Adaptive estimation for uncertain nonlinear systems with measurement noise: A sliding-mode observer approach

This article deals with the problem of adaptive estimation, that is, the simultaneous estimation of the state and time-varying parameters, in the presence of measurement noise and state disturbances, for a class of uncertain nonlinear systems. An adaptive observer is proposed based on a nonlinear time-varying parameter identification algorithm and a sliding-mode observer. The nonlinear time-varying parameter identification algorithm provides a fixed-time rate of convergence, to a neighborhood of the origin, while the sliding-mode observer ensures ultimate boundedness for the state estimation error attenuating the effects of the external disturbances. Linear matrix inequalities are provided for the synthesis of the adaptive observer while the convergence proofs are given based on the Lyapunov and input-to-state stability theory. Finally, some simulation results show the feasibility of the proposed approach.