Analysis of Stability and Performance of Economic Model Predictive Control with State-Independent Costs

TL;DR

This paper analyzes the stability and performance of economic model predictive control with state-independent costs, proposing modifications to ensure asymptotic stability and demonstrating effectiveness through a water network case study.

Contribution

It introduces a modified stage cost for stability, extends the approach to periodic systems, and validates the methods with a practical water distribution network example.

Findings

Closed-loop trajectories converge to the set of optimal steady states.

Modified stage cost guarantees asymptotic stability with minimal performance loss.

Case study confirms effectiveness in water distribution network control.

Abstract

This paper studies economic model predictive Control (EMPC) schemes, where the stage cost depends only on control inputs. Such problems arise in applications like water distribution networks and differ from standard EMPC since multiple steady states can correspond to the unique optimal steady input. We show that, under a strict dissipativity assumption related to the set of optimal steady states, the closed-loop trajectories converge asymptotically to this set, ensuring convergence of the economic cost to the optimal steady state cost. To enhance Lyapunov stability, we propose a modified stage cost that preserves the optimal input while guaranteeing asymptotic stability of a specific equilibrium with a slight performance loss. The approach is further extended to EMPC of a class of linear systems with periodic costs and disturbances by lifting it to a multi-step EMPC problem for periodic operations. A case study with a water distribution network demonstrates the effectiveness of the proposed methods in achieving both asymptotic convergence and stability.