$\mathcal{L}_1$ - $\mathcal{GP}$：带贝叶斯学习的$\mathcal{L}_1$自适应控制
$\mathcal{L}_1$-$\mathcal{GP}$: $\mathcal{L}_1$ Adaptive Control with Bayesian Learning
摘要：
我们提出了$\mathcal{L}_1$ - $\mathcal{GP}$，一种基于$\mathcal{L}_1$自适应控制和高斯过程回归（GPR）的安全同时控制和学习的体系结构。一方面，$\mathcal{L}_1$自适应控制提供了稳定性和瞬态性能保证，这允许GPR有效且安全地学习不确定动态。另一方面，学习的动态可以方便地纳入$\mathcal{L}_1$控制架构，而不牺牲鲁棒性和跟踪性能。随后，学习的动态可以导致不太保守的设计性能/鲁棒性权衡。我们通过数值模拟说明了所提出的架构的有效性。
英文摘要：
We present $\mathcal{L}_1$-$\mathcal{GP}$, an architecture based on $\mathcal{L}_1$ adaptive control and Gaussian Process Regression (GPR) for safe simultaneous control and learning. On one hand, the $\mathcal{L}_1$ adaptive control provides stability and transient performance guarantees, which allows for GPR to efficiently and safely learn the uncertain dynamics. On the other hand, the learned dynamics can be conveniently incorporated into the $\mathcal{L}_1$ control architecture without sacrificing robustness and tracking performance. Subsequently, the learned dynamics can lead to less conservative designs for performance/robustness tradeoff. We illustrate the efficacy of the proposed architecture via numerical simulations.
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