High-Confidence Data-Driven Ambiguity Sets for Time-Varying Linear Systems

Understand

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.