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

TL;DR

This paper introduces a safe, learning-based MPC framework that uses the cross-entropy method and Gaussian Processes to handle uncertain disturbances and non-differentiable objectives, demonstrated on a quadrotor.

Contribution

It combines a minimal intervention controller with CEM and Gaussian Processes to achieve safe, adaptive control for nonlinear systems with uncertain environments.

Findings

Successful trajectory tracking and obstacle avoidance under wind disturbances

High probabilistic safety achieved through control barrier functions

Effective handling of non-differentiable objectives in MPC

Abstract

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.