Adaptive observer design for a class of Lipschitz nonlinear systems with multirate outputs and uncertainties: Application to attitude estimation with gyro bias

Abstract

The design of an adaptive observer for a class of multi‐input multi‐output Lipschitz nonlinear systems with uncertainties and multirated outputs is proposed in this paper. The sampling instants of the different outputs can be asynchronous and irregular. The exponential convergence of the proposed observer is proved with the help of a Lyapunov approach. The stability is ensured, provided that some conditions, including a persistent excitation condition and a maximum value condition on the sample rate of each output, are verified. The performances of the observer are illustrated through simulations of the attitude estimation problem using sensors from an inertial measurement unit and considering gyro bias.

Parameter identification and state estimation for a diabetic glucose‐insulin model via an adaptive observer

“…To counteract the problems mentioned above, that is, the variability of the patients, the parameter uncertainties, and the effects of external perturbations, adaptive estimation is a long‐established approach, see, for instance References 10 and 11. Therefore, this work aims to design an adaptive observer robust to parametric uncertainties and external disturbances.…”