Quantized Consensus of Multi-agent Systems with Additive Noise

This paper investigates the average consensus problem of multiple discrete-time integrator agents under communication constraints and additive noise. In real applications, both quantization error and additive noise are often unavoidable and may terribly degrade the consensus performance. To handle quantization, we adopt a distributed dynamic encoding and decoding policy, under which the resolution of quantizers can change over time to tightly catch up the states and provide more accurate information. Moreover, bounded additive noise is considered. By generalizing the original noise-free protocol in [14], we propose a modified protocol with a new scaling function and prove that under our protocol, one can achieve approximate consensus even with 1 bit per channel use under the perturbation of additive noise. Furthermore we set up a quantitative relationship between the consensus performance, measured by the ultimate consensus error bound, and the number of available bits per channel use.