Stability and performance in transient average constrained economic MPC without terminal constraints

TL;DR

This paper analyzes the stability and performance of transient average constrained economic MPC without terminal constraints, establishing turnpike properties, performance bounds, and stability conditions.

Contribution

It introduces a novel stability and performance analysis framework for economic MPC without terminal constraints using turnpike properties and ISS Lyapunov functions.

Findings

Optimal open-loop solutions pass through the optimal steady-state.

Performance bounds are derived under controllability conditions.

Stability is established using a combined Lyapunov approach.

Abstract

In this paper, we investigate system theoretic properties of transient average constrained economic model predictive control (MPC) without terminal constraints. We show that the optimal open-loop solution passes by the optimal steady-state for consecutive time instants. Using this turnpike property and suitable controllability conditions, we provide closed-loop performance bounds. Furthermore, stability is proved by combining the rotated value function with an input-to-state (ISS) Lyapunov function of an extended state related to the transient average constraints. The results are illustrated with a numerical example.