Global Leader-following Consensus Of Multi-agent Systems Using Bounded Controls

As a fundamental problem in distributed control of multi-agent systems,consensus has attracted significant amount of attention in recent years,in part due to its pervasive applications in engineering,including unmanned air vehicles,mobile robots and autonomous underwater vehicles.In the early literature,much efforts have been made towards solving various consensus problems for identical linear dynamic systems.However,the majority of the early results do not take into consideration actuator saturation,which is ubiquitous in practical control systems.Thus,further investigations for multi-agent systems using bounded controls are in order.This dissertation systematically investigates global leader-following consensus of multi-agent systems subject to input saturation in a unified leader-follower framework.We focus on the consensus of four different classes multi-agent systems operating on different network topologies,neutrally stable systems,double integrator systems,general linear systems in continuous-time and general linear systems in discrete-time.The main contributions of this dissertation are stated as follows.1.Investigation on global leader-following consensus of two classes of multiagent systems,neutrally stable systems and double integrator systems,subject to input saturation.For neutrally stable systems,we establish that global consensus can be achieved by linear local feedback laws over a fixed communication topology,and with proper choices of relative potential functions,global consensus can also be achieved over a switching communication topology.For double integrator systems,we establish that global consensus can be achieved by linear local feedback laws over a fixed communication topology,and with the help of a simple saturation function in the local feedback laws,global consensus can also be achieved over a switching communication topology.2.Investigation on global leader-following consensus of a group of general continuous-time linear systems subject to input saturation.The follower agents and the leader agent are all described by a general continuous-time linear system that is asymptotically null controllable with bounded controls(ANCBC).Both a bounded state feedback control law and a bounded output feedback control law are constructed for each follower agent in the group.The feedback law for each input of an agent uses a multi-hop relay protocol,in which the agent obtains the information of other agents through multi-hop paths in the communication network.The number of hops each agent uses to obtain its information about other agents for an input is less than or equal to the sum of the number of eigenvalues at the origin and the number of pairs of non-zero imaginary eigenvalues of the sub-system corresponding to the input,and the feedback gains are constructed from the adjacency matrix of the communication network.It is shown that global leader-following consensus is achieved under the feedback control laws we have constructed when the communication topology among follower agents is a strongly connected and detailed balanced directed graph and the leader is a neighbor of at least one follower.3.Investigation on global leader-following consensus of a group of general discrete-time linear systems subject to input saturation.Similar to the continuous-time case,the follower agents and the leader agent are all described by a general discretetime linear system that is ANCBC.Both a bounded state feedback control law and a bounded output feedback control law are constructed for each follower agent in the group.The feedback law for each input of an agent uses a multi-hop relay protocol,in which the agent obtains the information of other agents through multi-hop paths in the communication network.The number of hops each agent uses to obtain its information about other agents for an input is less than or equal to the sum of the number of real eigenvalues on the unit circle and the number of pairs of complex eigenvalues on the unit circle of the eigenvalues of the sub-system corresponding to the input,and the feedback gains are constructed from the adjacency matrix of the communication network.It is shown that global leader-following consensus is achieved under the feedback control laws we have constructed when the communication topology among follower agents is a strongly connected and detailed balanced directed graph and the leader is a neighbor of at least one follower.