On the construction of local interaction rules that perform global linear computation

In this paper, time varying weights are found that enable distributed linear computation on networked systems. A method is provided for finding weights that are used to compute global linear transformations of network states. The method is composed of two parts, a path planner through the set of positive determinant matrices, and a numerical solver for optimal control problems. The method is used to demonstrate computations on a 10 node network. In order to demonstrate the practicality of implementing the solution, a computation is performed in hardware on a network of 4 mobile robots.