problem should not only achieve global convergence,but maintain the connectivity of the network graph as well.Since the potential function is an important tool for maintaining the connectivity of network graphs,the choice of proper potential function is a difficult point of the rendezvous problem.Typically,potential function is usu-ally a nonlinear function which makes the controller should be also nonlinear.Consequently,the analysis of closed loop system is another difficult point of the rendezvous problem.By applying the potential function,rendezvous problem can be solved under the output regulation framework by a distributed observer based feedforward control and a distributed internal model design,respectively.In this paper,by the internal model principle,we will study two leader-following rendezvous problem as what follows.1.Investigate the leader-following rendezvous with connectivity preservation problem of single-integrator multi-agent systems subject to a nonlinear leader system.A class of distributed nonlinear internal model is established and the e-quivalent cooperative stabilization problem is solved by a potential function based nonlinear distributed controller.It is interesting that this nonlinear stabilizer has the ability of maintaining the network connectivity.2.Investigate the leader-following rendezvous problem for a class of single-integrator multi-agent systems subject to an uncertain leader.The problem is first converted into an auxiliary cooperative stabilization with connectivity preser-vation problem.The later problem is then solved by a potential function based high-gain feedback control.The proposed design is interesting in that none of the adaptive law is required,and hence results in a lower dimension control design in contrast with the traditional adaptive internal model control design.The theoretical result is also illustrated by a simulation example,and the simulation of the example is implemented by MATLAB.