On a Stochastic Fundamental Lemma and Its Use for Data-Driven Optimal Control

Abstract

Data-driven control based on the fundamental lemma by Willems et al. is frequently considered for deterministic LTI systems subject to measurement noise. However, besides measurement noise, stochastic disturbances might also directly affect the dynamics. In this paper, we leverage Polynomial Chaos Expansions (PCE) to extend the deterministic fundamental lemma towards stochastic systems. This extension allows to predict future statistical distributions of the inputs and outputs for stochastic LTI systems in data-driven fashion, i.e., based on the knowledge of previously recorded input-output-disturbance data and of the disturbance distribution we perform data-driven uncertainty propagation. Finally, we analyze data-driven stochastic optimal control problems and we propose a conceptual framework for data-driven stochastic predictive control. Numerical examples illustrate the efficacy of the proposed concepts.

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Cited by in corpus (9)

• Towards data-driven stochastic predictive control
• Distributionally robust uncertainty quantification via data-driven stochastic optimal control
• Data-based system representations from irregularly measured data
• Necessary and Sufficient Conditions for Data-driven Model Reference Control
• Controller Synthesis from Noisy-Input Noisy-Output Data
• Sampling-based Stochastic Data-driven Predictive Control under Data Uncertainty - Extended Version
• Offline Uncertainty Sampling in Data-driven Stochastic MPC
• A new perspective on Willems' fundamental lemma: Universality of persistently exciting inputs
• Stochastic Data-driven Predictive Control of Linear Systems with Sub-Gaussian Disturbances using Causal Predictors