Sparsity Preserving Discretization With Error Bounds

James Anderson; Nikolai Matni; Yuxiao Chen

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arXiv · 1903.11267

Sparsity Preserving Discretization With Error Bounds

James Anderson·Nikolai Matni·Yuxiao Chen

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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 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 ground truth model.

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BibTeX RIS

James Anderson, Nikolai Matni, Yuxiao Chen. 2019-03-27. Sparsity Preserving Discretization With Error Bounds. https://arxiv.org/abs/1903.11267

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