Generalized adaptive gain sliding mode observer for uncertain nonlinear systems

This paper proposes a new generalized adaptive gain sliding mode observer (GAGSMO) for estimating the unavailable states of a class of multi-input multi-output uncertain nonlinear systems. To further improve the estimation performance of conventional sliding mode observer, the observer gains of GAGSMO are designed for the first time as the generalized bounded positive functions of the available output errors and the upper bounds of disturbance terms. Due to the features of the designed observer gains, the GAGSMO has stronger robustness than the conventional sliding mode observer in the presence of system uncertainties and nonlinearities. The finite-time error convergence of GAGSMO is proved by the Lyapunov stability theorem in conjunction with the introduced mapping functions. Then, by catching sight of the inherent feature of sliding motion, a recursive mechanism based only on available estimation information is formulated to update the designed observer gains online in the sliding mode stage. With the recursive mechanism, the chattering level of GAGSMO is minimized, and the estimation accuracy of GAGSMO is further improved. The effectiveness and excellent performance of the proposed GAGSMO are illustrated with two numerical examples.