A Low-Power Multi-High-Gain Observer Design for a Class of Nonlinear Systems

In this article, a low-power multi-high-gain observer (low-power MHGO) is proposed, where multiple low-power observers of order
$2n-2$
are used to improve the transient response of HGOs, as well as reducing their sensitivity to high-frequency measurement noise. The MHGO methodology is applied to low-power observers to aggregate the advantages of the traditional HGO, low-power HGO, and MHGO. It is shown that there exists a combination of the unknown parameters for which the weighted estimated states obtained from the observer are equal to the system's states. The unknown optimal parameters are estimated using a recursive least squares approach. It is shown that the low-power MHGO reduces the peaking using a design parameter. In addition, it is shown that the observer yields the same bounds on estimation errors as a low-power HGO, in terms of the asymptotic gain between estimate error and noise frequency. A simulation example demonstrates that the proposed observer exhibits peaking reduction with reduced noise sensitivity.