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This paper presents an approach to trajectory-centric learning control basedon contraction metrics and disturbance estimation for nonlinear systems subjectto matched uncertainties. The approach uses deep neural networks to learnuncertain dynamics while still providing guarantees of transient trackingperformance throughout the learning phase. Within the proposed approach, adisturbance estimation law is adopted to estimate the pointwise value of theuncertainty, with pre-computable estimation error bounds (EEBs). The learneddynamics, the estimated disturbances, and the EEBs are then incorporated in arobust Riemann energy condition to compute the control law that guaranteesexponential convergence of actual trajectories to desired ones throughout thelearning phase, even when the learned model is poor. On the other hand, withimproved accuracy, the learned model can help improve the robustness of thetracking controller, e.g., against input delays, and can be incorporated toplan better trajectories with improved performance, e.g., lower energyconsumption and shorter travel time.The proposed framework is validated on aplanar quadrotor example.

Guaranteed Nonlinear Tracking in the Presence of DNN-Learned Dynamics With Contraction Metrics and Disturbance Estimation