Funnel control in the presence of infinite-dimensional internal dynamics

TL;DR

This paper explores the application of funnel control to uncertain nonlinear systems with infinite-dimensional internal dynamics, demonstrating conditions for feasibility and providing an example with transport equations.

Contribution

It extends funnel control methods to systems with infinite-dimensional internal dynamics, including non-exponentially stable cases, and establishes conditions for prescribed performance.

Findings

Funnel control can be applied to certain infinite-dimensional systems.

Prescribed tracking performance is achievable even with non-exponentially stable dynamics.

Conditions for system class inclusion are identified.

Abstract

We consider output trajectory tracking for a class of uncertain nonlinear systems whose internal dynamics may be modelled by infinite-dimensional systems which are bounded-input, bounded-output stable. We describe under which conditions these systems belong to an abstract class for which funnel control is known to be feasible. As an illustrative example, we show that for a system whose internal dynamics are modelled by a transport equation, which is not exponentially stable, we obtain prescribed performance of the tracking error.