# Safe Online Control-Informed Learning

arXiv: https://arxiv.org/abs/2512.13868 · HTML: https://mlsanity.com/paper/2512.13868/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 15 Dec 2025.

## Builds on (most cited first, 10 of 10)

- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [Pontryagin Differentiable Programming: An End-to-End Learning and Control Framework](https://mlsanity.com/paper/1912.12970/) (2019)
- [Neural Certificates for Safe Control Policies](https://mlsanity.com/paper/2006.08465/) (2020)
- [Universal Planning Networks](https://mlsanity.com/paper/1804.00645/) (2018)
- [Safe Pontryagin Differentiable Programming](https://mlsanity.com/paper/2105.14937/) (2021)
- [MPC-Inspired Neural Network Policies for Sequential Decision Making](https://mlsanity.com/paper/1802.05803/) (2018)
- [Learning from Human Directional Corrections](https://mlsanity.com/paper/2011.15014/) (2020)
- [Online Control-Informed Learning](https://mlsanity.com/paper/2410.03924/) (2024)
- [Constrained Optimization From a Control Perspective via Feedback Linearization](https://mlsanity.com/paper/2503.12665/) (2025)

## Built on by (most cited first, 1 of 1)

- [Online Intention Prediction via Control-Informed Learning](https://mlsanity.com/paper/2604.09303/) (2026)

## Abstract (arXiv)

This paper proposes a Safe Online Control-Informed Learning framework for safety-critical autonomous systems. The framework unifies optimal control, parameter estimation, and safety constraints into an online learning process. It employs an extended Kalman filter to incrementally update system parameters in real time, enabling robust and data-efficient adaptation under uncertainty. A softplus barrier function enforces constraint satisfaction during learning and control while eliminating the dependence on high-quality initial guesses. Theoretical analysis establishes convergence and safety guarantees, and the framework's effectiveness is demonstrated on cart-pole and robot-arm systems.