论文标题
收缩$ \ MATHCAL {L} _1 $ - 适用于使用高斯进程的适应性控制
Contraction $\mathcal{L}_1$-Adaptive Control using Gaussian Processes
论文作者
论文摘要
我们提出$ \ MATHCAL {CL} _1 $ - $ \ MATHCAL {GP} $，一个控制框架，可以同时同时学习和控制不确定性的系统。这两个主要成分是基于收缩理论的$ \ MATHCAL {L} _1 $（$ \ Mathcal {Cl} _1 $）控制和贝叶斯学习，以高斯过程（GP）回归的形式进行。 $ \ Mathcal {Cl} _1 $控制器确保在提供安全证书时达到控制目标。此外，$ \ MATHCAL {CL} _1 $ - $ \ MATHCAL {GP} $将任何可用数据都包含到不确定性的GP模型中，这可以提高性能并使运动计划者可以安全地实现最佳性。这样，即使在学习瞬变期间，也总是保证系统的安全操作。我们提供了一些说明性的示例，用于在各种环境中对平面四四个系统的安全学习和控制。
We present $\mathcal{CL}_1$-$\mathcal{GP}$, a control framework that enables safe simultaneous learning and control for systems subject to uncertainties. The two main constituents are contraction theory-based $\mathcal{L}_1$ ($\mathcal{CL}_1$) control and Bayesian learning in the form of Gaussian process (GP) regression. The $\mathcal{CL}_1$ controller ensures that control objectives are met while providing safety certificates. Furthermore, $\mathcal{CL}_1$-$\mathcal{GP}$ incorporates any available data into a GP model of uncertainties, which improves performance and enables the motion planner to achieve optimality safely. This way, the safe operation of the system is always guaranteed, even during the learning transients. We provide a few illustrative examples for the safe learning and control of planar quadrotor systems in a variety of environments.
