An asynchronous distributed algorithm for computing a common fixed point of a family of paracontractions - Fullmer, Daniel; Ji Liu; Stephen Morse, A. (2016 IEEE 55th Conference on Decision and Control (CDC), 2016)
A distributed algorithm is described for finding a common fixed point of a family of m > 1 nonlinear maps M i : R n → R n assuming that each map is a paracontraction. The common fixed point is asynchronously computed in real time by m agents assuming each agent i knows only M i , the current estimates of the fixed point generated by its neighbors, and nothing more. Each agent recursively updates its estimate of the fixed point at its own event times, by utilizing estimates generated by each of its neighbors. Neighbor relations are characterized by a time-dependent directed graph N(t) whose vertices correspond to agents and whose arcs depict neighbor relations.