# Towards Robust Data-Driven Control Synthesis for Nonlinear Systems with Actuation Uncertainty

arXiv: https://arxiv.org/abs/2011.10730 · HTML: https://mlsanity.com/paper/2011.10730/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2020.

## Built on by (most cited first, 14 of 14)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
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- [Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty](https://mlsanity.com/paper/2106.07108/) (2021)
- [Safety Filters for Black-Box Dynamical Systems by Learning Discriminating Hyperplanes](https://mlsanity.com/paper/2402.05279/) (2024)
- [Safe Exploration in Model-based Reinforcement Learning using Control Barrier Functions](https://mlsanity.com/paper/2104.08171/) (2021)
- [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)
- [Synthesis and Deployment of Maximal Robust Control Barrier Functions through Adversarial Reinforcement Learning](https://mlsanity.com/paper/2604.13192/) (2026)
- [Sample Efficient Reinforcement Learning with Partial Dynamics Knowledge](https://mlsanity.com/paper/2312.12558/) (2023)
- [Enhancing Reinforcement Learning Agents with Local Guides](https://mlsanity.com/paper/2402.13930/) (2024)
- [Random Features Approximation for Control-Affine Systems](https://mlsanity.com/paper/2406.06514/) (2024)
- [Adversarially Robust Stability Certificates can be Sample-Efficient](https://mlsanity.com/paper/2112.10690/) (2021)
- [Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functions](https://mlsanity.com/paper/2208.10733/) (2022)
- [Safeguarded Progress in Reinforcement Learning: Safe Bayesian Exploration for Control Policy Synthesis](https://mlsanity.com/paper/2312.11314/) (2023)

## Abstract (arXiv)

Modern nonlinear control theory seeks to endow systems with properties such as stability and safety, and has been deployed successfully across various domains. Despite this success, model uncertainty remains a significant challenge in ensuring that model-based controllers transfer to real world systems. This paper develops a data-driven approach to robust control synthesis in the presence of model uncertainty using Control Certificate Functions (CCFs), resulting in a convex optimization based controller for achieving properties like stability and safety. An important benefit of our framework is nuanced data-dependent guarantees, which in principle can yield sample-efficient data collection approaches that need not fully determine the input-to-state relationship. This work serves as a starting point for addressing important questions at the intersection of nonlinear control theory and non-parametric learning, both theoretical and in application. We validate the proposed method in simulation with an inverted pendulum in multiple experimental configurations.