Quantized Consensus over Expander Networks and Communication Energy Minimization

Expander networks are highly connected sparse graphs, which play an important role in designing efficient communication networks. In this paper, we consider consensus control of discrete-time first-order agents with the communication graph being an expander network. Each agent has a real-valued state but can only exchange symbolic data with its neighbors. A distributed protocol is designed based on dynamic encoding and decoding with finite level uniform quantizers. The choice of the control parameters only depends on the number of agents, the maximum degree and the isoperimetric constant of the network. It is shown that under the protocol designed, averageconsensus can be achieved with an exponential convergence rate based on a single-bit information exchange between each pair of adjacent nodes at each time step. A performance index is given to characterize the total communication energy cost to achieve average-consensus and it is shown that the minimization of the communication energy cost leads to a tradeoff between the convergence rate and the number of quantization levels.