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

• 成果类型: Article
• 署名作者: Boskos, Dimitris; Cortes, Jorge; Martinez, Sonia
• 署名单位: Delft University of Technology; University of California System; University of California San Diego
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3273815
• 发表日期: 2024
• 页码: 797-812
• 关键词: Random variables; optimization; uncertainty; probability distribution; Noise measurement; Power system dynamics; aerodynamics; distributional uncertainty; estimation; Linear system observers; Stochastic systems

摘要

This article 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.