# Safe Learning-based Gradient-free Model Predictive Control Based on Cross-entropy Method

arXiv: https://arxiv.org/abs/2102.12124 · HTML: https://mlsanity.com/paper/2102.12124/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2021.

## Built on by (most cited first, 2 of 2)

- [Agile Decision-Making and Safety-Critical Motion Planning for Emergency Autonomous Vehicles](https://mlsanity.com/paper/2409.08665/) (2024)
- [DualShield: Safe Model Predictive Diffusion via Reachability Analysis for Interactive Autonomous Driving](https://mlsanity.com/paper/2601.15729/) (2026)

## Abstract (arXiv)

In this paper, a safe and learning-based control framework for model predictive control (MPC) is proposed to optimize nonlinear systems with a non-differentiable objective function under uncertain environmental disturbances. The control framework integrates a learning-based MPC with an auxiliary controller in a way of minimal intervention. The learning-based MPC augments the prior nominal model with incremental Gaussian Processes to learn the uncertain disturbances. The cross-entropy method (CEM) is utilized as the sampling-based optimizer for the MPC with a non-differentiable objective function. A minimal intervention controller is devised with a control Lyapunov function and a control barrier function to guide the sampling process and endow the system with high probabilistic safety. The proposed algorithm shows a safe and adaptive control performance on a simulated quadrotor in the tasks of trajectory tracking and obstacle avoidance under uncertain wind disturbances.