Prof A. Stephen Morse from Yale University delivered this Thursday on Apr 10 an impressive talk: A Distributed Algorithm for Solving a Linear Algebraic Equation.
In this talk a distributed algorithm was described by Prof Morse for solving a linear algebraic equation of the form Ax=b where A was a matrix for which the equation had at least one solution. The equation was simultaneously solved by m agents assuming each agent knew only a subset of the rows of the partitioned matrix [A b], the current estimates of the equation’s solution generated by its neighbors, and nothing more. According to Prof Morse, each agent recursively updated its estimate of a solution by utilizing the current estimates generated by each of its neighbors. Neighbor relations were characterized by a time-dependent directed graph N(t) whose vertices corresponded to agents and whose arcs depicted neighbor relations. For any matrix A for which the equation has a solution, the algorithm caused all agents’ estimates to converge exponentially fast to the same solution to Ax=b if and only if the sequence of neighbor graphs N(t), t=1,2,... was “repeatedly jointly strongly connected”. Moreover, in the absence of transmission delays, convergence to a solution occurred even if the times at which each agent updated its estimates were not synchronized with the update times of its neighbors.
Prof A. Stephen Morse was born in Mt. Vernon, New York. He received Ph.D. degree from Purdue University. He was associated with the Office of Control Theory and Application {OCTA} at the NASA Electronics Research Center in Cambridge, Mass. For most of his career, he has been with Yale University where he is presently the Dudley Professor of Engineering. His main interest is in system theory and he has done research in network synthesis, optimal control, multivariable control, adaptive control, urban transportation, vision-based control, hybrid and nonlinear systems, sensor networks, and coordination and control of large grouping of mobile autonomous agents. He is a Fellow of the IEEE and a co-recipient of the IEEE Control Systems Society's 1993 and 2005 George S. Axelby Outstanding Paper Awards. He has twice received the American Automatic Control Council's Best Paper Award and is a co-recipient of the Automatica Theory/Methodology Prize. He is the 1999 recipient of the IEEE Technical Field Award for Control Systems. He is the 2013 recipient of the American Automatic Control Councils Richard E. Bellman Control Heritage Award. He is a member of the US National Academy of Engineering and the Connecticut Academy of Science and Engineering.
