# Random Features Approximation for Control-Affine Systems

arXiv: https://arxiv.org/abs/2406.06514 · HTML: https://mlsanity.com/paper/2406.06514/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 38 references that are in the map.
- First posted on arXiv 10 Jun 2024.

## Builds on (most cited first, 17 of 17)

- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Learning-based Model Predictive Control for Safe Exploration](https://mlsanity.com/paper/1803.08287/) (2018)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [Active Learning for Nonlinear System Identification with Guarantees](https://mlsanity.com/paper/2006.10277/) (2020)
- [On the Error of Random Fourier Features](https://mlsanity.com/paper/1506.02785/) (2015)
- [Random Fourier Features for Kernel Ridge Regression: Approximation Bounds and Statistical Guarantees](https://mlsanity.com/paper/1804.09893/) (2018)
- [The Robotarium: A remotely accessible swarm robotics research testbed](https://mlsanity.com/paper/1609.04730/) (2016)
- [Random Fourier Features for Operator-Valued Kernels](https://mlsanity.com/paper/1605.02536/) (2016)
- [Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems](https://mlsanity.com/paper/1903.01577/) (2019)
- [Learning to Forecast Dynamical Systems from Streaming Data](https://mlsanity.com/paper/2109.09703/) (2021)
- [Towards Robust Data-Driven Control Synthesis for Nonlinear Systems with Actuation Uncertainty](https://mlsanity.com/paper/2011.10730/) (2020)
- [Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty](https://mlsanity.com/paper/2106.07108/) (2021)
- [Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics](https://mlsanity.com/paper/2011.07183/) (2020)
- [KCRL: Krasovskii-Constrained Reinforcement Learning with Guaranteed Stability in Nonlinear Dynamical Systems](https://mlsanity.com/paper/2206.01704/) (2022)
- [Torque Saturation in Bipedal Robotic Walking through Control Lyapunov Function Based Quadratic Programs](https://mlsanity.com/paper/1302.7314/) (2013)
- [Constraint-Guided Online Data Selection for Scalable Data-Driven Safety Filters in Uncertain Robotic Systems](https://mlsanity.com/paper/2311.13824/) (2023)

## Built on by (most cited first, 4 of 4)

- [Learning Linear Dynamics from Bilinear Observations](https://mlsanity.com/paper/2409.16499/) (2024)
- [Finite Sample Identification of Partially Observed Bilinear Dynamical Systems](https://mlsanity.com/paper/2501.07652/) (2025)
- [Hierarchical Decision Making with Structured Policies: A Principled Design via Inverse Optimization](https://mlsanity.com/paper/2606.28764/) (2026)
- [Certifiable Safe Model-Based Reinforcement Learning with Control-Affine Dynamics Approximation](https://mlsanity.com/paper/2607.16501/) (2026)

## Abstract (arXiv)

Modern data-driven control applications call for flexible nonlinear models that are amenable to principled controller synthesis and realtime feedback. Many nonlinear dynamical systems of interest are control affine. We propose two novel classes of nonlinear feature representations which capture control affine structure while allowing for arbitrary complexity in the state dependence. Our methods make use of random features (RF) approximations, inheriting the expressiveness of kernel methods at a lower computational cost. We formalize the representational capabilities of our methods by showing their relationship to the Affine Dot Product (ADP) kernel proposed by Casta~neda et al. (2021) and a novel Affine Dense (AD) kernel that we introduce. We further illustrate the utility by presenting a case study of data-driven optimization-based control using control certificate functions (CCF). Simulation experiments on a double pendulum empirically demonstrate the advantages of our methods.