Optimal Proportional-Integral Adaptive Observer Design for a Class of Uncertain Nonlinear Systems

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.