Universal output feedback controllers for nonlinear systems with unknown control direction

Abstract

This paper presents a unifying framework for the problem of robust global regulation via output feedback for nonlinear systems with integral input-to-state stable (iISS) inverse dynamics, subject to unknown control direction. It is shown that previous work in universal high-gain control with unknown sign of high-frequency gain can be included as special cases. The class of uncertain nonlinear systems studied in this paper extends those studied for output feedback control previously in several directions: unmeasured states and unknown parameters can appear non-linearly, no matching assumption is required, no growth condition of any kind is imposed on the non-linearities for large signals, the inverse dynamics satisfy the weaker condition of Sontag's integral input-to-state stability, and the sign of high-frequency gain may be unknown. A constructive strategy is proposed to design a dynamic output feedback control law, that drives the state to the origin while keeping all other closed-loop signals bounded.