Research On Several Cooperative Control Problems Of Multi-agent Systems In Signed Networks

Multi-agent systems are abstract descriptions of various interconnected groups in the real world,including biological communities,mechanical armies,and even industrial swarms,etc.There are diverse ways of interaction among their members,including but not limited to cooperation,competition,and even confrontation,which are usually expressed by signed networks among agents.The essential purpose of cooperative control of multi-agent systems is to exploit or mediate the relationships among agents to achieve the common goals of the group,which faces unique challenges and opportunities compared to conventional cooperative control that only considers cooperative relationships,and has received a great deal of attention.This thesis addresses a series of theoretical approaches to the problem of collaborative control of multi-agent systems under signed networks,including distributed dynamic average consensus consistency,bipartite consensus tracking,and enclosing control,laying the foundation for its application in complex network analysis,opinion Dynamics derivation,and unmanned swarms collaboration.Specific results include:1.To address the problems of slow control convergence and large steady-state error in existing dynamic average consensus studies,the finite-time/fixed-time dynamic average consensus protocols with zero steady-state error are designed by combining finite-time control theory and damping injection techniques,respectively.First,the correlation matrix in signed networks is introduced to describe the interrelationships among the agents? then,the mathematical expressions between the stability time of the system and the initial value of the state and the control parameters are established by applying Lyapunov’s stability theorem? finally,the upper bound of the stability time of the closed-loop error system is derived,and the results show that the stability time of the fixed-time dynamic average consensus protocol is not affected by the initial value of the system state and can be more universal than the finite-time protocol.2.A robust bipartite consensus tracking control scheme based on NN-UDE is designed for multi-agent systems with model uncertainties and unknown disturbances in signed networks,which can be used to improve the tolerance of unmanned clusters to various types of disturbances and errors in split pursuit scenarios.First,a parametric neural network（NN）is introduced to approximate the leader information with fractionalorder unknown dynamics? and then,an uncertainty and disturbance estimator（UDE）is designed to estimate the unknown external disturbances of the follower? the NN and UDE components are coupled to form the NN-UDE robust control scheme,and the feedforward terms generated by the two estimation schemes can effectively improve the system control performance.Simulation experiments show that the NN-UDE scheme can effectively weaken the chattering of control input and reduce the computational effort of the system comparing with the NN-only scheme.3.Based on the above study,a robust bipartite consensus tracking control scheme based on NN-EHGO is further designed for the multi-agent system without velocity information measurement.First,the shortcomings of the UDE scheme in dealing with the velocity immeasurability problem are analyzed,and an improved distributed extended high-gain observer（EHGO）is designed,which can simultaneously achieve the estimation of the unknown disturbances and velocity information? and then,the stability of the closed-loop error system is analyzed based on the singular perturbation method by introducing the linear mapping relationship between the dynamic parameters and the estimation error term,and it is demonstrated that the stability of the closed-loop error system can be adjusted by a single parameter.Finally,a nominal controller is designed based on the continuous sliding mode control（SMC）technique,and the robust bipartite consensus tracking control of the multi-agent system in signed networks is achieved by combining the feedforward information terms which generated by NN and EHGO.4.The target enclosing control problem of multi-agent systems in signed networks is studied,and an enclosing strategy is proposed based on signed graphs,which can be used for protective or adversarial missions such as loyal wingman or tracking and encirclement.First,by analyzing the characteristics of the traditional bipartite consensus protocol,the signed graph-based closing error paradigm is derived by innovatively introducing the target information into the bipartite consensus error expression? second,the enclosing control schemes based on distributed observers and neural network target estimators are designed respectively,which enable the whole multi-agent systems to follow the signed graph properties under the premise that the agent only interacts with its neighbors’ information and grouping to achieve the envelopment of dynamic targets from both sides? then,by constructing a complete Laplace matrix（CLM）and obtaining several mathematical properties of the CLM in terms of eigenvalues and eigenvectors,we support the application of Lyapunov’s theorem to the stability proof of closed-loop error systems?finally,by introducing the formation control vector into the enclosing error,the closed formation enclosing of target is achieved,which can extend the application prospects of this method on multi-unmanned systems.