Observer design for a class of nonlinear systems using dynamic scaling with application to adaptive control

A constructive algorithm for designing an observer for a class of nonlinear systems is presented. We follow the invariant manifold based approach which allows to shape the dynamics of the estimation error. However, this shaping relies on the solution of a PDE which becomes difficult for multi-output systems. In this paper we remove this restriction by adding to the reduced-order observer an output filter and a single dynamic scaling parameter. We show that this method can be applied to systems with unknown parameters, leading to a new class of adaptive controllers. As an application, we consider two examples: an induction motor with unknown load and a longitudinal controller for an aircraft with unknown aerodynamic properties.