### Jorge Cortés

#### Professor

High-confidence data-driven ambiguity sets for
time-varying linear systems

D. Boskos, J. Cortés, S. Martínez

SIAM Journal on Control and Optimization, submitted

### Abstract

This paper builds Wasserstein ambiguity sets for the
unknown probability distribution of dynamic random
variables leveraging noisy partial-state
observations. The constructed ambiguity sets contain
the true distribution of the data with quantifiable
probability and can be exploited to formulate robust
stochastic optimization problems with out-of-sample
guarantees. We assume the random variable evolves in
discrete time under uncertain initial conditions and
dynamics, and that noisy partial measurements are
available. All random elements have unknown
probability distributions and we make inferences
about the distribution of the state vector using
several output samples from multiple realizations of
the process. To this end, we leverage an observer to
estimate the state of each independent realization
and exploit the outcome to construct the ambiguity
sets. We illustrate our results in an economic
dispatch problem involving distributed energy
resources over which the scheduler has no direct
control.

pdf

Mechanical and Aerospace Engineering,
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