Research Of Second-order Consensus Control On Matrix-coupled Networks

Since discussing the coordination behavior of multi-agent systems can provide the necessary theoretical basis for new applications and new technologies that are constantly emerging and developing in military,industrial and civil fields,such as satellite cluster control,wireless sensor network target and tracking,aircraft control,multi-autonomous surface navigation formation,etc.,thus,as an extremely important basic problem of cooperative control,consensus control has been received attention and research by experts and scholars in many fields.It is well known that the movement of the objects in nature conforms to Newton’s second law.Therefore,second-order multi-agent systems extensively exist in the real world,and its better scientific understanding and technical support become more and more important,but most of the existing researches are only based on scalar-coupled networks.However,in some practical applications,the multi-dimensional states of individuals are interdependent,scalar-weights cannot show the inter-dependencies of multidimensional states among agents.Using the matrix-weights to describe the interactions between individuals will be more accurate,complete and effective,and thus more meaningful.Therefore,this dissertation takes second-order matrix-weighted continuous-time,discrete-time,and continuous-time and discrete-time hybrid multi-agent systems as the research objects,and studies the consensus issues under the cooperative interactions,antagonistic interactions,event-triggered mechanism and sampled data control.The main research contents are as below:The consensus problem of second-order matrix-weighted continuous-time multi-agent systems under cooperative interactions is investigated.A second-order matrix-weighted consensus algorithm is designed,and the dynamic behavior of the systems is analyzed.Based on Lyapunov stability theory,matrix theory and coupling strengths,a sufficient and necessary algebraic condition for the systems to achieve second-order consensus is established.With aid of the established property,a fairly straightforward algebraic graph condition is obtained,which ensures that the matrix-weighted systems admits second-order consensus.Moreover,owing to the existence of positive semi-definite connections,the clustering phenomena naturally exists,which shows that matrix coupling plays an important role in the convergence of the matrix-weighted systems.In order to obtain the required number of clusters via designing the matrix-weights in the actual scenario,an algebraic graph condition for the systems to reach cluster consensus is derived.The bipartite consensus problems of second-order matrix-weighted continuous-time multi-agent systems on structurally balanced and structurally unbalanced signed networks are studied.A matrix-weighted bipartite consensus algorithm is designed.For structurally balanced signed networks,under the proposed algorithm,based on matrix-valued Gauge transformation,stability theory and Lyapunov stability theory,a algebraic condition is obtained for achieving second-order bipartite consensus,a more direct algebraic graph condition is given for reaching bipartite consensus.Because of the existence of negative and positive semi-definite connections,the matrix-weighted structurally balanced signed networks may exist clustering phenomena.Using the obtained criteria,an algebraic graph condition for admitting cluster bipartite consensus is built.For structurally unbalanced signed networks,under the proposed algorithm,the nullspace of Laplace matrix is analyzed.Similarly,using matrix theory,Lyapunov stability theory and matrix-valued Gauge transformation,a algebraic condition for the system to admit bipartite consensus and a algebraic graph condition for achieving cluster bipartite consensus are obtained.The consensus problem of second-order matrix-weighted discrete-time multi-agent systems under directed cooperative interactions networks is considered.A matrix-weighted consensus protocol is designed.Under the designed control protocol,through variable transformation,stability theory and matrix theory,based on coupling gains,discrete interval and the eigenvalues of Laplacian matrix,consensus conditions on the directed network topology are derived,and some simplified and straightforward consensus conditions for undirected network topology are given.Besides,the qualitative and quantitative relationship among the consensus of the system and the coupling gains,discrete time interval,and the matrix-weighted network topology is also theoretically analyzed.The bipartite consensus problem of second-order matrix-weighted discrete-time multi-agent systems on antagonistic interactions based on the event-triggered mechanism is researched.So as to reduce communication and save resources,according to the matrix-weighted combined measurements of the velocity and position states,a matrix-weighted event-triggered control algorithm is designed.With the help of the stability theory,matrix-valued Gauge transformation,variable transformation and the inequality technique,the bipartite consensus criteria which are based on coupling gains,discrete interval,the parameters in the event-triggered rule and communication topology are established.Furthermore,the conditions to avoid the controller updating in each discrete-time are supplied.The consensus problem of second-order matrix-weighted hybrid multi-agent systems under directed cooperative interactions is discussed.A matrix-weighted hybrid consensus controller is designed.The sampled-data control method of velocity and position is utilized in continuous-time subsystem control protocol,which is low cost and more practical.For the cases of undirected network topology and directed network topology,combined with stability theory and matrix theory,the hybrid consensus conditions related to the sampling period,matrix-weighted network topology and coupling gain are derived by using variable transformation,inequality scaling techniques and recursive method.