  Data generated from dynamical systems with unknown dynamics enable the
learning of state observers that are: robust to modeling error, computationally
tractable to design, and capable of operating with guaranteed performance. In
this paper, a modular design methodology is formulated, that consists of three
design phases: (i) an initial robust observer design that enables one to learn
the dynamics without allowing the state estimation error to diverge (hence,
safe); (ii) a learning phase wherein the unmodeled components are estimated
using Bayesian optimization and Gaussian processes; and, (iii) a re-design
phase that leverages the learned dynamics to improve convergence rate of the
state estimation error. The potential of our proposed learning-based observer
is demonstrated on a benchmark nonlinear system. Additionally, certificates of
guaranteed estimation performance are provided.
