Page 129 - Distributed model predictive control for plant-wide systems

6

Cooperative Distributed

Predictive Control

6.1 Introduction

As has been introduced in Chapter 5, the optimization performance of the closed-loop sys-
tem under the control of distributed predictive control is usually not as good as that under the
control of centralized predictive control, especially when the strong coupling exists among
subsystems. As mentioned previously, the iterative algorithm is employed in solving each
subsystem-based predictive control, in which, each subsystem-based predictive control com-
municates several times with its neighbors and solves the Quadratic Programming problem
several times in each control period. Essentially, it improves the global performance through
minimizing the computational error, which refers to the difference between the input sequence
calculated at previous iterative and the input sequence calculated in current computation. How-
ever, the research direction of the whole optimization problem is not the gradient of the entire
cost function, and the optimal solution calculated by this method is Nash optimality but not
the global optimality.
Is there any other strategy to improve the global performance of the closed-loop system
under the control of distributed predictive control? The authors of [89, 98] proposed a strat-
egy where each subsystem-based predictive control optimizes not only the cost function of the
subsystem it corresponded, but also that of the whole system to improve the performance of
the entire closed-loop system. The advantage of improving the optimization performance of
the entire closed-loop system has been proved by the authors of [37, 48, 53], and some appli-
cations are also presented to validate this strategy [43, 48, 99]. To introduce the concept more
clearly, the unconstrained DPC [44, 53], both iterative and noniterative algorithms, based on
this coordination strategy are presented. In this strategy, each subsystem-based MPC requires
to be able to access to the required information of all subsystems for calculating its optimal
solution.
In this chapter, the first part provides the noniterative cooperative DPC formulation, the
closed-loop solution, the stability condition, and the analysis of why this coordination strategy
could improve the global performance. The second part presents the iterative cooperative DPC

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.