A Study On Consensus Of Multi-agent Systems With Random Interactions

Many biological groups in nature exhibit fascinating collectivebehaviours, and scientists have discovered that these complex colletivebehaviours are a result of simple local interactions of individuals withinthe group. The study of modeling and control of multi-agent systems hasreceived increasing attention from a range of researchers worldwide, and ithas been an important area of complex systems research. Based on theexisting related research works, this dissertation proposes multi-agentsystems models with time-varying interaction topology based onindividuals’ state, and consensus problems are investigated in detail. Themain contributions of this work are as follows:⑴The consensus problem of multi-agent systems withtopological-based random interactions has been considered in this thesis.System composed of multi-agents moving in the plane has time-varyingtopology, and one classic setup of interaction rule is that any pair of agentscan communicate with each other only if their distance is less than a giventhreshold. But when the group density fluctuates wildly, this metricapproach is no longer useful to the system’s achievement of consensus. Amodel with topological-based probabilistic interactions is proposed inwhich the probability of an agent being a neighbor of another depends ontheir distance and a random factor rather than of a preset radius. Accordingto this approach, the ones nearby have larger probability of interaction withthe reference agent as compared to those that are farther. Numericalsimulations show that agents are more prone to achieve a common velocitywith higher randomness of neighbor selection and a larger number of neighbors. And along with the increase of neighbor size, the convergencerate speeds up dramatically at first, then changes slowly.⑵The consensus problem of multi-agent systems with randominteractions based on the similarity of agents’ states has been investigatedin this thesis. The state of an agent moving in the plane contains positionand moving direction. This dissertation takes the influence of similarity ofdirections into consideration, because of the importance role of direction ofmotion in multi-agents system especially biological groups. An improvedmodel is proposed in this thesis where the selection of neighbors dependson both proximity of agents’ positions and similarity of agents’ movingdirections. In this way, agents are more likely to form links with thoseagents who have a similar direction to theirs and those agents who areproximal to them. It is mathematically proved that there exists a non-zeropositive lower bound of the selection probability because of theintroduction of similarity of directions. This bounded probabilityguarantees that the communication topological graph is connected inprobability which ensures the system’s achievement of consensus.Numerical simulations show that the rate of convergence has a positivecorrelation with the neighborhood size, and a negative correlation with theproximity factor as well as the similarity factor.