Adaptive observer design for nonlinear systems with parametric uncertainties in unmeasured state dynamics

This paper presents an adaptive observer design for nonlinear systems that have parametric uncertainties in the unmeasured state dynamics. Without persistency of excitation (PE) the convergence of the state estimation error to zero is proved. Under PE conditions, uniform global asymptotic stability of the origin of the state and parameter error is shown. Furthermore, if the regressor is sufficiently smooth, uniform local asymptotic stability of the origin is proved. Two simulation examples are shown to illustrate the results.