Peaking Attenuation of High-Gain Observers Using Adaptive Techniques: State Estimation and Feedback Control

This article presents a new state estimation scheme using the second-level adaptation technique and multiple high-gain observers (MHGO) for improving the transient response and attenuating undesired peaks of high-gain observers (HGOs). The proposed method, MHGO, considers state estimation as a convex combination of provided information by multiple HGOs. In this regard, it is shown that there exist some constant parameters in such combination that result in perfect state estimation; then, an adaptive algorithm is employed for estimating those parameters. The stability of the proposed scheme and convergence of state estimation to the state of the plant are guaranteed. In addition, MHGO is proved to be able to provide a state estimation with smaller peaks in comparison to a single HGO. The performance of MHGO in the presence of measurement noise is also investigated. We consider existence of abrupt external disturbances as well. To alleviate the effects of those disturbances and attenuate their resulting peaking, we present a resetting scheme. Moreover, the output feedback control problem is considered, and it is demonstrated that a separation principle is valid for MHGO. Finally, simulation results illustrate that MHGO provides an accurate state estimation, and MHGO-based controller is able to recover the performance of state feedback controller.