Linear-in-parameters neural adaptive observers for nonlinear systems in observability canonical form

Nonlinear adaptive observers that do not require knowledge of the dynamics of the system being observed are proposed. This objective is pursued by envisioning a linear-in-parameters adaptive law that allows one to estimate the system dynamics, which are assumed to be in observability canonical form, just from measurements of the output. In the case that a parametric model for the plant is known, the proposed adaptive observer asymptotically reconstructs both the state and the unknown parameters of the observed system. On the other hand, if a parametric model for the system is not available, then the reconstruction of both its state and of its model is practical. The effectiveness of these observers is validated by numerical simulations.