Research On Cooperative Consensus Tracking Problems Of Multi-agent Systems

In recent years,the study of cooperative control problem of multi-agent systems has received increasing attention and interest from various research communities.Wide applications have been found in several fields such as formation control of multiple autonomous robots,formation fly of unmanned air vehicle,information fusion of distributed sensor networks,multipoint surveillance,and so on.In the area of cooperative control of multi-agent systems,consensus is an important and fundamental problem,which means that a team of agents reaches an agreement on a common value by interacting with each other via a sensing or communication network.In general,the existing results of consensus problem mainly focus on two fundamental control problems,i.e.,leader-following consensus problem and leaderless consensus problem.The former requires all nodes converge to the leader's trajectory by suitable distributed control laws.This is also called cooperative consensus tracking problem.The latter requires all nodes converge to a common value,which is not prescribed.The common value depends on initial condition of all agents.In reality,for multi-agent systems,the introduction of a leader can broaden the applications that guaranteeing all agents to track the trajectory of the leader node.Therefore,this dissertation focuses on the cooperative consensus tracking problem of multi-agent systems.The communication network is a weighted directed graph with the leader as the root node.Each agent is modeled by a general system.By using algebraic graph theory,matrix theory,Lyapunov stability theory and neural network approximation theory,the corresponding effective distributed controllers are designed,and sufficient conditions are also presented to guarantee the cooperative consensus tracking.More specifically,the main innovation contributions of this dissertation are as follows.Firstly,distributed leader-following consensus for a class of general nonlinear multi-agent systems with communication constraints is investigated.In contrast to the existing literature,intermittent communications and time-varying topologies are considered to describe the communication mode among multi-agent systems,simultaneously,which reflects the reality more closely.On one hand,for a class of non-delayed general nonlinear multi-agent systems,an effective distributed control method is proposed.By constructing multiple Lyapunov functions and using the linear matrix inequality technique,some new sufficient conditions are provided.By using the proposed control method,all follower nodes asymptotically synchronize to the leader node if the communication rate is larger than a threshold value for each time interval.On the other hand,for a class of general nonlinear multi-agent with unknown time delays,a novel distributed control scheme is proposed.Based on the Lyapunov stability theory and some inequality technique,the definite relationship among the bound of unknown time delays,the admissible communication rate and each possible topology duration is presented.Moreover,the relationship reveals that these parameters have impacts on both the convergence speed and control cost.It is worth noting that the well-known master-slave synchronization of two chaotic systems can be regarded as a special case of the aforementioned results,thus the results are also useful for extending practical applications.Secondly,the distributed consensus tracking problem for heterogeneous nonlinear multi-agent systems is addressed.Each follower is modeled as a general nonlinear system with nonidentical and unknown time delays,nonlinear dynamics,and disturbances.An adaptive neural network consensus control method is presented.By constructing a new Lyapunov-Krasovskii function and using the approximation property of neural networks,the uncertainties of unknown system time delays,nonlinear dynamics,and disturbances can be effectively compensated.A graph-dependent Lyapunov proof provides error bounds that depend on the maximum time delays,the graph topology,and the agent dynamics properties,which is helpful to select suitable control parameters to improve the consensus performance.Compared to the existing results,the proposed control scheme can not only reduce the conservatism,but also have a good robustness to disturbances.Thirdly,the cooperative adaptive consensus tracking problem for heterogeneous nonlinear multi-agent systems in the presence of actuator faults is addressed.Each follower is modeled as a general nonlinear system with the unknown and nonidentical nonlinear dynamics,disturbances,and actuator failures.To maintain the systems' reliability and safety in the presence of actuator faults,cooperative fault tolerant neural network tracking controllers with online adaptive learning features is proposed.A developed robust compensation control term and an adaptive neural network control scheme can effectively eliminate the uncertainties that the unknown and nonidentical nonlinear dynamics,disturbances,and actuator failures bring.Of particular interest is that if the control gain is selected appropriately,the proposed control scheme can be implemented in a unified framework no matter whether there are faults or not.Furthermore,the fault detection and isolation is not needed to implement.With the help of linear quadratic regulator based optimal design,a graph-dependent Lyapunov proof provides error bounds that depend on the graph topology and some design parameters,which is helpful for designers to select suitable control parameters to improve the consensus performance.Finally,the cooperative consensus tracking problem of heterogeneous linear multi-agent systems based on geometric theory is studied,where the agent dynamics may not be the same.The study of heterogeneous multi-agent systems is more complex than the well-studied homogeneous case where all agents have the same dynamics.On one hand,a novel local dynamical synchronizer is addressed.Along with the synchronizer,under two basic control methods-synchronization of agent controllers and observers,three control protocols are presented,respectively.The corresponding control parameters can be obtained by solving algebraic Riccati equations based on optimal control design.On the other hand,a detailed geometric theory is given based on the Kalman observable form decomposition and a further characterization of that portion of the leader's dynamics that is hidden within the dynamics of each agent.The output regulator equations are expressed in the new coordinates.These new geometric ideas are used to design efficient reduced-order synchronizers that guarantee synchronization of the outputs of all agents to a leader.It shows that a combination of reduced-order synchronizer and a static state feedback control protocol can solve the consensus tracking problem.