Realize almost sure optimal consensus with quantized gossip-type subgradient algorithms

This paper concerns with the optimal consensus problem of multi-agent networks under imperfect communication. With the network issues, we resort to an integrated scheme of the standard gossip algorithm and the subgradient method for multiagent cooperative control. Under the proposed control strategy, agents are supposed to transfer desirable information through a quantized mechanism, and the dithering technique is adopted to deal with the triggered quantization errors. Detailed convergence analysis is carried out by the stochastic approximation method. It is demonstrated that multi-agent networks can achieve almost sure optimal consensus under the proposed algorithm through quantized communication. Related simulation work is further given to validate the derived theoretical results.