Determination Conditions For Controllability Of Multi-agent Systems Under Multiple Model

When studying the controllability of multi-agent systems,agents can be regarded as vertices and communication relations between agents as edges.Therefore,the controllability of corresponding topological structures can be studied instead.In this thesis,based on the graph theory,the controllability conditions of multi-agent systems are obtained,and the effects of different system models on controllability are studied.The emergence of controllability graphic representation of multi-agent systems raises several questions about how to directly establish controllability results based on topological structure.Arguably,the most serious challenge in this field is how to obtain sufficient conditions for system controllability through equivalent partition that plays an important role in graphical representation.This thesis provides two sufficient conditions:(1)The existence of the eigenvectors of the system matrix makes the equation based on the Laplace matrix valid;(2)Increase the number of leaders by reducing the number of followers by the same amount.The former integrates the research of different fields and obtains the sufficient condition of system controllability;The latter studies from the perspective of role exchange between leader and follower.In addition,this thesis defines a new concept--iso-neighbor node,proposes sufficient and necessary conditions for n-point graph controllability,and analyzes the difficulties when n is greater than 5.Besides,the limitation of equivalent partition in controllability analysis is also revealed.The above studies on controllability graphic representation of multi-agent system is based on(L _f,L _l)model.The mathematical proof shows that this model is equivalent to(L,B)model,that is,the above results can be applied to a wider range.We analyze the controllability differences between the iso-neighbor model and other models in multi-agent systems,and find that the iso-neighbor model can produce the same controllability with other models under certain conditions.Finally,this thesis studies the generalization theory under the different models mentioned above.This thesis first studies the influence of different models on the controllability of leader-follower systems based on Laplacian matrix,and obtains controllability results applicable to general models.The above study is based on three different controls,namely broadcast control,non-broadcast control andU_I control.This thesis proves that there is no correlation between the controllability of the system and the original system when the number of control inputs is increased in a fixed topology.Based on the above conclusions,we put forward the concept of hierarchical equivalent partition,and prove that under the general model,there is hierarchical equivalence partition that makes the system uncontrollable.