Research On Containment Control Of A Class Of Disturbed Second-order Nonlinear Multi-agent Systems

As one of the core concepts of multi-agent systems,the containment control problem extended by consensus research in cooperative control has attracted the attention of many scholars and experts.In this paper,the second-order nonlinear multi-agent containment control problem is discussed as follows:Containment problem is investigated for a class of second-order nonlinear multi-agent systems with disturbance and uncertain parameters firstly.The nonlinear function must satisfy Lipshitz condition,point out that the disturbances received by agents are bounded and the leaders are subject to bounded inputs.A distributed adaptive protocol is proposed based only on relative states of neighboring agents without using any global information(including Lipschitz constant and Laplacian matrix eigenvalues),such that the states of the followers converge to the convex hull formed by the states of the leaders with the evolution of time.Then the stability is analyzed by constructing Lyapunov function and Barbalat’s lemma.Finally,a simulation example is given to show the effectiveness of the proposed control protocol.Furthermore,considering that the Laplacian matrix of the directed graph is asymmetric,which makes it difficult to design appropriate controller and Lyapunov function,the consensus problem of the multi-agent system is mostly limited to the case where the communication topology is undirected.This thesis further studies the containment control problem of the multi-agent systems when the topology formed by the communication information between followers is a directed graph.By designing a distributed controller,a disturbance observer is proposed for the followers to estimate the disturbances of the linear exosystem asymptotically,which weakens the condition that the disturbance received by the follower needs to be bounded.Then by using La Salle’s invariance principle and designing a Lyapunov function with integral function to analyze the stability of the system.Finally,a numerical simulation is used to prove the efficiency of the protocol.