Optimal proportional-integral adaptive observer design for a class of uncertain nonlinear systems

Abstract

Proportional adaptive observers, which have only a proportional feedback loop of the output estimation error, may suffer large estimation errors due to disturbances. To improve steady-state estimation performance, this paper presents a proportional-integral adaptive observer for a class of uncertain nonlinear systems, which includes both a proportional feedback loop and an integral feedback loop of the output observation error. The additional integral loop improves steady-state estimation performance and robustness against disturbances. The proportional and the integral observer gains are optimally chosen by solving the L2 gain minimization problem, which leads to the minimal effect of disturbances on the estimation error. The effectiveness of the proposed adaptive observer is demonstrated through a numerical example. This new design approach on a proportional-integral adaptive observer can provide not only better estimation performance, but also a straightforward way to choose optimal observer gains.