Computational Properties of Unconstrained Linear Distributed Model Predictive Control

Abstract

Typical chemical plants are large-scale systems composed of a number of processing units, which are integrated with each other via material, energy and information flows. To achieve optimal plant operation, various control strategies have been developed. Although centralized control provides the best performance, its fragile fault tolerance makes it impractical to implement. In industrial practice, such large-scale systems are operated by decentralized controllers, which do not have the implementation problems of centralized controllers; however, the decentralized controllers, in general, most often give suboptimal performance and may lead to loss of closed-loop stability. These concerns motivate the recent interest in the development of distributed control schemes, particularly distributed model predictive control (DMPC). DMPC methods are applied to existing decentralized control networks and aim to bring their control performance closer to the centralized performance. Often iteratively, the local controllers in a distributed control network communicate with each other or a coordinator to adjust their actions. Since interactions between subsystems can be taken into consideration via information exchange, DMPCs are able to improve decentralized performance or even reproduce the centralized performance. Nevertheless, iterative communication also implies that DMPCs may have high computational and communication costs, which are seldom studied in the literature. The focus of this thesis is the computational properties, mainly convergence and computational complexity, of two linear coordinated DMPCs: prediction-driven coordinated DMPC and price-driven coordinated DMPC. First, by restricting the study to linear unconstrained systems, the DMPC algorithms are transformed into iterative forms. Subsequently, explicit expressions for their convergence accuracy, convergence rates and the computational complexities are derived. A series of numerical experiments were also conducted to study the two DMPC methods' empirical computational complexity. It was discovered that DMPC methods' computational load is closely related to the local MPC design as well as factors like size and number of subsystems.