  This work presents a new sufficient condition for synthesizing nonlinear
controllers that yield bounded closed-loop tracking error transients despite
the presence of unmatched uncertainties that are concurrently being learned
online. The approach utilizes contraction theory and addresses fundamental
limitations of existing approaches by allowing the contraction metric to depend
on the unknown model parameters. This allows the controller to incorporate new
model estimates generated online without sacrificing its strong convergence and
bounded transients guarantees. The approach is specifically designed for
trajectory tracking so the approach is more broadly applicable to adaptive
model predictive control as well. Simulation results on a nonlinear system with
unmatched uncertainties demonstrates the approach.

Systems and Control;Systems and Control;Optimization and Control