This paper presents a tracking controller for nonlinear systems with matched uncertainties based on contraction metrics and disturbance estimation that provides exponential convergence guarantees. Within the proposed approach, a disturbance estimator is proposed to estimate the pointwise value of the uncertainties, with a pre-computable estimation error bounds (EEB). The estimated disturbance and the EEB are then incorporated in a robust Riemannian energy condition to compute the control law that guarantees exponential convergence of actual state trajectories to desired ones. Simulation results on aircraft and planar quadrotor systems demonstrate the efficacy of the proposed controller, which yields better tracking performance than existing controllers for both systems.

This paper presents a contraction-based learning control architecture that allows for using model learning tools to learn matched model uncertainties while guaranteeing trajectory tracking performance during the learning transients. The architecture relies on a disturbance estimator to estimate the pointwise value of the uncertainty, i.e., the discrepancy between a nominal model and the true dynamics, with pre-computable estimation error bounds, and a robust Riemannian energy condition for computing the control signal. Under certain conditions, the controller guarantees exponential trajectory convergence during the learning transients, while learning can improve robustness and facilitate better trajectory planning. Simulation results validate the efficacy of the proposed control architecture.

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.