Quantized Consensus Of Based On Sequence Ayeraging

As communication network becomes prevalent, networked multi-agent systems(MAS) isbeing a hot area of research, and due to its wide applications in reality, the related theory isgradually perfected. The study of consensus problem is a fundamental problem in the area ofmulti-agent systems. Further average consensus problem is the most fundamental in the area ofconsensus problem. That is a system of networked multi-agents reaches an agreement on theaverage value of their initial states, through merely local interaction among agents. Due to theexchange of information between agents is based on the communication network, it is necessaryand important to consider some factors in communication network, for example, the topologybeing directed or undirected, bandwidth, switching topology and delay etc., which affect theaverage consensus results of multi-agent systems. So, the main contributions of this paper areas follows:1. First, for the fixed direct graph of connected network topology, which is strongly butnot balanced, we firstly show that the existing sequence averaging consensus methodjust reaches a weighted consensus instead of average consensus. Not only the topology isstrongly connected graph but also balanced graph, this case can reach the average consen-sus. Then, to solve the average consensus, we propose a push-sum consensus algorithmand surplus consensus algorithm via quantized data and prove that for the fixed stronglyconnected network, it can still achieve the exact mean-square average consensus. Finally,numerical simulations demonstrate the aforementioned conclusions.2. Second, we address the case of the time-varying network topologies, and find by ourinvestigation that if the network is jointly strongly connected, then the proposed push-sum average consensus algorithms still are effective. The convergence of algorithms isproved based on a lemma on the time-varying stochastic matrix theory, and the results ofsimulation accord with the theoretical analysis. Also, the results of simulation show theeffectiveness of the theoretical analysis.3. Third, we also investigate the effect of delay of communication on the convergence ofaverage consensus algorithm. The network of constant delays can be transformed to thecase of strongly connected network without delay by introducing the virtual node fordelay states, and thus the proposed average algorithms are still be effective. Similarly,the network of time-varying but bounded delays can be also transformed into the joint-ly strongly connected cases, and thus the proposed algorithms can be applied to here.Numerical simulations prove the correctness of the theoretical analysis.