Input-constrained funnel control of nonlinear systems

TL;DR

This paper introduces a model-free funnel control method for uncertain nonlinear multi-input, multi-output systems with input constraints, ensuring tracking errors stay within a prescribed performance funnel.

Contribution

A novel, low-complexity funnel controller that dynamically widens the performance funnel under input saturation, extending previous funnel control approaches.

Findings

Controller successfully maintains tracking within the performance funnel.

Dynamic funnel widening effectively handles input saturation.

Simulation demonstrates improved performance over existing methods.

Abstract

We study tracking control for uncertain nonlinear multi-input, multi-output systems modelled by $r$-th order functional differential equations (encompassing systems with arbitrary strict relative degree) in the presence of input constraints. The objective is to guarantee the evolution of the tracking error within a performance funnel with prescribed asymptotic shape (thus achieving desired transient and asymptotic accuracy objectives), for any sufficiently smooth reference signal. We design a novel funnel controller which, in order to satisfy the input constraints, contains a dynamic component which widens the funnel boundary whenever the input saturation is active. This design is model-free, of low-complexity and extends earlier funnel control approaches. We present a simulation where the controller is compared to these approaches.