Sparsity Preserving Discretization With Error Bounds⁎J. Anderson and Y. Chen are supported by PNNL on grant 424858. J. Anderson is additionally supported by ARPA-E through the GRID DATA program. N. Matni is supported in part by ONR awards N00014- 17-1-2191 and N00014-18-1-2833 and the DARPA Assured Autonomy (FA8750-18-C-0101) and Lagrange (W911NF-16-1-0552) programs. Issue 2 (2020) - Anderson, James; Matni, Nikolai; Chen, Yuxiao
Abstract: Typically when designing distributed controllers it is assumed that the state-space model of the plant consists of sparse matrices. However, in the discrete-time setting, if one begins with a continuous-time model, the discretization process annihilates any sparsity in the model. In this work we propose a discretization procedure that maintains the sparsity of the continuous-time model. We show that this discretization out-performs a simple truncation method in terms of its ability to approximate the "ground truth" model. Leveraging results from numerical analysis we are also be able to upper-bound the error between the dense discretization and our method. Furthermore, we show that in a robust control setting we can design a distributed controller on the approximate (sparse) model that stabilizes the dense model.