Maintaining a relevant dataset for data-driven MPC using Willems' fundamental lemma extensions
Résumé
This work explores the recent formulation of nonlinear Data-driven Model Predictive Control in the case of dynamic references. Indeed, the state-of-the-art methods rely on Willems fundamental lemma, and freeze the used dataset at some point. While this ensures consistent behavior, i.e., excitation and accuracy, for a given setpoint, this will likely fail when the reference, and thus the operating point, changes. To this end, we propose refined heuristics for dataset management. First, a singular value-based method induces regular dataset updates but still guarantees a minimum excitation level. Then, a double-dataset formulation aims at decoupling accuracy and excitation issues and leverages the singular value-based one. These heuristics are validated in real-time experiments on a heat-blower system.
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