# Correctness Guarantees for the Composition of Lane Keeping and Adaptive Cruise Control

arXiv: https://arxiv.org/abs/1609.06807 · HTML: https://mlsanity.com/paper/1609.06807/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Sep 2016.

## Built on by (most cited first, 7 of 7)

- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificates](https://mlsanity.com/paper/2101.05436/) (2021)
- [Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations](https://mlsanity.com/paper/2111.09971/) (2021)
- [Gameplay Filters: Robust Zero-Shot Safety through Adversarial Imagination](https://mlsanity.com/paper/2405.00846/) (2024)
- [Learning Robust Hybrid Control Barrier Functions for Uncertain Systems](https://mlsanity.com/paper/2101.06492/) (2021)
- [Exact Verification of ReLU Neural Control Barrier Functions](https://mlsanity.com/paper/2310.09360/) (2023)
- [Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagation](https://mlsanity.com/paper/2410.16281/) (2024)

## Abstract (arXiv)

This paper develops a control approach with correctness guarantees for the simultaneous operation of lane keeping and adaptive cruise control. The safety specifications for these driver assistance modules are expressed in terms of set invariance. Control barrier functions are used to design a family of control solutions that guarantee the forward invariance of a set, which implies satisfaction of the safety specifications. The control barrier functions are synthesized through a combination of sum-of-squares program and physics-based modeling and optimization. A real-time quadratic program is posed to combine the control barrier functions with the performance-based controllers, which can be either expressed as control Lyapunov function conditions or as black-box legacy controllers. In both cases, the resulting feedback control guarantees the safety of the composed driver assistance modules in a formally correct manner. Importantly, the quadratic program admits a closed-form solution that can be easily implemented. The effectiveness of the control approach is demonstrated by simulations in the industry-standard vehicle simulator Carsim.