Adaptive state observers using dynamic regressor extension and mixing

Abstract

In this paper we propose an adaptive state observer for a class of nonlinear systems with unknown parameters. Assuming that the system variables satisfy an algebraic constraint, a linear regression involving unknown parameters and unmeasurable states is established. The design proceeds adopting a gradient descent approach to minimize a quadratic criterion that is suggested by this regression. To separate the problems of state and parameter estimation we use the recently proposed dynamic regressor extension and mixing approach, whose main feature is that it allows to generate, out of an N-dimensional, linear vector regression, Nscalar regression models. Moreover, under a weak interval excitation assumption, it ensures finite-time parameter convergence. It is shown that the proposed observer is applicable to several practically interesting physical systems.