Distributed Tracking Control Of Homogeneous And Heterogeneous Linear Multi-Agent Systems

This thesis aims to investigate the distributed tracking control of high-order linear systems,both for homogeneous and heterogeneous cases,under the setting of "leader-follower" framework.We are expected to develop this line of research from three aspects.Firstly,to design the distributed control protocol for each follower to track the leader,when the followers are influenced by external disturbances.Secondly,to weaken the assumption on the interaction topology between the followers,ensuring that the followers finally fall into the convex hull formed by multiple leaders,which is known as the containment control problem.At last,to consider not only collaborative interactions,but also the antagonistic interactions formed between the agents,to see how the group of agents would behave.The main contributions of this thesis are listed as follows.1.The problem of optimal distributed tracking control of multi-agent linear systems subject to external disturbances is addressed.The concepts of distributed control,optimal control theory and differential game theory are utilized to formulate this optimal tracking problem into a multi-player zero-sum differential graphical game,which provides a new perspective on the distributed tracking of multiple agents influenced by disturbances.In the presented differential graphical game,the dy-namics of the tracking error and performance indice for each node depend on both local neighbor information and disturbances.It is shown that the solution to the multi-agent differential graphical game in the presence of disturbances requires the solution to coupled Hamilton-Jacobi-Isaacs(HJI)equations.Policy iteration(PI)learning algorithm is provided to find the solution to these coupled HJI equations and its convergence is proven.It is also shown that L2-bounded tracking error can be guaranteed in the presence of dynamical disturbances using this technique.An online PI algorithm is given to solve the zero-sum game in real time.A numerical example is provided to show the effectiveness of the online approach.2.The problem of L2-gain output feedback(OPFB)tracking of linear multi-agent systems subject to external disturbances is investigated.Both homogeneous and heterogeneous multi-agent systems are considered.For the case of homogeneous multi-agent systems,it is shown that the L2-gain static OPFB tracking problem of MAS can be cast into the L2-gain static OPFB problem for a set of decoupled systems that depend on the graph topology.A modified Riccati equation is introduced which gives the OPFB gain and the coupling gain of the proposed static OPFB control protocol.An algorithm is provided to calculate the static OPFB gain.For the case of heterogeneous multi-agent systems,it is shown that the L2-gain tracking problem can be cast into the L2-gain static OPFB problem of a set of decoupled systems plus a coupling condition on their dynamic compensators that depends on the graph topology.A certain novel gain matrix is introduced in the dynamics of the control protocol to improve the performance.A numerical example is provided to show the effectiveness of the proposed method.3.The problem of cooperative output regulation of heterogeneous linear multi-agent systems is considered.It is noted that unlike the disturbances considered in the above situations,the disturbance here under the output regulation framework is actually generated by the leader.Compared to the existing results,we aim to investigate the effectiveness of the local dynamic compensator(the one derived in the L2-gain OPFB tracking problem of heterogeneous systems)on handling the output regulation problem.Based on such a dynamic compensator,distributed control protocols are proposed.Numerical examples are provided to verify the effectiveness of the proposed method.4.The problem of output containment control of heterogeneous linear multi-agent systems is studied.Unlike the single leader case,we consider multiple leaders here.By introducing a new neighborhood output error of follower agents,the output containment control problem can be formulated into a cooperative output regulation problem.A modified dynamic compensator is provided to handle the case with multiple leaders.Based on such a dynamic compensator,distributed control protocols are proposed.We obtain a milder assumption on the topology among the followers,that every follower agent is reachable from at least one leader agent,which in the existing literature is assumed to be strongly connected.A numerical example is provided to verify the effectiveness of the proposed method.5.The problem of bipartite tracking for high order linear multi-agent systems with a leader is investigated.Both homogeneous and heterogeneous systems are con-sidered.Negative edge weights are introduced in modelling the communication graph between agents,to represent the antagonistic interactions.A mechanism is provided for a group of agents to behave from cooperative tracking to bipartite tracking,with the help of structurally balanced theory on signed graphs.LQR(linear quadratic regulator)-based optimal control approach is used to derive the distributed protocol for the follower agent to achieve bipartite tracking of the leader.An equivalent observation is made between the proposed protocol and the protocol for the case of cooperative tracking.A modified dynamic compensator is provided to handle the case of bipartite tracking.Based on such a dynamic compensator,the distributed control protocols are introduced.Numerical examples are given to show the effectiveness of the proposed method.