On Quantized Consensus For Multi-Agent Systems With Directed Network Topologies

Multi-agent systems have broad applications, because of their only little cost and strong adaptivity under adverse environment. Multi-agent systems include many aspects, such as distributed coordinated control, convex optimization and so on. In particularly, distributed consensus questions have received increasing attention in various field. However, in a real world scenario, the digital communication channels are subject to bandwidth, which they must make the information transmitted among agents in digital networks usually quantize prior to being communicated. Therefore, the dissertation mainly focuses on consensus in directed networks with logarithmic quantized information communication. Moreover, in a real world scenario, multi-agent systems with communication delays in the directed network usually exist, communication delays may has a topic of significance on quantized consensus for the multi-agent systems. Thus, the main contents include the following two aspects:Firstly consensus in directed networks with logarithmic quantized information communication. This paper studies the weighted average consensus problem for a group of agents over unbalanced directed networks under finite-level logarithmic quantization strategy. Different from the existing work, they studied the quantized consensus problem about balanced graph, not but the directed unbalanced strongly connected network. Simultaneously, the convergence analysis for the closed-loop multi-agent system is mainly carried out by constructing a generalized quadratic Lyapunov function. The conclusion fully demonstrated the convergence heavily relied on the left eigenvector associated with the maximal eigenvalue of the update adjacency matrix of the key parameters in the fixed directed network. Moreover, it is not to make use of the algebraic spectral theory of undirected graphs and the theory of matrix decomposition. Finally, a numerical example is given to verify the obtained theoretical results.Secondly this paper studies the quantized consensus problem for multi-agent systems with communication delays under general fixed directed topologies. Under the influence of the communication delays, this paper studies quantized consensus problem under the limited quantized information communication transmitting along each connected digital channel and proposes the distributed protocol with finite-level uniform quantization scheme. It is established that, quantized consensus can be achieved as long as the directed network is periodical strongly connected and communication delays is bounded. Simultaneously, because the network is dynamically switching, the same left eigenvalue of the update adjacency matrix inexistence. However, the theory of the fixed directed networks’convergence analysis is no longer applicable. Consequently, the convergence analysis for the closed-loop multi-agent system is mainly carried out by constructing non-quadratic Lyapunov function method and input-to-output stability theory. Moreover the aim of the convergence analysis is to avoid system augmentation.Finally, it uses well widely into the digital network framework in the nature.