Funnel control of nonlinear systems

TL;DR

This paper introduces a funnel control method for nonlinear systems modeled by r-th order functional differential equations, ensuring prescribed tracking accuracy despite unknown control directions and dead zones.

Contribution

It develops a novel control structure that guarantees tracking error within a predefined funnel for a broad class of nonlinear systems with specific stability and high-gain properties.

Findings

Guarantees tracking error within a prescribed funnel for all system members.

Handles systems with unknown control directions and dead-zone effects.

Ensures stability and accuracy in nonlinear system tracking.

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 accuracy objectives. Two fundamental properties underpin the system class: bounded-input bounded-output stable internal dynamics, and a high-gain property (an antecedent of which is the concept of sign-definite high-frequency gain in the context of linear systems).