Page 215 - Distributed model predictive control for plant-wide systems

9

Cooperative Distributed Predictive

Control with Constraints

9.1 Introduction

Consider that the performance of a distributed model predictive control (DMPC) is, in most
cases, not as good as that of a centralized MPC. How to improve the performance of the entire
system with limited local computation is a problem remained to be solved.
To improve the global performance of the entire system, Chapter 6 provides a com-
monly used coordination strategy, called as cooperative DMPC (C-DMPC), where each
subsystem-based MPC optimizes the cost over the entire system to improve the global
performance of closed-loop system. This coordination strategy can dramatically improve
the global optimization performance of closed-loop system, when the global information is
available for each subsystem-based MPC. Thus it is worthy to develop a stabilized C-DMPC
that only communicates once a control period.
As mentioned in Chapter 8, control design of the stabilizing DMPC is an important and chal-
lenging problem [27, 50, 51]. In noniterative DMPC, the future state sequences of upstream
neighbors, which are calculated based on the solution in the previous time instant, may not be
equal to the predictive states calculated by the corresponding subsystem at the current time
instant, and the errors between them are hard to estimate. The remaining part of the optimal
control sequence calculated at the previous time instant may not be a feasible solution at the
current time instant. These factors make it difficult to design DMPC. Farina and Scattolini [50]
and Dunbar [51] gave two methods on designing stabilizing LCO-DMPC. However, compar-
ing to LCO-DMPC, both the predictive model and the optimization problem of C-DMPC are
different from that of LCO-DMPC; to design a constraint C-DMPC that guarantees the stability
of closed-loop system is still an interesting problem remained to be studied.
In this chapter, a stabilizing C-DMPC where each subsystem-based MPC only communi-
cates with the other subsystems once a sampling time is proposed. The consistency constraints,
which limit the error between the optimal inputs sequence calculated at the previous time
instant, referred to as the presumed inputs, and the optimal inputs sequence calculated at
the current time instant to within a prescribed bound, are designed and included in the opti-
mization problem of each subsystem-based MPC. Moreover, a dual mode predictive control

Distributed Model Predictive Control for Plant-Wide Systems, First Edition. Shaoyuan Li and Yi Zheng.
© 2015 John Wiley & Sons (Asia) Pte Ltd. Published 2015 by John Wiley & Sons (Asia) Pte Ltd.