Towards Funnel MPC for nonlinear systems with relative degree two

TL;DR

This paper extends Funnel MPC, a control scheme for nonlinear systems, to handle systems with relative degree two by incorporating derivative-based terms, ensuring output tracking within prescribed bounds.

Contribution

It introduces a novel extension of Funnel MPC for relative degree two systems, including derivative terms in the stage cost for guaranteed feasibility.

Findings

Extended Funnel MPC to relative degree two systems

Proved initial and recursive feasibility for new class of systems

Demonstrated effectiveness through theoretical analysis

Abstract

Funnel MPC, a novel Model Predictive Control (MPC) scheme, allows guaranteed output tracking of smooth reference signals with prescribed error bounds for nonlinear multi-input multi-output systems. To this end, the stage cost resembles the high-gain idea of funnel control. However, rigorous proofs for initial and recursive feasibility without incorporating additional output constraints in the Funnel MPC scheme are only available for systems with relative degree one and stable internal dynamics. In this paper, we extend these results to systems with relative degree two by incorporating also a term based on the idea of a derivative funnel in the stage cost.