Intelligent Distributed Systems

Abstract

Abstract : We have shown that it is possible to improve the convergence rates for periodic gossiping algorithms by using convex combination rules rather than standard averaging rules. On a ring graph, we have discovered how to sequence the gossips within a period to achieve the best possible convergence rate and we have related this optimal value to the classic edge coloring problem in graph theory. We have developed an algorithm which solves the distributed averaging problem on tree graphs in finite time. We developed an asynchronous, distributed algorithm for solving a linear algebraic equation of the form Ax = b assuming that each processing agent knows a subset of the rows of of the partitioned matrix [A b], current estimates of the solution generated by each of its current neighbors, and nothing more. Necessary and sufficient conditions are derived forall estimates to converge to the same solution. We have shown that the most general class of algorithms for maintaining a rigid formation in two dimension space will go into an unintended circular orbit a constant angular frequency if there is a mismatch in shared data. In three dimensions, such mismatches can cause a formation to exhibit an unintended helical motion. We have developed techniques to eliminate these behaviors.