# Robust Safe Control Synthesis with Disturbance Observer-Based Control Barrier Functions

arXiv: https://arxiv.org/abs/2201.05758 · HTML: https://mlsanity.com/paper/2201.05758/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2022.

## Built on by (most cited first, 3 of 3)

- [Safe and Efficient Reinforcement Learning Using Disturbance-Observer-Based Control Barrier Functions](https://mlsanity.com/paper/2211.17250/) (2022)
- [Safe Uncertainty-Aware Learning of Robotic Suturing](https://mlsanity.com/paper/2505.16596/) (2025)
- [Learning Dynamics under Environmental Constraints via Measurement-Induced Bundle Structures](https://mlsanity.com/paper/2505.19521/) (2025)

## Abstract (arXiv)

In a complex real-time operating environment, external disturbances and uncertainties adversely affect the safety, stability, and performance of dynamical systems. This paper presents a robust stabilizing safety-critical controller synthesis framework with control Lyapunov functions (CLFs) and control barrier functions (CBFs) in the presence of disturbance. A high-gain input observer method is adapted to estimate the time-varying unmodelled dynamics of the CBF with an error bound using the first-order time derivative of the CBF. This approach leads to an easily tunable low order disturbance estimator structure with a design parameter as it utilizes only the CBF constraint. The estimated unknown input and associated error bound are used to ensure robust safety and exponential stability by formulating a CLF-CBF quadratic program. The proposed method is applicable to both relative degree one and higher relative degree CBF constraints. The efficacy of the proposed approach is demonstrated using a numerical simulations of an adaptive cruise control system and a Segway platform with an external disturbance.