**8. Distributed MPC**

At the beginning of research on NCSs, more attention was paid on single plant through net‐ work. Recently, fruitful research results on multi-plant, especially, on multi-agent net‐ worked control systems have been obtained. The aim of this section is to review a classification of a number of distributed control architectures for large scale systems. Atten‐ tion is focused on the design approaches based on model predictive control. The controllers apply MPC policies to their local subsystems. They exchange their predictions by communi‐ cation and incorporate the information from other controllers into their local MPC problem so as to coordinate with each other. For the considered architecture, the underlying ration‐ ale, the fields of application, the merits and limitations are discussed and the main referen‐ ces to the literature are reported.

#### **8.1. Background**

Technological and economical reasons motivate the development of process plants, manu‐ facturing systems, traffic networks, water or power networks [140] with an ever increasing complexity. In addition, there is an increasing interest in networked control systems, where dedicated local control networks can be augmented with additional networked (wired and/or wireless) actuator/sensor devices have become cheap and easy-to-install [141, 142]. These large scale systems are composed by many physically or geographically divided sub‐ systems. Each subsystem interacts with some so called neighbouring subsystems by their states and their inputs. The technical target is to achieve some global performance of entire system (or a common goal of all subsystems). Actually, it is difficult to control with a cen‐ tralized control structure due to the required inherent computational complexity, robustness and reliability problems and communication bandwidth limitations.

For all these reasons, many distributed control structures have been developed and applied over the recent decades.

### **8.2. The reasons why DMPC is adopted**

**Figure 4.** The networked predictive control system.

100 Advances in Discrete Time Systems

duced time delay is not discussed here.

data dropout.

**8. Distributed MPC**

ces to the literature are reported.

**8.1. Background**

But, the random network delay in the forward and feedback channels makes the control de‐ sign and stability analysis much more difficult. In [100] proposes a predictive control scheme for NCS with random network delay in both the feedback and forward channels and also provides an analytical stability criteria for closed-loop networked predictive control (NPC) systems. Furthermore, [138] can overcome the effects caused by both the unknown network delay and data dropout. Recently, [139] mainly focus on the random transmission data dropout existing in both feedback and forward channels in NCSs. So, the network-in‐

In fact, using the networked predictive control scheme presented in this section, the control performance of the closed-loop system with data dropout is very similar to the one without

At the beginning of research on NCSs, more attention was paid on single plant through net‐ work. Recently, fruitful research results on multi-plant, especially, on multi-agent net‐ worked control systems have been obtained. The aim of this section is to review a classification of a number of distributed control architectures for large scale systems. Atten‐ tion is focused on the design approaches based on model predictive control. The controllers apply MPC policies to their local subsystems. They exchange their predictions by communi‐ cation and incorporate the information from other controllers into their local MPC problem so as to coordinate with each other. For the considered architecture, the underlying ration‐ ale, the fields of application, the merits and limitations are discussed and the main referen‐

Technological and economical reasons motivate the development of process plants, manu‐ facturing systems, traffic networks, water or power networks [140] with an ever increasing complexity. In addition, there is an increasing interest in networked control systems, where **About MPC.** The aim of this section is to review the distributed control approaches adopt‐ ed, and to provide a wide list of references focusing the attention on the methods based on MPC. This choice is motivated by the ever increasing popularity of MPC in the process in‐ dustry, see e.g. the survey papers [143, 144] on the industrial applications of linear and non‐ linear MPC. Moreover, in recent years many MPC algorithms have been developed to guarantee some fundamental properties, such as the stability of the resulting closed-loop system or its robustness with respect to a wide class of external disturbances and/or model uncertainties, see e.g. the survey paper [2]. Especially, MPC is also a natural control frame‐ work to deal with the design of coordinated, distributed control systems because of its abili‐ ty to handle input and state constraints, and also because it can account for the actions of other actuators in computing the control action of a given set of control actuators in realtime. Therefore, MPC is now recognized as a very powerful approach with well established theoretical foundations and proven capability to handle the problems of large scale systems.

#### **Other control structures**

1) *Centralized Control.* MPC is normally implemented in a centralized fashion. One controller is able to acquire the information of the global system, computes all the control inputs for the system, and could obtain a good global performance. In large-scale interconnected sys‐ tems, such as power systems, water distribution systems, traffic systems, etc., such a central‐ ized control scheme may not suitable or even possible apply to large scale system for some reasons: (1) there are hundreds of inputs and outputs. It requires a large computational ef‐ forts in online implementation (2) when the centralized controller fails, the entire system is out of control and the control integrity cannot be guaranteed when a control component fails (3) in some cases, e.g. in multi-intelligent vehicle system, the global information is un‐ available to each controller and (4) objections to centralized control are often not computa‐ tional, however, but organizational. All subsystems rely upon the central agent, making plantwide control difficult to coordinate and maintain. These obstacles deter implementa‐ tion of centralized control for large-scale plants.

In recent years, there is a trend for the development of decentralized and distributed MPC due to the disadvantages of centralized MPC mentioned above (e.g.,[145, 146]).

