Extended high gain observer design for state and parameter estimation

This paper investigates the design of an extended high gain observer to estimate the state together with some unknown constant parameters for a class of nonlinear systems. We firstly consider the case where all the parameters are known. A high gain state observer is proposed and its exponential convergence is carried out under a well defined persistent excitation condition. Then, the case where some parameters involved in the system equations are unknown is considered using a suitable augmentation of the nonlinear system with the parameters dynamics. Thanks to the introduction of the notion of characteristic indices associated to the unknown parameters, an extended high gain observer is designed to simultaneously estimate the state together with the unknown parameters. It is shown that the exponential convergence of the extended high gain observer is ensured under the persistent excitation condition that has been already considered for the state observer together with an additional persistent excitation to handle the parameter estimation process.