Gaussian process (GP) regression has been widely used in supervised machine
learning due to its flexibility and inherent ability to describe uncertainty in
function estimation. In the context of control, it is seeing increasing use for
modeling of nonlinear dynamical systems from data, as it allows the direct
assessment of residual model uncertainty. We present a model predictive control
(MPC) approach that integrates a nominal system with an additive nonlinear part
of the dynamics modeled as a GP. Approximation techniques for propagating the
state distribution are reviewed and we describe a principled way of formulating
the chance constrained MPC problem, which takes into account residual
uncertainties provided by the GP model to enable cautious control. Using
additional approximations for efficient computation, we finally demonstrate the
approach in a simulation example, as well as in a hardware implementation for
autonomous racing of remote controlled race cars, highlighting improvements
with regard to both performance and safety over a nominal controller.

本文提出了一种使用高斯过程回归模型的模型预测控制方法，用于建模非线性动态系统并计算模型残差不确定性以实现谨慎控制。通过近似计算实现计算效率，并在模拟实验和硬件实现中展示了该方法在自主赛车方面的表现改进。