*Article* **Robust Nonlinear Tracking Control with Exponential Convergence Using Contraction Metrics and Disturbance Estimation**

**Pan Zhao \*, Ziyao Guo and Naira Hovakimyan**

Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA; ziyaog2@illinois.edu (Z.G.); nhovakim@illinois.edu (N.H.)

**\*** Correspondence: panzhao2@illinois.edu

**Abstract:** 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.

**Keywords:** robust control; nonlinear control; uncertain systems; disturbance estimation; robot safety
