An overview on recent progress of extended state observers for uncertain systems: Methods, theory, and applications

Extended state observer (ESO) is featured with online estimating both the system's states and the total effect of external disturbance as well as nonlinear uncertain dynamics. The original ESO design, proposed for the cascade-of-integrator system without measurement noise, has been well studied with theoretical foundation and many successful applications. In the last years, multifarious modified ESOs have also been developed to handle many engineering systems captured by the models with general nonlinear structure, time-delay, the noises with stochastic properties, and etc. This paper aims to comprehensively investigate the representative modified ESOs in recent years. Firstly, the ESO's design and tuning law are illustrated for general uncertain systems with multiple control inputs, multiple measured outputs and various uncertainties. The quantitative results regarding the estimation errors of ESO are also presented. Next, the extended state-based Kalman-typed filters to handle state estimation problem against both stochastic noises and uncertain dynamics are introduced. The consistency, stability, and asymptotic optimization of the proposed filters are rigorously shown. Furthermore, some novel designs of ESO to deal with the estimation problem of uncertain nonlinear systems with time-delay and measurement biases are discussed. We believe this overview will be helpful for practitioners in applications of recent modified ESOs.