Funnel control of linear systems with arbitrary relative degree under output measurement losses

TL;DR

This paper presents a funnel control method for linear minimum phase systems with arbitrary relative degree, ensuring tracking performance despite output measurement losses, with explicit conditions on measurement loss durations.

Contribution

It introduces a control law that guarantees prescribed tracking performance under output measurement losses with explicit bounds based on system dynamics.

Findings

Guarantees tracking error within a prescribed funnel during measurement availability

Explicit bounds on measurement loss durations for stability

Validated with a mass-on-car system simulation

Abstract

We consider tracking control of linear minimum phase systems with known arbitrary relative degree which are subject to possible output measurement losses. We provide a control law which guarantees the evolution of the tracking error within a (shifted) prescribed performance funnel whenever the output signal is available. The result requires a maximal duration of measurement losses and a minimal time of measurement availability, which both strongly depend on the internal dynamics of the system, and are derived explicitly. The controller is illustrated by a simulation of a mass-on-car system.