Adaptive state estimation for a class of nonlinear systems: a high gain approach

In this paper, we propose a new adaptive estimation approach for a class of uncertain nonlinear systems such that the classical restrictive observer matching condition is not verified. That is, it is assumed that the relative degree of the outputs w.r.t the uncertain parameters vector is greater or equal than two. To solve this problem, we generate auxiliary outputs and we construct a high gain observer in cascade with an adaptive observer to achieve the objective of states and uncertain parameters reconstruction. Based on a Lyapunov analysis, we establish the convergence of both estimation and adaptation errors. Theoretical results are validated via some numerical simulations for an example of a nonlinear mechanical system.