Funnel MPC with feasibility constraints for nonlinear systems with arbitrary relative degree

TL;DR

This paper extends Funnel MPC to nonlinear systems with arbitrary relative degree, ensuring tracking within a performance funnel without terminal conditions or long horizons.

Contribution

It introduces a novel stage cost for Funnel MPC applicable to arbitrary relative degree systems, guaranteeing feasibility and control objectives without terminal conditions.

Findings

Control objectives are always achieved.

Feasibility is maintained without terminal conditions.

The method applies to systems with arbitrary relative degree.

Abstract

We study tracking control for nonlinear systems with known relative degree and stable internal dynamics by the recently introduced technique of Funnel MPC. The objective is to achieve the evolution of the tracking error within a prescribed performance funnel. We propose a novel stage cost for Funnel MPC, extending earlier designs to the case of arbitrary relative degree, and show that the control objective as well as initial and recursive feasibility are always achieved - without requiring any terminal conditions or a sufficiently long prediction horizon. We only impose an additional feasibility constraint in the optimal control problem.