  This paper presents an approach to trajectory-centric learning control based
on contraction metrics and disturbance estimation for nonlinear systems subject
to matched uncertainties. The approach uses deep neural networks to learn
uncertain dynamics while still providing guarantees of transient tracking
performance throughout the learning phase. Within the proposed approach, a
disturbance estimation law is adopted to estimate the pointwise value of the
uncertainty, with pre-computable estimation error bounds (EEBs). The learned
dynamics, the estimated disturbances, and the EEBs are then incorporated in a
robust Riemann energy condition to compute the control law that guarantees
exponential convergence of actual trajectories to desired ones throughout the
learning phase, even when the learned model is poor. On the other hand, with
improved accuracy, the learned model can help improve the robustness of the
tracking controller, e.g., against input delays, and can be incorporated to
plan better trajectories with improved performance, e.g., lower energy
consumption and shorter travel time.The proposed framework is validated on a
planar quadrotor example.
