Adaptive variable structure state estimation for uncertain systems with persistently bounded disturbances

作者：Wu Huai Ning^*; Shi Peng

来源：International Journal of Robust and Nonlinear Control, 2010, 20(17): 2003-2015.

DOI：10.1002/rnc.1567

• adaptive bounding technique
• linear matrix inequality (LMI)
• nonlinear systems
• persistently bounded disturbances
• state estimation
• variable structure techniques

This paper develops an adaptive state estimator design methodology for nonlinear systems with unknown nonlinearities and persistently bounded disturbances. In the proposed estimation scheme, the boundary layer strategy in variable structure techniques is utilized to design a continuous state estimator such that the undesirable chattering phenomenon is avoided; and the adaptive bounding technique is used for online estimation of the unknown bounding parameter. The existence condition of the adaptive estimators is provided in terms of linear matrix inequality (LMI). Since the orthogonal projection of the state estimation error onto the null space of the linear measurement distribution matrix is used in the derivation process, the update law of bounding parameter estimate is represented in terms of the available measurement error. The proposed estimator can ensure that the state estimation error is uniformly ultimately bounded (UUB) with an ultimate bound. Furthermore, using the existing LMI optimization technique, a suboptimal adaptive state estimator can be obtained in the sense of minimizing an upper bound of the peak gains in the ultimate bound. Finally, a simulation example is given to illustrate the effectiveness of the proposed design method.

• 单位
  1; 北京航空航天大学; 北京大学