A Stochastic Fundamental Lemma with Reduced Disturbance Data Requirements
For researchers in data-driven control of stochastic systems, this work incrementally reduces data requirements by leveraging causality and polynomial chaos expansions.
The paper proposes a variant of the stochastic fundamental lemma that eliminates the need for past disturbance data in Hankel matrices, enabling prediction of future input-output trajectories for stochastic LTI systems using only the disturbance distribution. The method is validated through a numerical example.
Recently, the fundamental lemma by Willems et al. has been extended towards stochastic LTI systems subject to process disturbances. Using this lemma requires previously recorded data of inputs, outputs, and disturbances. In this paper, we exploit causality concepts of stochastic control to propose a variant of the stochastic fundamental lemma that does not require past disturbance data in the Hankel matrices. Our developments rely on polynomial chaos expansions and on the knowledge of the disturbance distribution. Similar to our previous results, the proposed variant of the fundamental lemma allows to predict future input-output trajectories of stochastic LTI systems. We draw upon a numerical example to illustrate the proposed variant in data-driven control context.