Distributed Dynamic Quantile Solver With Plug-and-Play Operation

In this paper, we propose a continuous-time distributed algorithm for the dynamic quantile problem. The problem is to find the quantile of time-varying signals in a network of agents, each of which having the signal of its own. For example, this problem includes finding the median, maximum, or the second largest value of the signals. The proposed algorithm guarantees convergence from arbitrary initial conditions and does not use the decaying gains. Hence our algorithm is suitable for plug-and-play operation, where agents may freely join or leave the network during the operation. An application to a simplified electricity market problem is presented to show the effectiveness of the design.