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

In this paper, 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.