SD-DPC: Sparse Dictionary Differentiable Predictive Control
Abstract
We present sparse dictionary differentiable predictive control (SD-DPC), a framework for learning sparse, interpretable feedback policies for nonlinear systems from data. A prediction model is first identified by rollout-based sparse identification of nonlinear dynamics (SINDy), building on gradient-based and multistep formulations. The policy is then parameterized as a sparse combination of dictionary functions and trained by differentiating a constrained finite-horizon predictive-control objective through this model, so that its terms are selected by closed-loop performance rather than by imitating a previously trained controller. The result is an explicit feedback law with only a handful of terms. Across three benchmark control problems, SD-DPC satisfies the constraints in almost all test scenarios, outperforms a policy distilled onto the same terms by up to an order of magnitude, and requires orders of magnitude less memory and online computation than an optimization benchmark, while admitting explicit sensitivity bounds.
Related
- Sparse Dictionary Learning for Measure-Valued Data via Linearized Optimal Transport: Efficient Algorithms and Sample Complexity
- CuPIQP: A Batched and Differentiable QP Solver on GPUs for Robot Learning and Control
- IKLayer: A Differentiable Inverse Kinematics Layer for Whole-Body Control
- RapidDOC: Riccati-Preconditioned Implicit Differentiation for Differentiable Optimal Control under Operator Mismatch
- A Function-Space Framework for BDDC Preconditioning in Control- and State-Constrained Sparse Optimal Control
BibTeX
@misc{garmroodi2026sddpc,
title = {{SD-DPC: Sparse Dictionary Differentiable Predictive Control}},
author = {Ali Reza Daneshvar Garmroodi and Jan Drgoňa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02466},
eprint = {2610.02466},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02466},
}
RIS
TY - UNPB
TI - SD-DPC: Sparse Dictionary Differentiable Predictive Control
AU - Ali Reza Daneshvar Garmroodi
AU - Jan Drgoňa
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.02466
UR - https://arxiv.org/abs/2610.02466
AB - We present sparse dictionary differentiable predictive control (SD-DPC), a framework for learning sparse, interpretable feedback policies for nonlinear systems from data. A prediction model is first identified by rollout-based sparse identification of nonlinear dynamics (SINDy), building on gradient-based and multistep formulations. The policy is then parameterized as a sparse combination of dictionary functions and trained by differentiating a constrained finite-horizon predictive-control objective through this model, so that its terms are selected by closed-loop performance rather than by imitating a previously trained controller. The result is an explicit feedback law with only a handful of terms. Across three benchmark control problems, SD-DPC satisfies the constraints in almost all test scenarios, outperforms a policy distilled onto the same terms by up to an order of magnitude, and requires orders of magnitude less memory and online computation than an optimization benchmark, while admitting explicit sensitivity bounds.
ER -