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In this paper, we propose an approximate projected consensus algorithm for anetwork to cooperatively compute the intersection of convex sets. Instead ofassuming the exact convex projection proposed in the literature, we allow eachnode to compute an approximate projection and communicate it to its neighbors.The communication graph is directed and time-varying. Nodes update their statesby weighted averaging. Projection accuracy conditions are presented for theconsidered algorithm. They indicate how much projection accuracy is required toensure global consensus to a point in the intersection set when thecommunication graph is uniformly jointly strongly connected. We show that$\pi/4$ is a critical angle error of the projection approximation to ensure abounded state. A numerical example indicates that this approximate projectedconsensus algorithm may achieve better performance than the exact projectedconsensus algorithm in some cases.

An Approximate Projected Consensus Algorithm for Computing Intersection of Convex Sets