Funnel control of nonlinear systems

Abstract

Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by r-th order functional differential equations, encompassing inter alia systems with unknown "control direction" and dead-zone input effects. A control structure is developed which ensures that, for every member of the underlying system class and every admissible reference signal, the tracking error evolves in a prescribed funnel chosen to reflect transient and asymptotic performance objectives. Two fundamental properties underpin the system class: boundedinput bounded-output stable internal dynamics, and a weak high-gain property (an antecedent of which is the concept of sign-definite high-frequency gain in the context of linear systems).