2) *Decentralized Control.* Most large-scale and networked control systems are based on a de‐ centralized architecture, that is, the system is divided into several subsystems, each control‐ led by a different agent that does not share information with the rest. Each of the agents implements an MPC based on a reduced model of the system and on partial state informa‐ tion, which in general results in an optimization problem with a lower computational bur‐ den. Figure 5 shows a decentralized control structure, where the system under control is assumed to be composed by two subsystems S1 and S2, with states, control and output vari‐ ables (*x*1, *u*1,*y*1) and (*x*2, *u*2,*y*2), respectively, and the interaction between the subsystems is due the inputs and the outputs of different pairs are weak. These interactions can either be direct (input coupling) or caused by the mutual effects of the internal states of the subsys‐ tems under control, like in Figure 5.

**Distributed MPC.** While these paradigms (centralized control and decentralized Control) to process control have been successful, there is an increasing interest in developing distribut‐ ed model predictive control (DMPC) schemes, where agents share information in order to improve closed-loop performance, robustness and fault-tolerance. As a middle ground be‐ tween the decentralized and centralized strategies, distributed control preserves the topolo‐ gy and flexibility of decentralized control yet offers a nominal closed-loop stability guarantee.

Discrete-Time Model Predictive Control http://dx.doi.org/10.5772/51122 103

For each decentralized MPC, a sequence of open-loop controls are determined through the solution of a constrained optimal control problem. A local objective is used. A subsystem model, which ignores the interactions, is used to obtain a prediction of future process behav‐ ior along the control horizon. For distributed control, one natural advantage that MPC offers over other controller paradigms is its ability to generate a prediction of future subsystem be‐ havior. If the likely influence of interconnected subsystems is known, each local controller can possibly determine suitable feedback action that accounts for these external influences. Intuitively, one expects this additional information to help improve systemwide control per‐ formance. Thus the distributed control framework is usually adopted in large-scale plants [151], in spite of that the dynamic performance of centralized frame work is better than it.

**Figure 6.** Distributed control of a two input (*u*1,*u*2)-two output (*y*1,*y*2) system.

In distributed control structures, like the simple example shown in Figure 6, it is assumed that some information is transmitted among the local regulators (*R*1and *R*2 in Figure 6), so that each one of them has some knowledge on the behavior of the others. When the local regulators are designed with MPC, the information transmitted typically consists of the fu‐

For example, in [147], a MPC algorithm was proposed under the main assumptions that the system is nonlinear, discrete-time and no information is exchanged between local control‐ lers.The decentralized framework has the advantages of being flexible to system structure, error-tolerance, less computational efforts and no global information requirements [148].

**Figure 5.** Decentralized control of a two input (*u*1,*u*2)-two output (*y*1,*y*2) system.

In plants where the subsystems interact weakly, local feedback action provided by these subsystem (decentralized) controllers may be sufficient to overcome the effect of interac‐ tions. For such cases, a decentralized control strategy is expected to work adequately. On the contrary, it is well known that strong interactions can even prevent one from achieving sta‐ bility and/or performance with decentralized control, see for example [149, 150], where the role played by the so-called fixed modes in the stabilization problem is highlighted.

**Distributed MPC.** While these paradigms (centralized control and decentralized Control) to process control have been successful, there is an increasing interest in developing distribut‐ ed model predictive control (DMPC) schemes, where agents share information in order to improve closed-loop performance, robustness and fault-tolerance. As a middle ground be‐ tween the decentralized and centralized strategies, distributed control preserves the topolo‐ gy and flexibility of decentralized control yet offers a nominal closed-loop stability guarantee.

2) *Decentralized Control.* Most large-scale and networked control systems are based on a de‐ centralized architecture, that is, the system is divided into several subsystems, each control‐ led by a different agent that does not share information with the rest. Each of the agents implements an MPC based on a reduced model of the system and on partial state informa‐ tion, which in general results in an optimization problem with a lower computational bur‐ den. Figure 5 shows a decentralized control structure, where the system under control is assumed to be composed by two subsystems S1 and S2, with states, control and output vari‐ ables (*x*1, *u*1,*y*1) and (*x*2, *u*2,*y*2), respectively, and the interaction between the subsystems is due the inputs and the outputs of different pairs are weak. These interactions can either be direct (input coupling) or caused by the mutual effects of the internal states of the subsys‐

For example, in [147], a MPC algorithm was proposed under the main assumptions that the system is nonlinear, discrete-time and no information is exchanged between local control‐ lers.The decentralized framework has the advantages of being flexible to system structure, error-tolerance, less computational efforts and no global information requirements [148].

In plants where the subsystems interact weakly, local feedback action provided by these subsystem (decentralized) controllers may be sufficient to overcome the effect of interac‐ tions. For such cases, a decentralized control strategy is expected to work adequately. On the contrary, it is well known that strong interactions can even prevent one from achieving sta‐ bility and/or performance with decentralized control, see for example [149, 150], where the

role played by the so-called fixed modes in the stabilization problem is highlighted.

tems under control, like in Figure 5.

