Jorge Cortés

Professor





Data-driven ambiguity sets with probabilistic guarantees for dynamic processes
D. Boskos, J. Cortés, S. Martínez
IEEE Transactions on Automatic Control 66 (7) (2021), to appear


Abstract

This paper studies the evolution of ambiguity sets employed in distributionally robust optimization problems. We assume that the unknown distribution of the observed data evolves according to known dynamics. For compactly supported distributions, we study how the assimilation of samples during a fixed time interval can be leveraged to make inferences about the unknown distribution of the process at the end of the sampling horizon. Under perfect knowledge of the dynamics' flow map, we provide sufficient conditions that relate the solutions' growth with the sampling rate to establish a reduction of the ambiguity set size as the horizon increases. Further, we characterize the exploitable sample history that results in a guaranteed reduction of ambiguity sets under errors in the computation of the flow and when the dynamics is subject to bounded unknown disturbances. We consider samples collected both through full and partial-state measurements. In the latter case, we exploit the observability properties of the system governing the data evolution to recover its state using multiple output samples.

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Mechanical and Aerospace Engineering, University of California, San Diego
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