{"ID":3006120,"CreatedAt":"2026-06-03T03:09:48.883664427Z","UpdatedAt":"2026-06-04T19:14:31.964469513Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.02938","arxiv_id":"2606.02938","title":"Koopman operator learning for predictive control via Khatri-Rao kernel regression","abstract":"This paper develops a data-driven realization of the generalized Koopman operator (GeKo), in which states and inputs are lifted independently and the dynamics are expressed as a tensor bilinear system. The first contribution is a time-sequenced multi-step Khatri-Rao kernel regression formulation that exposes the operator to evolved snapshots along trajectories rather than only single one-step pairs, which reduces compounded prediction error. Secondly, we develop a kernel- and input-agnostic structured SVD reduction that compresses the lifted state and input spaces while preserving the Khatri-Rao realization. We instantiate the framework with random Fourier features and describe a complete predictive-control pipeline, including a multi-step roll-out diagnostic that guides the choice of MPC horizon. The framework is validated on the chaotic Lorenz system, where the learned reduced-order GeKo model stabilizes an unstable equilibrium from a range of initial conditions.","short_abstract":"This paper develops a data-driven realization of the generalized Koopman operator (GeKo), in which states and inputs are lifted independently and the dynamics are expressed as a tensor bilinear system. The first contribution is a time-sequenced multi-step Khatri-Rao kernel regression formulation that exposes the operat...","url_abs":"https://arxiv.org/abs/2606.02938","url_pdf":"https://arxiv.org/pdf/2606.02938v1","authors":"[\"Mircea Lazar\"]","published":"2026-06-01T22:38:23Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}