# Enhancing Feasibility and Safety of Nonlinear Model Predictive Control with Discrete-Time Control Barrier Functions

arXiv: https://arxiv.org/abs/2105.10596 · HTML: https://mlsanity.com/paper/2105.10596/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2021.

## Built on by (most cited first, 11 of 11)

- [MEGA-DAgger: Imitation Learning with Multiple Imperfect Experts](https://mlsanity.com/paper/2303.00638/) (2023)
- [Online Control Barrier Functions for Decentralized Multi-Agent Navigation](https://mlsanity.com/paper/2303.04313/) (2023)
- [Reinforcement Learning-based Receding Horizon Control using Adaptive Control Barrier Functions for Safety-Critical Systems](https://mlsanity.com/paper/2403.17338/) (2024)
- [GSON: A Group-based Social Navigation Framework with Large Multimodal Model](https://mlsanity.com/paper/2409.18084/) (2024)
- [Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Models](https://mlsanity.com/paper/2205.05787/) (2022)
- [Meta-Reinforcement Learning for Robust and Non-greedy Control Barrier Functions in Spacecraft Proximity Operations](https://mlsanity.com/paper/2602.07335/) (2026)
- [Socially-Aware Shared Control Navigation for Assistive Mobile Robots in the Built Environment](https://mlsanity.com/paper/2405.17279/) (2024)
- [Safe model-based Reinforcement Learning via Model Predictive Control and Control Barrier Functions](https://mlsanity.com/paper/2512.04856/) (2025)
- [Learning Safety-Guaranteed, Non-Greedy Control Barrier Functions Using Reinforcement Learning](https://mlsanity.com/paper/2602.00366/) (2026)
- [Distributed Model Predictive Control with Adaptive Safety Zones for Multi-Fleet Drone Operations](https://mlsanity.com/paper/2606.20651/) (2026)
- [Conflict-Predictive Variable Horizons in Multi-Drone Distributed Model Predictive Control](https://mlsanity.com/paper/2609.13270/) (2026)

## Abstract (arXiv)

Safety is one of the fundamental problems in robotics. Recently, one-step or multi-step optimal control problems for discrete-time nonlinear dynamical system were formulated to offer tracking stability using control Lyapunov functions (CLFs) while subject to input constraints as well as safety-critical constraints using control barrier functions (CBFs). The limitations of these existing approaches are mainly about feasibility and safety. In the existing approaches, the feasibility of the optimization and the system safety cannot be enhanced at the same time theoretically. In this paper, we propose two formulations that unifies CLFs and CBFs under the framework of nonlinear model predictive control (NMPC). In the proposed formulations, safety criteria is commonly formulated as CBF constraints and stability performance is ensured with either a terminal cost function or CLF constraints. Slack variables with relaxing technique are introduced on the CBF constraints to resolve the tradeoff between feasibility and safety so that they can be enhanced at the same. The advantages about feasibility and safety of proposed formulations compared with existing methods are analyzed theoretically and validated with numerical results.