Model Reduction and Neural Networks
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Abstract
Abstract
Abstract We study Galerkin model reduction for unconstrained linear-quadratic optimal control problems and show that state-space reduction alone already induces a reduced control structure via the optimality conditions. As a result, the solely state-reduced and the combined control- and state-reduced problems are equivalent, allowing fast optimization over a reduced control space without introducing additional approximation error. We derive lower and upper a posteriori error bounds for the optimal control and use them within an online-adaptive algorithm that constructs sufficiently accurate reduced spaces while solving the control problem. Convergence of the algorithm is proven, and numerical results demonstrate that combined control and state-space reduction yields significant speed-ups without loss of accuracy compared to state-space reduction alone.
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@article{Kartmann2026Optimality,
title = {Optimality-based control space reduction for high-dimensional control spaces},
author = {Michael Kartmann and Stefan Volkwein},
journal = {Computational Science and Engineering},
year = {2026},
doi = {10.1007/s44207-026-00014-x},
url = {https://doi.org/10.1007/s44207-026-00014-x}
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