Funnel MPC for nonlinear systems with arbitrary relative degree

TL;DR

This paper introduces a novel Funnel MPC scheme capable of controlling nonlinear systems with any relative degree, overcoming previous limitations by using a weighted sum of error derivatives, ensuring feasibility without terminal conditions.

Contribution

The paper develops a modified stage cost function for Funnel MPC that guarantees initial and recursive feasibility for systems with arbitrary relative degree, without extra terminal or output constraints.

Findings

Proves feasibility for systems with any relative degree.

Eliminates need for terminal conditions or long horizons.

Provides explicit bounds on weights for stability.

Abstract

The Model Predictive Control (MPC) scheme Funnel MPC enables output tracking of smooth reference signals with prescribed error bounds for nonlinear multi-input multi-output systems with stable internal dynamics. Earlier works achieved the control objective for system with relative degree restricted to one or incorporated additional feasibility constraints in the optimal control problem. Here we resolve these limitations by introducing a modified stage cost function relying on a weighted sum of the tracking error derivatives. The weights need to be sufficiently large and we state explicit lower bounds. Under these assumptions we are able to prove initial and recursive feasibility of the novel Funnel MPC scheme for systems with arbitrary relative degree - without requiring any terminal conditions, a sufficiently long prediction horizon or additional output constraints.