Robust adaptive observer for nonlinear systems with unmodeled dynamics

Unmodeled dynamics exist in almost all applications of observers due to the impossibility of using exact and detailed models. It is highly desired that the observers can dominate the effects of unmodeled dynamics independently to prevent the state estimations from diverging and to get the precise estimations. Based on adaptive nonlinear damping, this paper presents a robust adaptive observer for multiple-input multiple-output nonlinear systems with unknown parameters, uncertain nonlinearities, disturbances and unmodeled dynamics. The observer only has one adaptive parameter no matter how high the order of the system is and how many unknown parameters there are. With the proposed observer, neither estimating the unknown parameters or solving linear matrix inequalities is needed. It is shown that the state estimation error is uniformly bounded and can be made arbitrarily small.