Event-Triggered Robust H_∞ Consensus Control Of Uncertain Linear Multi-Agent Systems

As the basis for the coordinated control of multi-agent systems,the consensus control problem has broad application prospects.Different from traditional control algorithms that rely on continuous communication between agents,event-triggered control strategies can reduce the communication frequency of the system,thereby alleviating the communication burden.In addition,due to the existence of external disturbances and imprecise modeling,the system model is usually accompanied by parameter uncertainties,then the robustness of the control algorithm is also extremely important.The main research contents and innovative works of this thesis are as follows:1.Aiming at the excessive communication burden caused by relying on continuous communication in the traditional robust H∞ consensus control of multi-agent systems,a event-triggered robust H∞ consensus control algorithm for the linear multi-agent systems with external disturbances and model uncertainties under undirected networks is proposed.By introducing the system transformations based on consensus error,the consensus problem of the multi-agent systems is transformed into the stability problem of a set of subsystems with dimensionality reduction.Design an event-triggered mechanism with an exponential decay term so that the system excludes Zeno behavior.It is proved that the Linear Matrix Inequality(LMI)sufficient condition for the multi-agent systems to achieve robust H∞ consensus is obtained,and then the LMI is decoupled based on the eigenvalues of the Laplacian matrix,which greatly reduces the computational complexity and the parameters of the control law are determined by solving the decoupled LMI.Finally,the correctness of the theoretical results is verified by numerical simulation of a classical mass-spring system.2.Aiming at the problem of system matrix asymmetry brought by directed communication networks,a event-triggered robust H∞ consensus control algorithm for the uncertain linear multi-agent systems under directed networks is proposed.By introducing generalized algebraic connectivity for strongly connected graphs,the problem that Laplacian matrix is asymmetric and has complex eigenvalues caused by directed graphs is solved.Based on the relative state of neighbor agents at event times,an event-triggered control algorithm is proposed,and it is proved that the LMI sufficient conditions for the system to achieve robust H∞ consensus are obtained.Then,by solving the decoupled LMIs,the parameters of control law are determined.Finally,the validity of the theoretical results is verified by numerical simulation.3.Aiming at the problem that the states of the multi-agent systems cannot be completely measured,a output feedback event-triggered robust H∞ consensus control algorithm for the uncertain linear multi-agent systems under the directed networks is proposed.An observer based on eventtriggered communication is designed to estimate the actual state of each agent.The consensus function is defined by introducing measurement error and state estimation,and the consensus problem of the multi-agent systems is transformed into the stability problem of dimension-expanding error system.Then it is proved that the LMI sufficient conditions for the system to achieve robust H∞ consensus are obtained,and the parameters of control law are determined by solving the decoupled LMIs.Finally,the correctness of the theoretical results is verified by a numerical simulation example of a mass-spring system where only the displacement state can be measured.