Distributed Economic MPC for Dynamically Coupled Linear Systems With Uncertainties

Abstract

In this article, we propose a novel economic model-predictive control (MPC) algorithm for a group of disturbed linear systems and implement it in a distributed manner. The system consists of multiple subsystems interacting with each other via dynamics and aims to optimize an economic objective. Each subsystem is subject to constraints both on states and inputs as well as unknown but bounded disturbances. First, we divide the computation of control inputs into several local optimization problems based on each subsystem's local information. This is done by introducing compatibility constraints to confine the difference between the actual information and the previously published reference information of each subsystem, which is the key feature of the proposed distributed algorithm. Then, to ensure the satisfaction of both state and input constraints under disturbances, constraints are tightened on the state and the input of nominal systems by considering explicitly the effect of uncertainties. Moreover, based on an overall optimal steady state, a dissipativity constraint and a terminal constraint are designed and incorporated in the local optimization problems to establish recursive feasibility and guarantee stability for the resulting closed-loop system. Finally, the efficiency of the distributed economic MPC algorithm is demonstrated in a building temperature control case study.