Exploiting Micro-Structure in the Generalized Riccati Recursion for Optimal Control
Abstract
Optimal Control Problems (OCPs) have been applied to a variety of applications. Such problems are often transcribed into a Nonlinear Program (NLP) for which solution methods typically solve a Linear Quadratic (LQ) subproblem. To efficiently solve this LQ subproblem, the Riccati recursion exploits the block-diagonal structure that arises from discretizing an OCP using a Multiple Shooting method. However, reformulating general dynamics constraints to fit the required problem structure to use the Riccati recursion introduces additional micro-structure within these block matrices that remains unexploited. This work demonstrates how structure-exploiting solvers such as Fatrop can benefit from exploiting not only the block-diagonal structure but also the micro-structure within those blocks. We propose a structure-exploiting LU decomposition algorithm and integrate it within the Riccati recursion. Numerical results on randomized linear systems and two OCP examples demonstrate a reduction in computation time of the search direction of up to 20%, with the largest speedup observed for relative zero block sizes around 0.25 and large stage-wise equality constraint jacobians.
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BibTeX
@misc{callens2026exploiting,
title = {{Exploiting Micro-Structure in the Generalized Riccati Recursion for Optimal Control}},
author = {Louis Callens and Wilm Decré},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29238},
eprint = {2608.29238},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29238},
}
RIS
TY - UNPB
TI - Exploiting Micro-Structure in the Generalized Riccati Recursion for Optimal Control
AU - Louis Callens
AU - Wilm Decré
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.29238
UR - https://arxiv.org/abs/2608.29238
AB - Optimal Control Problems (OCPs) have been applied to a variety of applications. Such problems are often transcribed into a Nonlinear Program (NLP) for which solution methods typically solve a Linear Quadratic (LQ) subproblem. To efficiently solve this LQ subproblem, the Riccati recursion exploits the block-diagonal structure that arises from discretizing an OCP using a Multiple Shooting method. However, reformulating general dynamics constraints to fit the required problem structure to use the Riccati recursion introduces additional micro-structure within these block matrices that remains unexploited. This work demonstrates how structure-exploiting solvers such as Fatrop can benefit from exploiting not only the block-diagonal structure but also the micro-structure within those blocks. We propose a structure-exploiting LU decomposition algorithm and integrate it within the Riccati recursion. Numerical results on randomized linear systems and two OCP examples demonstrate a reduction in computation time of the search direction of up to 20%, with the largest speedup observed for relative zero block sizes around 0.25 and large stage-wise equality constraint jacobians.
ER -