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, most model learning methods developed within adaptive nonlinear control are limited to certain types of uncertainties, called matched uncertainties  . 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 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.
High-performance feedback control requires an accurate model of the underlying dynamical system which is 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, most model learning methods developed within adaptive nonlinear control are limited to certain types of uncertainties, called matched uncertainties , because the certainty equivalency principle can be employed in the design phase . This work develops a universal adaptive control framework that extends the certainty equivalence principle to nonlinear systems with unmatched uncertainties through two key innovations. The first is introducing parameter-dependent storage functions that guarantee closed-loop tracking of a desired trajectory generated by an adapting reference model. The second is modulating the learning rate so the closed-loop system remains stable during the learning transients. The analysis is first presented under the lens of contraction theory, and then expanded to general Lyapunov functions which can be synthesized via feedback linearization, backstepping, or optimization-based techniques. The proposed approach is more general than existing methods as the uncertainties can be unmatched and the system only needs to be stabilizable. The developed algorithm can be combined with learned feedback policies , facilitating transfer learning and bridging the sim-to-real gap. Simulation results showcase the method
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analysis is first presented under the lens of contraction theory, and then expanded to general Lyapunov functions which can be synthesized via feedback linearization, backstepping, or optimization-based techniques. The
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