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We present $\mathcal{L}_1$-$\mathcal{GP}$, an architecture based on$\mathcal{L}_1$ adaptive control and Gaussian Process Regression (GPR) for safesimultaneous control and learning. On one hand, the $\mathcal{L}_1$ adaptivecontrol provides stability and transient performance guarantees, which allowsfor GPR to efficiently and safely learn the uncertain dynamics. On the otherhand, the learned dynamics can be conveniently incorporated into the$\mathcal{L}_1$ control architecture without sacrificing robustness andtracking performance. Subsequently, the learned dynamics can lead to lessconservative designs for performance/robustness tradeoff. We illustrate theefficacy of the proposed architecture via numerical simulations.

$\mathcal{L}_1$-$\mathcal{GP}$: $\mathcal{L}_1$ Adaptive Control with Bayesian Learning