Global Tracking and State Estimation with Nonsmooth Impacts for a Mass Confined to an N-Dimensional Half-Space

Abstract

Abstract:We formulate tracking and state-estimation problems of a translating mass moving in an n-dimensional space and impacting on a hyperplane. Due to the discontinuous trajectories arising from the nonsmooth impacts, we use hybrid systems stability analysis tools to establish that 1) a tracking control algorithm and 2) an observer algorithm guarantee global exponential stability. Then, based on a separation principle, we combine the two constructions above to design a dynamic output feedback controller ensuring asymptotic tracking.