A novel class of adaptive observers for dynamic nonlinear uncertain systems

Abstract

Numerous techniques have been proposed in the literature to improve the performance of high‐gain observers with noisy measurements. One such technique is the linear extended state observer, which is used to estimate the system's states and to account for the impact of internal uncertainties, undesirable nonlinearities, and external disturbances. This observer's primary purpose is to eliminate these disturbances from the input channel in real‐time. This enables the observer to precisely track the system states while compensating for the various sources of uncertainty that can influence the system's behaviour. So, in this paper, a novel nonlinear higher‐order extended state observer (NHOESO) is introduced to enhance the performance of high‐gain observers under noisy measurement conditions. The NHOESO is designed to observe the system states and total disturbance while eliminating the latter in real time from the input channel. It is capable of handling disturbances of higher‐order derivatives, including internal uncertainties, undesirable nonlinearities, and external disturbances. The paper also presents two innovative schemes for parametrizing the NHOESO parameters in the presence of measurement noise. These schemes are named time‐varying bandwidth NHOESO (TVB‐NHOESO) and online adaptive rule update NHOESO (OARU‐NHOESO). Numerical simulations are conducted to validate the effectiveness of the proposed schemes, using a nonlinear uncertain system as a test case. The results demonstrate that the OARU technique outperforms the TVB technique in terms of its ability to sense the presence of noise components in the output and respond accordingly. However, it is noted that the OARU technique is slower than the TVB technique and requires more complex parameter tuning to adaptively account for the measurement noise.