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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 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.
This paper introduces an $mathcal{L}_1$ adaptive control augmentation for geometric tracking control of quadrotors. In the proposed design, the $mathcal{L}_1$ augmentation handles nonlinear (time- and state-dependent) uncertainties in the quadrotor d
The metrization of the space of neural responses is an ongoing research program seeking to find natural ways to describe, in geometrical terms, the sets of possible activities in the brain. One component of this program are the {em spike metrics}, no
Let $L$ be a finite extension of $mathbb{Q}_p$, and $rho_L$ be an $n$-dimensional semi-stable non crystalline $p$-adic representation of $mathrm{Gal}_L$ with full monodromy rank. Via a study of Breuils (simple) $mathcal{L}$-invariants, we attach to $
This article considers the $mathcal{H}_infty$ static output-feedback control for linear time-invariant uncertain systems with polynomial dependence on probabilistic time-invariant parametric uncertainties. By applying polynomial chaos theory, the con
We use set-theoretic tools to make a model-theoretic contribution. In particular, we construct a emph{single} $mathcal{L}_{omega_1,omega}$-sentence $psi$ that codes Kurepa trees to prove the consistency of the following: (1) The spectrum of $psi$ i