Adaptive observer design and parameter estimation for a class of uncertain systems

In this paper, we re-visit the adaptive observer design of a class of uncertain nonlinear systems, where the nonlinearities before the unknown parameters are functions of unmeasured states. A nonlinear reduced-observer is developed by using Lyapunov techniques to estimate unmeasured states. The proposed observer design removes the global Lipschitz restriction. It is shown that the developed adaptive observer achieves parameter convergence. An adaptation law for parameter estimation is developed by introducing a new variable. Online adaptation of unknown parameters can extract more information from the system. In addition, we investigate the convergence of the observed systems with the observer gain and adaptation gain. The presented result is useful since knowing convergence rate is helpful in the construction of control Lyapunov functions and in the analysis of system performance. Simulation results are presented to demonstrate the effectiveness of the proposed observer.