Exploring the Links between the Fundamental Lemma and Kernel Regression

arXiv:2403.05368v1 Announce Type: cross
Abstract: Generalizations and variations of the fundamental lemma by Willems et al. are an active topic of recent research. In this note, we explore and formalize the links between kernel regression and known nonlinear extensions of the fundamental lemma. Applying a transformation to the usual linear equation in Hankel matrices, we arrive at an alternative implicit kernel representation of the system trajectories while keeping the requirements on persistency of excitation. We show that this representation is …

abstract arxiv cs.lg cs.sy eess.sy explore extensions kernel linear math.oc regression research transformation type