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) [1], 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 reduces the long-horizon prediction error by up to a factor of five relative to one-step and lifted linear baselines fitted on the same data, and stabilizes an unstable equilibrium.
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BibTeX
@misc{lazar2026koopman,
title = {{Koopman operator learning for predictive control via Khatri-Rao kernel regression}},
author = {Mircea Lazar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.02938},
eprint = {2606.02938},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.02938},
}
RIS
TY - UNPB
TI - Koopman operator learning for predictive control via Khatri-Rao kernel regression
AU - Mircea Lazar
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2606.02938
UR - https://arxiv.org/abs/2606.02938
AB - This paper develops a data-driven realization of the generalized Koopman operator (GeKo) [1], 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 reduces the long-horizon prediction error by up to a factor of five relative to one-step and lifted linear baselines fitted on the same data, and stabilizes an unstable equilibrium.
ER -