Towards reliable data-based optimal and predictive control using extended DMD

While Koopman-based techniques like extended Dynamic Mode Decomposition are nowadays ubiquitous in the data-driven approximation of dynamical systems, quantitative error estimates were only recently established. To this end, both sources resulting from a finite dictionary and finitely-many data points generation surrogate model have to be taken into account. We generalize rigorous analysis control setting while simultaneously reducing impact curse dimensionality by using proposed bilinear approach. In particular, we establish uniform bounds on state-dependent quantities constraints or performance index enabling data-based optimal predictive with guarantees.