The controllability Gramian of lattice graphs Abstract   The control of networked dynamical systems continues to receive much attention across the engineering and scientific research fields. Here, we investigate the control of lattice systems which provides analytical insight into the relationship between network structure and controllability. First we derive the exact expression for the individual elements of the controllability Gramian of infinite lattice systems. Second, we focus on nearest neighbor lattices for which the distance between nodes appears in the expression for the controllability Gramian. We show that common control energy metrics scale exponentially with respect to the maximum of all the distances between driver nodes and target nodes.

Learning a Lattice Planner Control Set for Autonomous Vehicles This paper introduces a method to compute a sparse lattice planner control set that is suited to a particular task by learning from a representative dataset of vehicle paths. To do this, we use a scoring measure similar to the Fru0027echet distance and propose an algorithm for evaluating a given control set according to the scoring measure. Control actions are then selected from a dense control set according to an objective function that rewards improvements in matching the dataset while also encouraging sparsity. This method is evaluated across several experiments involving real and synthetic datasets, and it is shown to generate smaller control sets when compared to the previous stateoftheart lattice control set computation technique, with these smaller control sets maintaining a high degree of manoeuvrability in the required task. This results in a planning time speedup of up to 4.31x when using the learned control set over the stateoftheart computed control set. In addition, we show the learned control sets are better able to capture the driving style of the dataset in terms of path curvature.