Universal Adaptive Control for Uncertain Nonlinear Systems

Precise motion planning and control require accurate models which are often difficult, expensive, or time-consuming to obtain. Online model learning is an attractive approach that can handle model variations while achieving the desired level of performance. However, several model learning methods developed within adaptive nonlinear control are limited to certain systems or types of uncertainties. In particular, the so-called unmatched uncertainties pose significant problems for existing methods if the system is not in a particular form. This work presents an adaptive control framework for nonlinear systems with unmatched uncertainties that addresses several of the limitations of existing methods through two key innovations. The first is leveraging contraction theory and a new type of contraction metric that, when coupled with an adaptation law, is able to track feasible trajectories generated by an adapting reference model. The second is a natural modulation of the learning rate so the closed-loop system remains stable during learning transients. The proposed approach is more general than existing methods as it is able to handle unmatched uncertainties while only requiring the system be nominally contracting in closed-loop. Additionally, it can be used with learned feedback policies that are known to be contracting in some metric, facilitating transfer learning and bridging the sim2real gap. Simulation results demonstrate the effectiveness of the method.