Adaptive Stabilization of Non-Linearizable Systems under a Matching Assumption

In this paper we study the problem of adaptive stabilization of linearly parametrized nonlinear systems that satisfy a matching assumption. We show that, under these conditions, adaptive regulation is possible for a class of non-feedback linearizable systems. This class consists of systems for which there exists a parametrized state feedback control such that the closed loop system defines a strictly passive map. Furthermore, we provide a constructive procedure to calculate the required control law, which consists of the solution of an inverse optimal nonlinear control problem.