Transient performance of MPC for tracking without terminal constraints

TL;DR

This paper analyzes the transient performance of MPC for tracking without terminal constraints, providing bounds on closed-loop performance and showing asymptotic optimality as horizon length increases.

Contribution

It derives a transient performance bound for MPC tracking schemes without terminal costs, offering insights for parameter selection and proving asymptotic optimality.

Findings

Provides a bound on closed-loop performance over arbitrary intervals.

Shows asymptotic convergence to infinite horizon optimal solution.

Offers guidelines for parameter tuning in MPC for tracking.

Abstract

Model predictive control (MPC) for tracking is a recently introduced approach, which extends standard MPC formulations by incorporating an artificial reference as an additional optimization variable, in order to track external and potentially time-varying references. In this work, we analyze the performance of such an MPC for tracking scheme without a terminal cost and terminal constraints. We derive a transient performance estimate, i.e. a bound on the closed-loop performance over an arbitrary time interval, yielding insights on how to select the scheme's parameters for performance. Furthermore, we show that in the asymptotic case, where the prediction horizon and observed time interval tend to infinity, the closed-loop solution of MPC for tracking recovers the infinite horizon optimal solution.