Group Consensus For First- And Second-order Heterogeneous Multi-agent Systems

Multi-agent systems(MASs)are widely used in various fields.Therefore,the collaborative control of MASs has been paid much attention by many researchers.As one of the typical problems of collaborative control,consensus means that all the agents can reach the same state or output over time.Since an agent transfers information and exchanges data with each other through the communication networks,different network environments and communication factors will affect the consistency of the system,such as sampling,quantization and communication disturbance.How to design a consensus protocol so that an MAS achieves the final collaborative goal is worth studying.Similar to humans or other biological population,the agents in an MAS may also be divided into different groups to complete a relatively complicated assignment.Due to the technical limitations or practical requirements,the dynamic structures of the agents in a system may be different to better achieve the collaboration.Compared with homogeneous MASs,the dynamic structure of HMASs and the interaction between agents are more complex.The design of consensus protocol for HMASs is more difficult when there exists the influence of multiple communication factors.Thus,this dissertation investigates the group consensus problem for the HMASs composed of single integrators and double integrators under various network environments and communication factors.By designing appropriate consensus protocols,the corresponding conditions of consensus are given with the help of Lyapunov method,matrix theory,graph theory and other related theories.The main contents and contributions of this dissertation are summarized as follows:Firstly,for a sampled-data HMAS composed of the first-order and second-order agents under directed topology,two kinds of control protocols are proposed to ensure that the agents not only can be divided into different groups according to the given requirements,but also can reach the consensus asymptotically.Based on the properties of similar matrix and Laplacian matrix,the conditions and the detailed theoretical analysis for achieving consensus are provided.Meanwhile,the final convergence value of each group is also given.Furthermore,a control protocol with sampled and quantized data is designed that can make the HMAS reach group consensus asymptotically in a mean-square sense.It can be found that the consensus errors almost converge to zero when the quantized error tends to zero.Secondly,for the HMAS composed of linear first-order and second-order agents,where all the agents' control inputs are bounded and the second-order agents' velocity information is unmeasured,a group consensus protocol with pinning scheme is provided to guarantee that the agents in the HMAS under an undirected connected topology can converge to desired consensus values according to the given grouping.Furthermore,we investigate group consensus for the HMAS under multiple communication constraints,where the dynamics of the second-order agents are represented by linear and nonlinear EL dynamics.To guarantee that the HMAS with or without uncertain parameters can reach the desired group consensus,two different control protocols are designed and the consensus criteria are also provided.Some simulation examples show the effectiveness of the theoretical results.Thirdly,for an HMAS without any disturbance,a continuous finite-time consensus protocol with a pinning and grouping scheme is proposed.By using the Lyapunov theory,La Salle's invariance principle and homogeneity with dilation principle,it is proved that all the agents can be divided into different groups as specified and the states can converge to desired consensus values in finite time under the proposed protocol.Meanwhile,a finite-time group consensus protocol is given when the velocity is unmeasured.On that basis,a continuous integral sliding mode is introduced into the proposed finite-time group consensus protocol to deal with the group consensus problem for the HMAS with uncertain disturbances.It can be seen that the HMAS with one or more pinning agents can achieve accurate finite-time group consensus in spite of the uncertain disturbances by using the protocol.Moreover,the control input is chattering-free.Finally,for two coupled HMASs with bidirectional actions,where each system consists of double-integrator and single-integrator nodes with different nonlinear dynamics,a control protocol is designed based on the adaptive theory to ensure that the outer consensus(a special group consensus)between systems under the identical and nonidentical topologies can be achieved.The detailed theoretical proofs are provided based on Lyapunov method and La Salle's invariance principle.Meanwhile,the adaptive controller is also given for the second-order systems with different nonlinear dynamics under identical and nonidentical topologies.