102 Advances in Discrete Time Systems

**Figure 5.** Decentralized control of a two input (*u*1,*u*2)-two output (*y*1,*y*2) system.

For each decentralized MPC, a sequence of open-loop controls are determined through the solution of a constrained optimal control problem. A local objective is used. A subsystem model, which ignores the interactions, is used to obtain a prediction of future process behav‐ ior along the control horizon. For distributed control, one natural advantage that MPC offers over other controller paradigms is its ability to generate a prediction of future subsystem be‐ havior. If the likely influence of interconnected subsystems is known, each local controller can possibly determine suitable feedback action that accounts for these external influences. Intuitively, one expects this additional information to help improve systemwide control per‐ formance. Thus the distributed control framework is usually adopted in large-scale plants [151], in spite of that the dynamic performance of centralized frame work is better than it.

**Figure 6.** Distributed control of a two input (*u*1,*u*2)-two output (*y*1,*y*2) system.

In distributed control structures, like the simple example shown in Figure 6, it is assumed that some information is transmitted among the local regulators (*R*1and *R*2 in Figure 6), so that each one of them has some knowledge on the behavior of the others. When the local regulators are designed with MPC, the information transmitted typically consists of the fu‐ ture predicted control or state variables computed locally, so that any local regulator can predict the interaction effects over the considered prediction horizon. With reference to the simple case of Figure 6, the MPC regulators *R*1and *R*2are designed to control the subsystems *S*1 and*S*2, respectively. If the information was exchange among the local regulators (*R*1and *R*2) concerns the predicted evolution of the system states (*x*1and*x*2), any local regulator needs only to know the dynamics of the subsystem directly controlled (*S*1and*S*2).

methods are mentioned. The basic idea of each method and some method applications are stated. Despite the extensive literature that exists on predictive control and robustness to uncertainty, very little attention has been paid to the case of stochastic uncertainty. SMPC is emerging to adopt a stochastic uncertainty description (instead of a set-based descrip‐ tion). Some of the recent advances in this area are reviewed. We show that many impor‐ tant practical and theoretical problems can be formulated in the MPC framework, such as DMPC. Some considerable attention has been directed to NCSs. Although the network makes it convenient to control large distributed systems, there also exist many control issues, such as network delay and data dropout, which cannot be addressed using conven‐ tional control theory, sampling and transmission methods. Results from our recent re‐ search are summarized in Section 7. We have proposed a new networked control scheme, which can overcome the effects caused by the network delay. In the last section we re‐ view a number of distributed control architectures based on model predictive control. For the considered architectures, the underlying rationale, the fields of application, the mer‐

Discrete-Time Model Predictive Control http://dx.doi.org/10.5772/51122 105

The work of Yuanqing Xia was supported by the National Basic Research Program of China (973 Program) (2012CB720000), the National Natural Science Foundation of China (60974011), Program for New Century Excellent Talents in University of China (NCET-08-0047), the Ph.D. Programs Foundation of Ministry of Education of China (20091101110023, 20111101110012), and Program for Changjiang Scholars and Innovative Research Team in University, and Beijing Municipal Natural Science Foundation (4102053,4101001). The work of Magdi S. Mahmoud is supported by the research group

and Magdi S. Mahmoud2

2 Systems Engineering Department, King Fahd University of Petroleum and Minerals, Saudi

its and limitations are discussed.

project no. RG1105-1 from DSR-KFUPM.

, Yuanqing Xia1\*, Mengyin Fu1

\*Address all correspondence to: xia\_yuanqing@bit.edu.cn

1 School of Automation, Beijing Institute of Technology, China

**Acknowledgements**

Li Dai1

Arabia

**Author details**

In any case, it is apparent that the performance of the closed-loop system depends on the decisions that all the agents take. Hence, cooperation and communication policies become very important issues.

With respect to available results in this direction, several DMPC methods have been pro‐ posed in the literature that deal with the coordination of separate MPCs. These communi‐ cate in order to obtain optimal input trajectories in a distributed manner see [145, 146, 152] for reviews of results in this area. Some distributed MPC formulations are available in the literatures [153-157].

#### **8.3. DMPC over network information exchange**

However, all of the above results are based on the assumption of continuous sampling of the entire plant state vector and assuming no delays and perfect communication between sub‐ systems. In practice, individual subsystems exchange information over a communication network, especially wireless communication network, where the data is transmitted in dis‐ crete packets. These packets may be lost during communication. Moreover, the communica‐ tion media is a resource that is usually accessed in a mutually exclusive manner by neighborhood agents. This means that the throughput capacity of such networks is limited. Thus, how to improve the global performance of each subsystem with the limited network communication or limited available information is a valuable problem.

Previous work on MPC design for systems subject to asynchronous or delayed measure‐ ments has primarily focused on centralized MPC design [158], [159] and little attention has been given to the design of DMPC. In [160], the issue of delays in the communica‐ tion between distributed controllers was addressed. The authors of [161] consider the design of distributed MPC schemes for nonlinear systems in a more common setting. That is, measurements of the state are not available continuously but asynchronously and with delays.
