In this paper, a safe and learning-based control framework for model predictive control (MPC) is proposed to optimize nonlinear systems with a gradient-free 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 gradient-free 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.

中文翻译：

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基于交叉熵的基于安全学习的无梯度模型预测控制

本文提出了一种基于安全和基于学习的模型预测控制（MPC）控制框架，以在不确定的环境扰动下优化具有无梯度目标函数的非线性系统。该控制框架以最小的干预方式将基于学习的MPC与辅助控制器集成在一起。基于学习的MPC通过增量高斯过程扩展了先前的名义模型，以学习不确定的干扰。交叉熵方法（CEM）被用作具有无梯度目标函数的MPC的基于采样的优化器。设计了具有控制Lyapunov功能和控制屏障功能的最小干预控制器，以指导采样过程并使系统具有较高的概率安全性。