On discount functions for economic model predictive control without terminal conditions

TL;DR

This paper explores the use of various discount functions in economic model predictive control without terminal conditions, demonstrating that suitable discounting can improve stability and performance even with short prediction horizons.

Contribution

It extends stability guarantees to a broad class of discount functions in E-MPC without terminal conditions, and shows improved performance with appropriate discounting.

Findings

Different discount functions influence stability and performance.

Suitable discounting can reduce the need for long prediction horizons.

Numerical examples confirm improved performance with certain discount functions.

Abstract

In this paper, we investigate discounted economic model predictive control (E-MPC) schemes without terminal conditions in scenarios where the optimal operating behavior is a periodic orbit. For such a setting, it is known that a linearly discounted stage cost guarantees asymptotic stability of any arbitrarily small neighborhood of the optimal orbit if the prediction horizon is sufficiently long. However, in some examples very long prediction horizons are needed to achieve the desired performance. In this work, we extend these results by providing the same qualitative stability guarantees for a large class of discount functions. Numerical examples illustrate the influence of the discount function and show that with suitable discounting we can achieve significantly better performance than the linearly discounted E-MPC, even for short prediction horizons.