Research On The Controllability And Stability Of Multi-agent Systems

The controllability and stabilization of multi-agent systems are hot topics in multi-agent systems.Based on the corresponding topological structure of multi-agent systems,taking advantage of matrix theory,graph theory and so on,we studied the controllability and stabilization of multi-agent systems from the perspective of graph theory.The main contents of this paper are as follows:·The controllability of multi-agent systems based on path and cycle graphs is stud-ied.For paths or cycles,sufficient and necessary conditions are presented for determining the locations of leaders under which the controllability can be real-ized.Specifically,the controllability of a path is shown to be determined by a set generated only from its odd factors,and the controllability of a cycle is determined by whether the distance between 2 leaders belongs to a set generated from its even(odd)factors when the number of its nodes is even(odd).For both graphs,the dimension of the controllable subspace is also derived.Moreover,the technique used in the derivation of the above results is further used to get sufficient and necessary conditions for several different types of graphs generated from path and cycle topologies.These types of graphs can be regarded as typical topologies in the study of multi-agent controllability,and accordingly the obtained results have meaningful enlightenment for the research in this field.·Using the graph division theory,the concept of same neighbors partitions is pro-posed.Based on same neighbors partitions,a necessary condition for determining the controllability of multi-agent system is given.The controllability problem of cooperation-competition multi-agent systems which is presented by weighted and directed signed graphs is studied.Graph partitions such as structural balance and almost equitable partition(AEP)are considered.Based on graph partition theory,the paper presented that the controllability of the structurally balanced graph is equivalent to that of the associated nonnegative graph.Furthermore,a graph-theoretic necessary condition is proposed for the controllability of directed signed networks and an algorithm is given for the computation of the partition.Finally,the upper bound on the controllable subspace is derived by utilizing the coarsest AEP under leaders when the system is uncontrollable.·The stabilizability and formation control of cooperation-competition multi-agent systems are studied.The agents run a consensus protocol using a signed Lapla-cian which is different from the conventional one.By taking advantage of the proposed structurally balanced independent strongly connected components of the signed graph,a sufficient and necessary condition is presented to solve the decen-tralized stabilizability problem.Besides,formation control is considered and the sufficient and necessary condition is provided by applying the proposed results.Several simulations are given to illustrate the theoretical results.The problem of stabilization of heterogeneous multi-agent systems is addressed.Under tree graphs(including paths and stars),it is indicated that the stabilization problem without self-feedback is solvable if and only if each agent is stable.Under cycle graphs,a sufficient condition for the stabilization problem via harmonic control is provided and an algorithm of designing the interconnection gains is presented.Furthermore,a sufficient and necessary condition for stabilization problem via harmonic control under cycle graphs is first given when the graph contains less than 5 nodes.